Superconducting quantum computing is a branch of
solid state physics and quantum computing that implements
superconducting
Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases g ...
electronic circuit
An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or Conductive trace, traces through which electric current can flow. It is a t ...
s using superconducting qubits as artificial atoms, or
quantum dot
Quantum dots (QDs) or semiconductor nanocrystals are semiconductor particles a few nanometres in size with optical and electronic properties that differ from those of larger particles via quantum mechanical effects. They are a central topic i ...
s. For superconducting qubits, the two logic states are the
ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state ...
and the
excited state
In quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Add ...
, denoted
respectively.
[ Research in superconducting quantum computing is conducted by companies such as ]Google
Google LLC (, ) is an American multinational corporation and technology company focusing on online advertising, search engine technology, cloud computing, computer software, quantum computing, e-commerce, consumer electronics, and artificial ...
, IBM
International Business Machines Corporation (using the trademark IBM), nicknamed Big Blue, is an American Multinational corporation, multinational technology company headquartered in Armonk, New York, and present in over 175 countries. It is ...
, IMEC
Interuniversity Microelectronics Centre (IMEC; officially stylised as imec) is an international Research and development, research & development organization, active in the fields of nanoelectronics and Digital electronics, digital technologies ...
, BBN Technologies
Raytheon BBN (originally Bolt, Beranek and Newman, Inc.) is an American research and development company based in Cambridge, Massachusetts.
In 1966, the Franklin Institute awarded the firm the Frank P. Brown Medal, in 1999 BBN received the ...
, Rigetti
Rigetti Computing, Inc. is a Berkeley, California-based developer of Superconducting quantum integrated circuits used for quantum computers. Rigetti also develops a cloud platform called Forest that enables programmers to write quantum algorith ...
, and Intel
Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California, and Delaware General Corporation Law, incorporated in Delaware. Intel designs, manufactures, and sells computer compo ...
. Many recently developed QPUs ( quantum processing units, or quantum chips) use superconducting architecture.
, up to 9 fully controllable qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical syste ...
s are demonstrated in the 1D array
An array is a systematic arrangement of similar objects, usually in rows and columns.
Things called an array include:
{{TOC right
Music
* In twelve-tone and serial composition, the presentation of simultaneous twelve-tone sets such that the ...
, and up to 16 in 2D architecture.[ In October 2019, the Martinis group, partnered with ]Google
Google LLC (, ) is an American multinational corporation and technology company focusing on online advertising, search engine technology, cloud computing, computer software, quantum computing, e-commerce, consumer electronics, and artificial ...
, published an article demonstrating novel quantum supremacy
''Quantum Supremacy: How the Quantum Computer Revolution Will Change Everything'' is a non-fiction book by the American futurist and physicist Michio Kaku. The book, Kaku's eleventh, was initially published on 2 May 2023 by Doubleday. The book ...
, using a chip composed of 53 superconducting qubits.
Background
Classical computation
A computation is any type of arithmetic or non-arithmetic calculation that is well-defined. Common examples of computation are mathematical equation solving and the execution of computer algorithms.
Mechanical or electronic devices (or, hist ...
models rely on physical implementations consistent with the laws of classical mechanics
Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...
. Classical descriptions are accurate only for specific systems consisting of a relatively large number of atoms. A more general description of nature is given by quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
. Quantum computation
A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing takes advantage of this behavior using specialized hardware. C ...
studies quantum phenomena applications beyond the scope of classical approximation, with the purpose of performing quantum information
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both t ...
processing and communication. Various models of quantum computation exist, but the most popular models incorporate concepts of qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical syste ...
s and quantum gate
In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. Quantum logic gates are the building blocks of quantu ...
s (or gate-based superconducting quantum computing).
Superconductors are implemented due to the fact that at low temperatures they have infinite conductivity and zero resistance. Each qubit is built using semiconductor circuits with an LC circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can act ...
: a capacitor and an inductor.
Superconducting capacitors and inductors are used to produce a resonant circuit that dissipates almost no energy, as heat can disrupt quantum information. The superconducting resonant circuits are a class of artificial atoms that can be used as qubits. Theoretical and physical implementations of quantum circuits are widely different. Implementing a quantum circuit had its own set of challenges and must abide by DiVincenzo's criteria
The DiVincenzo criteria are conditions necessary for constructing a quantum computer, conditions proposed in 1996 by the theoretical physicist David P. DiVincenzo, as being those necessary to construct such a computer—a computer first proposed ...
, conditions proposed by theoretical physicist David P DiVincenzo, which is set of criteria for the physical implementation of superconducting quantum computing, where the initial five criteria ensure that the quantum computer is in line with the postulates of quantum mechanics and the remaining two pertaining to the relaying of this information over a network.
We map the ground and excited states of these atoms to the 0 and 1 state as these are discrete and distinct energy values and therefore it is in line with the postulates of quantum mechanics. In such a construction however an electron can jump to multiple other energy states and not be confined to our excited state; therefore, it is imperative that the system be limited to be affected only by photons with energy difference required to jump from the ground state to the excited state. However, this leaves one major issue, we require uneven spacing between our energy levels to prevent photons with the same energy from causing transitions between neighboring pairs of states. Josephson junctions are superconducting elements with a nonlinear inductance, which is critically important for qubit implementation.[ The use of this nonlinear element in the resonant superconducting circuit produces uneven spacings between the energy levels.
]
Qubits
A qubit is a generalization of a bit
The bit is the most basic unit of information in computing and digital communication. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as ...
(a system with two possible states
State most commonly refers to:
* State (polity), a centralized political organization that regulates law and society within a territory
**Sovereign state, a sovereign polity in international law, commonly referred to as a country
**Nation state, a ...
) capable of occupying a quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödi ...
of both states. A quantum gate, on the other hand, is a generalization of a logic gate
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for ...
describing the transformation
Transformation may refer to:
Science and mathematics
In biology and medicine
* Metamorphosis, the biological process of changing physical form after birth or hatching
* Malignant transformation, the process of cells becoming cancerous
* Trans ...
of one or more qubits once a gate is applied given their initial state. Physical implementation of qubits and gates is challenging for the same reason that quantum phenomena are difficult to observe in everyday life given the minute scale on which they occur. One approach to achieving quantum computers is by implementing superconductors
Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases ...
whereby quantum effects are macroscopically observable, though at the price of extremely low operation temperature
Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
s.
Superconductors
Unlike typical conductors, superconductors possess a critical temperature
Critical or Critically may refer to:
*Critical, or critical but stable, medical states
**Critical, or intensive care medicine
*Critical juncture, a discontinuous change studied in the social sciences.
*Critical Software, a company specializing in ...
at which resistivity plummets to zero and conductivity is drastically increased. In superconductors, the basic charge carriers are pairs of electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
s (known as Cooper pairs
In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
), rather than single fermion
In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...
s as found in typical conductors. Cooper pairs are loosely bound and have an energy state lower than that of Fermi Energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature.
In a Fermi ga ...
. Electrons forming Cooper pairs possess equal and opposite momentum and spin so that the total spin
Spin or spinning most often refers to:
* Spin (physics) or particle spin, a fundamental property of elementary particles
* Spin quantum number, a number which defines the value of a particle's spin
* Spinning (textiles), the creation of yarn or thr ...
of the Cooper pair is an integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
spin. Hence, Cooper pairs are boson
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have half odd-intege ...
s. Two such superconductors which have been used in superconducting qubit models are niobium
Niobium is a chemical element; it has chemical symbol, symbol Nb (formerly columbium, Cb) and atomic number 41. It is a light grey, crystalline, and Ductility, ductile transition metal. Pure niobium has a Mohs scale of mineral hardness, Mohs h ...
and tantalum
Tantalum is a chemical element; it has Symbol (chemistry), symbol Ta and atomic number 73. It is named after Tantalus, a figure in Greek mythology. Tantalum is a very hard, ductility, ductile, lustre (mineralogy), lustrous, blue-gray transition ...
, both d-band superconductors.
Bose–Einstein condensates
Once cooled to nearly absolute zero
Absolute zero is the lowest possible temperature, a state at which a system's internal energy, and in ideal cases entropy, reach their minimum values. The absolute zero is defined as 0 K on the Kelvin scale, equivalent to −273.15 ° ...
, a collection of bosons collapse into their lowest energy quantum state (the ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state ...
) to form a state of matter known as Bose–Einstein condensate
In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low Density, densities is cooled to temperatures very close to absolute zero#Relation with Bose–Einste ...
. Unlike fermions, bosons may occupy the same quantum energy level (or quantum state
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system ...
) and do not obey the Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that o ...
. Classically, Bose-Einstein Condensate can be conceptualized as multiple particles occupying the same position in space and having equal momentum
In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...
. Because interactive forces between bosons are minimized, Bose-Einstein Condensates effectively act as a superconductor. Thus, superconductors are implemented in quantum computing because they possess both near infinite conductivity and near zero resistance. The advantages of a superconductor over a typical conductor, then, are twofold in that superconductors can, in theory, transmit signals nearly instantaneously and run infinitely with no energy loss. The prospect of actualizing superconducting quantum computers becomes all the more promising considering NASA
The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the federal government of the United States, US federal government responsible for the United States ...
's recent development of the Cold Atom Lab in outer space where Bose-Einstein Condensates are more readily achieved and sustained (without rapid dissipation) for longer periods of time without the constraints of gravity
In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...
.
Electrical circuits
At each point of a superconducting electronic circuit (a network of electrical element
In electrical engineering, electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks. All electrical networks can be ...
s), the condensate wave function
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
describing charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* '' Charge!!'', an album by The Aqu ...
flow is well-defined by some complex
Complex commonly refers to:
* Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe
** Complex system, a system composed of many components which may interact with each ...
probability amplitude
In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The square of the modulus of this quantity at a point in space represents a probability density at that point.
Probability amplitu ...
. In typical conductor electrical circuits, this same description is true for individual charge carrier
In solid state physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. ...
s except that the various wave functions are averaged in macroscopic analysis, making it impossible to observe quantum effects. The condensate wave function
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
becomes useful in allowing design and measurement of macroscopic quantum effects. Similar to the discrete atomic energy level
A quantum mechanics, quantum mechanical system or particle that is bound state, bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical mechanics, classical pa ...
s in the Bohr model
In atomic physics, the Bohr model or Rutherford–Bohr model was a model of the atom that incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's nuclear Rutherford model, model, i ...
, only discrete numbers of magnetic flux quanta can penetrate a superconducting loop. In both cases, quantization results from complex amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
continuity. Differing from microscopic implementations of quantum computers (such as atom
Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
s or photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...
s), parameters of superconducting circuits are designed by setting (classical) values to the electrical elements composing them such as by adjusting capacitance
Capacitance is the ability of an object to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related ...
or inductance
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
.
To obtain a quantum mechanical description of an electrical circuit, a few steps are required. Firstly, all electrical elements must be described by the condensate wave function amplitude and phase rather than by closely related macroscopic current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (hydr ...
and voltage
Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
descriptions used for classical circuits. For instance, the square of the wave function amplitude at any arbitrary point in space corresponds to the probability of finding a charge carrier there. Therefore, the squared amplitude corresponds to a classical charge distribution. The second requirement to obtain a quantum mechanical description of an electrical circuit is that generalized Kirchhoff's circuit laws
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirc ...
are applied at every node of the circuit network to obtain the system's equations of motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathem ...
. Finally, these equations of motion must be reformulated to Lagrangian mechanics
In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the d'Alembert principle of virtual work. It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his presentation to the ...
such that a quantum Hamiltonian is derived describing the total energy of the system.
Technology
Manufacturing
Superconducting quantum computing devices are typically designed in the radio-frequency spectrum, cooled in dilution refrigerator
A 3He/4He dilution refrigerator is a cryogenics, cryogenic device that provides continuous cooling to temperatures as low as 2 Kelvin, mK, with no moving parts in the low-temperature region. The cooling power is provided by the heat o ...
s below 15 mK and addressed with conventional electronic instruments, e.g. frequency synthesizer
A frequency synthesizer is an electronic circuit that generates a range of frequencies from a single reference frequency. Frequency synthesizers are used in devices such as radio receivers, televisions, mobile telephones, radiotelephones, walkie ...
s and spectrum analyzer
A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that most co ...
s. Typical dimensions fall on the range of micrometers, with sub-micrometer resolution, allowing for the convenient design of a Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonian ...
system with well-established integrated circuit
An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...
technology. Manufacturing superconducting qubits follows a process involving lithography
Lithography () is a planographic method of printing originally based on the miscibility, immiscibility of oil and water. The printing is from a stone (lithographic limestone) or a metal plate with a smooth surface. It was invented in 1796 by ...
, depositing of metal, etching
Etching is traditionally the process of using strong acid or mordant to cut into the unprotected parts of a metal surface to create a design in intaglio (incised) in the metal. In modern manufacturing, other chemicals may be used on other type ...
, and controlled oxidation
Redox ( , , reduction–oxidation or oxidation–reduction) is a type of chemical reaction in which the oxidation states of the reactants change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is ...
as described in. Manufacturers continue to improve the lifetime of superconducting qubits and have made significant improvements since the early 2000s.
Josephson junctions
One distinguishable attribute of superconducting quantum circuits is the use of Josephson junction
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. The effect is named after the British physicist Brian Josephson, who predicted in 1962 ...
s. Josephson junctions are an electrical element
In electrical engineering, electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks. All electrical networks can be ...
which does not exist in normal conductors. Recall that a junction is a weak connection between two leads of wire (in this case a superconductive wire) on either side of a thin layer of insulator material only a few atom
Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
s thick, usually implemented using shadow evaporation technique. The resulting Josephson junction device exhibits the Josephson Effect
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. The effect is named after the British physicist Brian Josephson, who predicted in 1962 ...
whereby the junction produces a supercurrent. An image of a single Josephson junction is shown to the right. The condensate wave function on the two sides of the junction are weakly correlated, meaning that they are allowed to have different superconducting phases. This distinction of nonlinearity
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...
contrasts continuous superconducting wire for which the wave function across the junction must be continuous
Continuity or continuous may refer to:
Mathematics
* Continuity (mathematics), the opposing concept to discreteness; common examples include
** Continuous probability distribution or random variable in probability and statistics
** Continuous ...
. Current flow through the junction occurs by quantum tunneling
In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...
, seeming to instantaneously "tunnel" from one side of the junction to the other. This tunneling phenomenon is unique to quantum systems. Thus, quantum tunneling is used to create nonlinear inductance, essential for qubit design as it allows a design of anharmonic oscillators for which energy levels are discretized (or quantized) with nonuniform spacing between energy levels, denoted .[ In contrast, the ]quantum harmonic oscillator
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, ...
''cannot'' be used as a qubit as there is no way to address only two of its states, given that the spacing between every energy level and the next is exactly the same.
Qubit archetypes
The three primary superconducting qubit archetypes are the phase
Phase or phases may refer to:
Science
*State of matter, or phase, one of the distinct forms in which matter can exist
*Phase (matter), a region of space throughout which all physical properties are essentially uniform
*Phase space, a mathematica ...
, charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* '' Charge!!'', an album by The Aqu ...
and flux
Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications in physics. For transport phe ...
qubit. Many hybridizations of these archetypes exist including the fluxonium, transmon
In quantum computing, and more specifically in superconducting quantum computing, a transmon is a type of Superconductivity, superconducting charge qubit designed to have reduced sensitivity to charge noise. The transmon was developed by Jens Koch ...
, Xmon, and quantronium. For any qubit implementation the logical quantum states
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system re ...
are mapped to different states of the physical system (typically to discrete energy level
A quantum mechanics, quantum mechanical system or particle that is bound state, bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical mechanics, classical pa ...
s or their quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödi ...
s). Each of the three archetypes possess a distinct range of Josephson energy to charging energy ratio. Josephson energy refers to the energy stored in Josephson junctions when current passes through, and charging energy is the energy required for one Cooper pair to charge the junction's total capacitance. Josephson energy can be written as
: ,
where is the critical current parameter of the Josephson junction, is (superconducting) flux quantum, and is the phase difference
In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is expressed in such a s ...
across the junction.[ Notice that the term indicates nonlinearity of the Josephson junction.][ Charge energy is written as
: ,
where is the junction's capacitance and is electron charge.][ Of the three archetypes, phase qubits allow the most of Cooper pairs to tunnel through the junction, followed by flux qubits, and charge qubits allow the fewest.
]
Phase qubit
The phase qubit possesses a Josephson to charge energy ratio on the order of magnitude . For phase qubits, energy levels correspond to different quantum charge oscillation amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
s across a Josephson junction, where charge and phase
Phase or phases may refer to:
Science
*State of matter, or phase, one of the distinct forms in which matter can exist
*Phase (matter), a region of space throughout which all physical properties are essentially uniform
*Phase space, a mathematica ...
are analogous to momentum and position respectively as analogous to a quantum harmonic oscillator
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, ...
. Note that in this context phase is the complex argument of the superconducting wave function (also known as the superconducting order parameter
In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic s ...
), not the phase between the different states of the qubit.
Flux qubit
The flux qubit (also known as a persistent-current qubit) possesses a Josephson to charging energy ratio on the order of magnitude . For flux qubits, the energy levels correspond to different integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
numbers of magnetic flux quanta trapped in a superconducting ring.
Fluxonium
Fluxonium qubits are a specific type of flux qubit whose Josephson junction is shunted by a linear inductor of where .[ In practice, the linear inductor is usually implemented by a Josephson junction array that is composed of a large number (can be often ) of large-sized Josephson junctions connected in a series. Under this condition, the Hamiltonian of a fluxonium can be written as:
: .
One important property of the fluxonium qubit is the longer qubit lifetime at the half flux sweet spot, which can exceed 1 millisecond.] Another crucial advantage of the fluxonium qubit biased at the sweet spot is the large anharmonicity, which allows fast local microwave control and mitigates spectral crowding problems, leading to better scalability.
Charge qubit
The charge qubit, also known as the Cooper pair box, possesses a Josephson to charging energy ratio on the order of magnitude . For charge qubits, different energy levels correspond to an integer number of Cooper pair
In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper. ...
s on a superconducting island (a small superconducting area with a controllable number of charge carriers). Indeed, the first experimentally realized qubit was the Cooper pair box, achieved in 1999.
Transmon
Transmons are a special type of qubit with a shunted capacitor specifically designed to mitigate noise
Noise is sound, chiefly unwanted, unintentional, or harmful sound considered unpleasant, loud, or disruptive to mental or hearing faculties. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrat ...
. The transmon qubit model was based on the Cooper pair box (illustrated in the table above in row one column one). It was also the first qubit to demonstrate quantum supremacy
''Quantum Supremacy: How the Quantum Computer Revolution Will Change Everything'' is a non-fiction book by the American futurist and physicist Michio Kaku. The book, Kaku's eleventh, was initially published on 2 May 2023 by Doubleday. The book ...
. The increased ratio of Josephson to charge energy mitigates noise. Two transmons can be coupled using a coupling capacitor.[ For this 2-qubit system the Hamiltonian is written
: ,
where is ]current density
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ...
and is surface charge density.[
]
Xmon
The Xmon is very similar in design to a transmon in that it originated based on the planar transmon model. An Xmon is essentially a tunable transmon. The major distinguishing difference between transmon and Xmon qubits is the Xmon qubits is grounded with one of its capacitor pads.
Gatemon
Another variation of the transmon qubit is the Gatemon. Like the Xmon, the Gatemon is a tunable variation of the transmon. The Gatemon is tunable via gate voltage.
Unimon
In 2022 researchers from IQM Quantum Computers, Aalto University
Aalto University (; ) is a public university, public research university located in Espoo, Finland. It was established in 2010 as a merger of three major Finnish universities: the Helsinki University of Technology, the Helsinki School of Economic ...
, and VTT Technical Research Centre of Finland discovered a novel superconducting qubit known as the Unimon. A relatively simple qubit, the Unimon consists of a single Josephson junction shunted by a linear inductor (possessing an inductance not depending on current) inside a (superconducting) resonator
A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a reso ...
. Unimons have increased anharmonicity and display faster operation time resulting in lower susceptibility to noise errors.[ In addition to increased anharmonicity, other advantages Unimon qubit include decreased susceptibility to flux noise and complete insensitivity to dc charge noise.][
In the table above, the three superconducting qubit archetypes are reviewed. In the first row, the qubit's electrical circuit diagram is presented. The second row depicts a quantum Hamiltonian derived from the circuit. Generally, the Hamiltonian is the sum of the system's kinetic and ]potential
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...
energy components (analogous to a particle in a potential well
A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy ( kinetic energy in the case of a gravitational potential well) because it is cap ...
). For the Hamiltonians denoted, is the superconducting wave function phase difference across the junction, is the capacitance associated with the Josephson junction, and is the charge on the junction capacitance. For each potential depicted, only solid wave functions are used for computation. The qubit potential is indicated by a thick red line, and schematic wave function solutions are depicted by thin lines, lifted to their appropriate energy level for clarity.
Note that particle mass corresponds to an inverse function
In mathematics, the inverse function of a function (also called the inverse of ) is a function that undoes the operation of . The inverse of exists if and only if is bijective, and if it exists, is denoted by f^ .
For a function f\colon ...
of the circuit capacitance and that the shape of the potential is governed by regular inductor
An inductor, also called a coil, choke, or reactor, is a Passivity (engineering), passive two-terminal electronic component, electrical component that stores energy in a magnetic field when an electric current flows through it. An inductor typic ...
s and Josephson junctions. Schematic wave solutions in the third row of the table show the complex amplitude of the phase variable. Specifically, if a qubit's phase is measured while the qubit occupies a particular state, there is a non-zero probability of measuring a specific value ''only'' where the depicted wave function oscillates. All three rows are essentially different presentations of the same physical system.
Single qubits
The GHz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...
energy gap between energy levels of a superconducting qubit is designed to be compatible with available electronic equipment, due to the terahertz gap
Terahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency
(THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the International Telecommunicat ...
(lack of equipment in the higher frequency band
Spectral bands are regions of a given spectrum, having a specific range of wavelengths or frequencies. Most often, it refers to electromagnetic bands, regions of the electromagnetic spectrum.
More generally, spectral bands may also be means in ...
). The superconductor energy gap implies a top limit of operation below ~1THz beyond which Cooper pairs break, so energy level separation cannot be too high. On the other hand, energy level separation cannot be too small due to cooling considerations: a temperature of 1 K implies energy fluctuations of 20 GHz. Temperatures of tens of millikelvins are achieved in dilution refrigerator
A 3He/4He dilution refrigerator is a cryogenics, cryogenic device that provides continuous cooling to temperatures as low as 2 Kelvin, mK, with no moving parts in the low-temperature region. The cooling power is provided by the heat o ...
s and allow qubit operation at a ~5 GHz energy level separation. Qubit energy level separation is frequently adjusted by controlling a dedicated bias current
In electronics, biasing is the setting of DC (direct current) operating conditions (current and voltage) of an electronic component that processes time-varying signals. Many electronic devices, such as diodes, transistors and vacuum tubes, wh ...
line, providing a "knob" to fine tune the qubit parameters.
Single qubit gates
A single qubit gate is achieved by rotation in the Bloch sphere
In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system ( qubit), named after the physicist Felix Bloch.
Mathematically each quantum mechanical syst ...
. Rotations between different energy levels of a single qubit are induced by microwave
Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...
pulses sent to an antenna or transmission line
In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
coupled to the qubit with a frequency
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
resonant with the energy separation between levels. Individual qubits may be addressed by a dedicated transmission line
In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
or by a shared one if the other qubits are off resonance
Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...
. The axis of rotation
Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersect ...
is set by quadrature amplitude modulation
Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signa ...
of microwave pulse, while pulse length determines the angle of rotation
The angular displacement (symbol θ, , or φ) – also called angle of rotation, rotational displacement, or rotary displacement – of a physical body is the angle (in units of radians, degrees, turns, etc.) through which the body rotates (r ...
.
More formally (following the notation of [) for a driving signal
:
of frequency , a driven qubit Hamiltonian in a rotating wave approximation is
: ,
where is the qubit resonance and are ]Pauli matrices
In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices that are traceless, Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (), they are occasionally denoted by tau () ...
.
To implement a rotation about the axis, one can set and apply a microwave pulse at frequency for time . The resulting transformation is
: .
This is exactly the rotation operator by angle about the axis in the Bloch sphere. A rotation about the axis can be implemented in a similar way. Showing the two rotation operators is sufficient for satisfying universality as every single qubit unitary operator may be presented as (up to a global phase
Phase or phases may refer to:
Science
*State of matter, or phase, one of the distinct forms in which matter can exist
*Phase (matter), a region of space throughout which all physical properties are essentially uniform
*Phase space, a mathematica ...
which is physically inconsequential) by a procedure known as the decomposition. Setting results in the transformation
:
up to the global phase and is known as the NOT gate
Not or NOT may also refer to:
Language
* Not, the general declarative form of "no", indicating a negation of a related statement that usually precedes
* ... Not!, a grammatical construction used as a contradiction, popularized in the early 1990 ...
.
Coupling qubits
The ability to couple qubits is essential for implementing 2-qubit gates. Coupling two qubits can be achieved by connecting both to an intermediate electrical coupling circuit. The circuit may be either a fixed element (such as a capacitor) or be controllable (like the DC-SQUID). In the first case, decoupling qubits during the time the gate is switched off is achieved by tuning qubits out of resonance one from another, making the energy gaps between their computational states different. This approach is inherently limited to nearest-neighbor coupling since a physical electrical circuit must be laid out between connected qubits. Notably, D-Wave Systems
D-Wave Quantum Inc. is a quantum computing company with locations in Palo Alto, California and Burnaby, British Columbia. D-Wave claims to be the world's first company to sell computers that exploit quantum effects in their operation. D-Wa ...
' nearest-neighbor coupling achieves a highly connected unit cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector
In mathematics, a unit vector i ...
of 8 qubits in Chimera graph configuration. Quantum algorithm
In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite seq ...
s typically require coupling between arbitrary qubits. Consequently, multiple swap operations are necessary, limiting the length of quantum computation possible before processor decoherence
Quantum decoherence is the loss of quantum coherence. It involves generally a loss of information of a system to its environment. Quantum decoherence has been studied to understand how quantum systems convert to systems that can be expla ...
.
Quantum bus
Another method of coupling two or more qubits is by way of a quantum bus, by pairing qubits to this intermediate. A quantum bus is often implemented as a microwave cavity
A microwave cavity or radio frequency cavity (RF cavity) is a special type of resonator, consisting of a closed (or largely closed) metal structure that confines electromagnetic fields in the microwave or radio frequency, RF region of the spect ...
modeled by a quantum harmonic oscillator. Coupled qubits may be brought in and out of resonance with the bus and with each other, eliminating the nearest-neighbor limitation. Formalism describing coupling is cavity quantum electrodynamics
Cavity Quantum Electrodynamics (cavity QED) is the study of the interaction between light confined in a reflective cavity and atoms or other particles, under conditions where the quantum nature of photons is significant. It could in principle be ...
. In cavity quantum electrodynamics, qubits are analogous to atoms interacting with an optical photon cavity with a difference of GHz (rather than the THz regime of electromagnetic radiation). Resonant excitation exchange among these artificial atoms is potentially useful for direct implementation of multi-qubit gates. Following the dark state manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a N ...
, the Khazali-Mølmer scheme[ performs complex multi-qubit operations in a single step, providing a substantial shortcut to the conventional circuit model.
]
Cross resonant gate
One popular gating mechanism uses two qubits and a bus, each tuned to different energy level separations. Applying microwave excitation to the first qubit, with a frequency resonant with the second qubit, causes a rotation of the second qubit. Rotation direction depends on the state of the first qubit, allowing a controlled phase gate construction.
Following the notation of,[ the drive Hamiltonian describing the excited system through the first qubit driving line is formally written
: ,
where is the shape of the microwave pulse in time, is resonance frequency of the second qubit, are the ]Pauli matrices
In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices that are traceless, Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (), they are occasionally denoted by tau () ...
, is the coupling coefficient between the two qubits via the resonator, is qubit detuning, is stray (unwanted) coupling between qubits, and is the reduced Planck constant
The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...
. The time integral
In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental oper ...
over determines the angle of rotation. Unwanted rotations from the first and third terms of the Hamiltonian can be compensated for with single qubit operations. The remaining component, combined with single qubit rotations, forms a basis for the su(4) Lie algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi ident ...
.
Geometric phase gate
Higher levels (outside of the computational subspace) of a pair of coupled superconducting circuits can be used to induce a geometric phase on one of the computational states of the qubits. This leads to an entangling conditional phase shift of the relevant qubit states. This effect has been implemented by flux-tuning the qubit spectra and by using selective microwave driving. Off-resonant driving can be used to induce differential ac-Stark shift, allowing the implementation of all-microwave controlled-phase gates.
Heisenberg interactions
The Heisenberg model of interactions, written as
,
serves as the basis for analog quantum simulation of spin systems and the primitive for an expressive set of quantum gates, sometimes referred to as ''fermionic simulation'' (or ''fSim'') gates. In superconducting circuits, this interaction model has been implemented using flux-tunable qubits with flux-tunable coupling, allowing the demonstration of quantum supremacy. In addition, it can also be realized in fixed-frequency qubits with fixed-coupling using microwave drives.[ The fSim gate family encompasses arbitrary XY and ZZ two-qubit unitaries, including the iSWAP, the CZ, and the SWAP gates (see ]Quantum logic gate
In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. Quantum logic gates are the building blocks of qua ...
).
Qubit readout
Architecture-specific readout, or measurement
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events.
In other words, measurement is a process of determining how large or small a physical quantity is as compared to ...
, mechanisms exist. Readout of a phase qubit is explained in the qubit archetypes table above. A flux qubit state is often read using an adjustable DC-SQUID
A squid (: squid) is a mollusc with an elongated soft body, large eyes, eight cephalopod limb, arms, and two tentacles in the orders Myopsida, Oegopsida, and Bathyteuthida (though many other molluscs within the broader Neocoleoidea are also ...
magnetometer
A magnetometer is a device that measures magnetic field or magnetic dipole moment. Different types of magnetometers measure the direction, strength, or relative change of a magnetic field at a particular location. A compass is one such device, ...
. States may also be measured using an electrometer
An electrometer is an electrical instrument for measuring electric charge or electrical potential difference. There are many different types, ranging from historical handmade mechanical instruments to high-precision electronic devices. Modern ...
. A more general readout scheme includes a coupling to a microwave resonator
A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a reso ...
, where resonance frequency of the resonator is dispersively shifted by the qubit state.[
] Multi-level systems (qudits) can be readout using electron shelving.
DiVincenzo's criteria
DiVincenzo's criteria
The DiVincenzo criteria are conditions necessary for constructing a quantum computer, conditions proposed in 1996 by the theoretical physicist David P. DiVincenzo, as being those necessary to construct such a computer—a computer first proposed ...
is a list describing the requirements for a physical system to be capable of implementing a logical qubit. DiVincenzo's criteria is satisfied by superconducting quantum computing implementation. Much of the current development effort in superconducting quantum computing aim to achieve interconnect, control, and readout in the 3rd dimension with additional lithography
Lithography () is a planographic method of printing originally based on the miscibility, immiscibility of oil and water. The printing is from a stone (lithographic limestone) or a metal plate with a smooth surface. It was invented in 1796 by ...
layers.The list of DiVincenzo's criteria for a physical system to implement a logical qubit is satisfied by the implementation of superconducting qubits. Although DiVincenzo's criteria as originally proposed consists of five criteria required for physically implementing a quantum computer, the more complete list consists of seven criteria as it takes into account communication over a computer network capable of transmitting quantum information between computers, known as the “quantum internet”. Therefore, the first five criteria ensure successful quantum computing, while the final two criteria allow for quantum communication.
# A scalable physical system with well characterized qubits. "Well characterized implies that that Hamiltonian function
In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (gene ...
must be well-defined i.e. the energy eigenstates of the qubit should be able to be quantified.. A scalable system is self-explanatory, it indicates that this ability to regulate a qubit should be augmentable for multiple more qubits. Herein lies the major issue Quantum Computers face, as more qubits are implemented it leads to an exponential increase in cost and other physical implementations which pale in comparison to the enhanced speed it may offer.[ As superconducting qubits are fabricated on a chip, the many-qubit system is readily scalable. Qubits are allocated on the 2D surface of the chip. The demand for well characterized qubits is fulfilled with (a) qubit non-linearity (accessing only two of the available energy levels) and (b) accessing a single qubit at a time (rather than the entire many-qubit system) by way of per-qubit dedicated control lines and/or frequency separation, or tuning out, of different qubits.
# Ability to initialize the state of qubits to a simple fiducial state.] A fiducial state is one that is easily and consistently replicable and is useful in quantum computing as it may be used to guarantee the initial state of qubits. One simple way to initialize a superconducting qubit is to wait long enough for the qubits to relax to the ground state. Controlling qubit potential with tuning knobs allows faster initialization mechanisms.
# Long relevant decoherence times[. Decoherence of superconducting qubits is affected by multiple factors. Most decoherence is attributed to the quality of the Josephson junction and imperfections in the chip substrate. Due to their mesoscopic scale, superconducting qubits are relatively short lived. Nevertheless, thousands of gate operations have been demonstrated in these many-qubit systems. Recent strategies to improve device coherence include purifying the circuit materials and designing qubits with decreased sensitivity to noise sources.][
# A "universal" set of quantum gates.][ Superconducting qubits allow arbitrary rotations in the Bloch sphere with pulsed microwave signals, implementing single qubit gates. and couplings are shown for most implementations and for complementing the universal gate set.] This criterion may also be satisfied by coupling two transmons with a coupling capacitor.[
# Qubit-specific measurement ability.][ In general, single superconducting qubits are used for control or for measurement.
# Interconvertibility of stationary and flying qubits.][ While stationary qubits are used to store information or perform calculations, flying qubits transmit information macroscopically. Qubits should be capable of converting from being a stationary qubit to being a flying qubit and vice versa.
# Reliable transmission of flying qubits between specified locations.][
The final two criteria have been experimentally proven by research performed by ]ETH
Eth ( , uppercase: ⟨Ð⟩, lowercase: ⟨ð⟩; also spelled edh or eð), known as in Old English, is a letter used in Old English, Middle English, Icelandic, Faroese (in which it is called ), and Elfdalian.
It was also used in Sca ...
with two superconducting qubits connected by a coaxial cable
Coaxial cable, or coax (pronounced ), is a type of electrical cable consisting of an inner Electrical conductor, conductor surrounded by a concentric conducting Electromagnetic shielding, shield, with the two separated by a dielectric (Insulat ...
.
Challenges
One of the primary challenges of superconducting quantum computing is the extremely low temperatures at which superconductors like Bose-Einstein Condensates exist. Other basic challenges in superconducting qubit design are shaping the potential well and choosing particle mass such that energy separation between two specific energy levels is unique, differing from all other interlevel energy separation in the system, since these two levels are used as logical states of the qubit.
Superconducting quantum computing must also mitigate quantum noise
Quantum noise is noise arising from the indeterminate state of matter in accordance with fundamental principles of quantum mechanics, specifically the uncertainty principle and via zero-point energy fluctuations. Quantum noise is due to the appa ...
(disruptions of the system caused by its interaction with an environment) as well as leakage (information being lost to the surrounding environment). One way to reduce leakage is with parity measurement Parity measurement (also referred to as Operator measurement) is a procedure in quantum information science used for error detection in quantum qubits. A parity measurement checks the equality of two qubits to return a true or false answer, which ca ...
s.[ Another strategy is to use qubits with large anharmonicity.][ Many current challenges faced by superconducting quantum computing lie in the field of microwave engineering.][ As superconducting quantum computing approaches larger scale devices, researchers face difficulties in qubit coherence, scalable ]calibration
In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known ...
software, efficient determination of fidelity
Fidelity is the quality of faithfulness or loyalty. Its original meaning regarded duty in a broader sense than the related concept of '' fealty''. Both derive from the Latin word , meaning "faithful or loyal". In the City of London financial m ...
of quantum states across an entire chip, and qubit and gate fidelity.[ Moreover, superconducting quantum computing devices must be reliably reproducible at increasingly large scales such that they are compatible with these improvements.][
Journey of superconducting quantum computing:
Although not the newest development, the focus began to shift onto superconducting qubits in the latter half of the 1990s when quantum tunneling across Josephson junctions became apparent which allowed for the realization that quantum computing could be achieved through these superconducting qubits.]
At the end of the century in 1999, a paper was published by Yasunobu Nakamura, which exhibited the initial design of a superconducting qubit which is now known as the "charge qubit". This is the primary basis point on which later designs amended upon. These initial qubits had their limitations in respect to maintaining long coherence times and destructive measurements. The further amendment to this initial breakthrough lead to the invention of the phase and flux qubit and subsequently resulting in the transmon qubit which is now widely and primarily used in Superconducting Quantum Computing.The transmon qubit has enhanced original designs and has further cushioned charge noise from the qubit.[
The journey has been long, arduous and full of breakthroughs but has seen significant advancements in the recent history and has massive potential for revolutionizing computing.
Recent Advances in Josephson Junction–Based QPUs
A recent paper by Mohebi and Mohseni provides additional insight into the engineering challenges and innovations necessary for advancing superconducting quantum processing units (QPUs):
# Decoherence and Noise Mitigation: The paper emphasizes that decoherence—primarily due to quasiparticle tunneling—is a major obstacle that limits qubit performance. Improved material innovations and optimized control techniques are essential to reduce noise and enhance qubit coherence.]
# Fabrication and Reproducibility: Achieving consistent and reproducible Josephson junctions is crucial for scaling up superconducting QPUs. The study discusses advanced lithography techniques and control of junction geometry as methods to minimize fluctuations in critical current, thereby enhancing qubit fidelity.[
# Balancing Qubit Parameters: The authors highlight the trade-offs between achieving large anharmonicity (to suppress charge noise) and maintaining the nonlinearity required for effective qubit operation. Striking the optimal balance between these factors is pivotal for the development of robust, scalable quantum processors.][
Future of superconducting quantum computing:
The sector's leading industry giants, like Google, IBM and Baidu, are using superconducting quantum computing and transmon qubits to make leaps and bounds in the area of quantum computing.
In August 2022, Baidu released its plans to build a fully integrated top to bottom quantum computer which incorporated superconducting qubits. This computer will be all encompassing with hardware, software and applications fully integrated. This is a first in the world of quantum computing and will lead to ground-breaking advancements.
IBM released the following roadmap publicly that they have set for their quantum computers which also incorporated superconducting qubits and the transmon qubit.
: 2021: In 2021, IBM came out with their 127-qubit processor.]
: 2022: On November 9, IBM announced its 433 qubit processor called "Osprey".
: 2023: IBM plan on releasing their Condor quantum processor with 1,121 qubits.[
: 2024: IBM plan on releasing their Flamingo quantum processor with 1,386+ qubits.][
: 2025: IBM plan on releasing their Kookaburra quantum processor with 4,158+ qubits.][
: 2026 and beyond: IBM plan on releasing a quantum processor that scaled beyond 10,000 qubits to a 100,000 qubits.][
Google in 2016, implemented 16 qubits to convey a demonstration of the Fermi-Hubbard Model. In another recent experiment, Google used 17 qubits to optimize the ]Sherrington-Kirkpatrick model
In condensed matter physics, a spin glass is a magnetic state characterized by randomness, besides cooperative behavior in freezing of spins at a temperature called the "freezing temperature," ''T''f. In ferromagnetic solids, component atoms' ...
. Google produced the Sycamore quantum computer which performed a task in 200 seconds that would have taken 10,000 years on a classical computer.
References
Further reading
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External links
IBM Quantum
offers access to over 20 quantum computer systems.
* Th
IBM Quantum Experience
offers free access to writing quantum algorithms and executing them on 5 qubit quantum computers.
IBM's roadmap for quantum computing
shows 65 qubit systems available in 2020 and 127 qubits to be available sometime in 2021.
{{Superconductivity
Quantum information science
Quantum electronics
Superconductivity