|
Quantum Random Circuits
Quantum random circuits (QRC) is a concept of incorporating an element of randomness into the local unitary operations and measurements of a quantum circuit. The idea is similar to that of random matrix theory which is to use the QRC to obtain almost exact results of non-integrable, hard-to-solve problems by averaging over an ensemble of outcomes. This incorporation of randomness into the circuits has many possible advantages, some of which are (i) the validation of quantum computers, which is the method that Google used when they claimed quantum supremacy in 2019, and (ii) understanding the universal structure of non-equilibrium and thermalization processes in quantum many-body dynamics. Quantum Random Circuits The constituents of some general quantum circuits would be qubits, unitary gates, and measurements. The time evolution of the quantum circuits is discrete in time t \in \mathbb, and the states are evolved step by step in time by the application of unitary operators U_t \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unitarity (physics)
In quantum physics, unitarity is (or a unitary process has) the condition that the time evolution of a quantum state according to the Schrödinger equation is mathematically represented by a unitary operator. This is typically taken as an axiom or basic postulate of quantum mechanics, while generalizations of or departures from unitarity are part of speculations about theories that may go beyond quantum mechanics. A unitarity bound is any inequality that follows from the unitarity of the evolution operator, i.e. from the statement that time evolution preserves inner products in Hilbert space. Hamiltonian evolution Time evolution described by a time-independent Hamiltonian is represented by a one-parameter family of unitary operators, for which the Hamiltonian is a generator: U(t) = e^. In the Schrödinger picture, the unitary operators are taken to act upon the system's quantum state, whereas in the Heisenberg picture, the time dependence is incorporated into the observable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measurement In Quantum Mechanics
In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule. For example, a quantum particle like an electron can be described by a quantum state that associates to each point in space a complex number called a probability amplitude. Applying the Born rule to these amplitudes gives the probabilities that the electron will be found in one region or another when an experiment is performed to locate it. This is the best the theory can do; it cannot say for certain where the electron will be found. The same quantum state can also be used to make a prediction of how the electro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Circuit
In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly other actions. The minimum set of actions that a circuit needs to be able to perform on the qubits to enable quantum computation is known as DiVincenzo's criteria. Circuits are written such that the horizontal axis is time, starting at the left hand side and ending at the right. Horizontal lines are qubits, doubled lines represent classical bits. The items that are connected by these lines are operations performed on the qubits, such as measurements or gates. These lines define the sequence of events, and are usually not physical cables. The graphical depiction of quantum circuit elements is described using a variant of the Penrose graphical notation. Richard Feynman used an early version of the quantum circuit notation in 1986. Rever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution. Random matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques like mean-field theory, diagrammatic methods, the cavity method, or the replica method to compute quantities like traces, spectral densities, or scalar products between eigenvectors. Many physical phenomena, such as the spectrum of nuclei of heavy atoms, the thermal conductivity of a lattice, or the emergence of quantum chaos, can be modeled mathematically as problems concerning large, random matrices. Applications Physics In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms. Wigner postulated that the spacings between the lines in the spectrum of a heavy atom nucleus should resemble the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 concentrates on quantum computing and its uses for various tasks. Reception Scott Aaronson, professor of computer science at the University of Texas at Austin, severely panned Kaku's book on his blog, Shtetl-Optimized. Aaronson wrote, "beating out a crowded field, this is the worst book about quantum computing, for some definition of the word 'about,' that I’ve ever encountered," describing the book as a "kindergarten of lies." After pointing out several substantial factual errors, Aaronson concluded that "the bulk of the book is actually about stuff with no direct relation to quantum computing at all—the origin of life, climate change, energy generation, cancer, curing aging, etc.—except with ungrounded speculations tacked onto the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Circuit
In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly other actions. The minimum set of actions that a circuit needs to be able to perform on the qubits to enable quantum computation is known as DiVincenzo's criteria. Circuits are written such that the horizontal axis is time, starting at the left hand side and ending at the right. Horizontal lines are qubits, doubled lines represent classical bits. The items that are connected by these lines are operations performed on the qubits, such as measurements or gates. These lines define the sequence of events, and are usually not physical cables. The graphical depiction of quantum circuit elements is described using a variant of the Penrose graphical notation. Richard Feynman used an early version of the quantum circuit notation in 1986. Rever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Nature Of Quantum Measurements
Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; in everyday conversation, however, these terms are often used interchangeably. In probability theory, the formal concept of a ''stochastic process'' is also referred to as a ''random process''. Stochasticity is used in many different fields, including image processing, signal processing, computer science, information theory, telecommunications, chemistry, ecology, neuroscience, physics, and cryptography. It is also used in finance (e.g., stochastic oscillator), due to seemingly random changes in the different markets within the financial sector and in medicine, linguistics, music, media, colour theory, botany, manufacturing and geomorphology. Etymology The word ''stochastic'' in English was originally used as an adjective with the definit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noisy Intermediate-scale Quantum Era
The current state of quantum computing is referred to as the noisy intermediate-scale quantum (NISQ) era, characterized by quantum processors containing up to 1,000 qubits which are not advanced enough yet for fault-tolerance or large enough to achieve quantum advantage. These processors, which are sensitive to their environment (noisy) and prone to quantum decoherence, are not yet capable of continuous quantum error correction. This intermediate-scale is defined by the quantum volume, which is based on the moderate number of qubits and gate fidelity. The term NISQ was coined by John Preskill in 2018. According to Microsoft Azure Quantum's scheme, NISQ computation is considered level 1, the lowest of the quantum computing implementation levels. In October 2023, the 1,000 qubit mark was passed for the first time by Atom Computing's 1,180 qubit quantum processor. However, as of 2024, only two quantum processors have over 1,000 qubits, with sub-1,000 quantum processors still rem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boson Sampling
Boson sampling is a restricted model of non-universal quantum computation introduced by Scott Aaronson and Alex Arkhipov after the original work of Lidror Troyansky and Naftali Tishby, that explored possible use of boson scattering to evaluate expectation values of permanents of matrices. The model consists of sampling from the probability distribution of identical bosons scattered by a linear interferometer. Although the problem is well defined for any bosonic particles, its photonic version is currently considered as the most promising platform for a scalable implementation of a boson sampling device, which makes it a non-universal approach to linear optical quantum computing. Moreover, while not universal, the boson sampling scheme is strongly believed to implement computing tasks that are hard to implement with classical computers by using far fewer physical resources than a full linear-optical quantum computing setup. This advantage makes it an ideal candidate for demonstrati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of logic gate, gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superconducting Quantum Computing
Superconducting quantum computing is a branch of Solid-state physics, solid state physics and quantum computing that implements superconductivity, superconducting electronic circuits using superconducting qubits as artificial atoms, or quantum dots. For superconducting qubits, the two logic states are the ground state and the excited state, denoted , g\rangle \text , e\rangle respectively. Research in superconducting quantum computing is conducted by companies such as Google, IBM, IMEC, BBN Technologies, Rigetti Computing, Rigetti, and Intel. Many recently developed QPUs (quantum processing units, or quantum chips) use superconducting architecture. , up to 9 fully controllable qubits are demonstrated in the 1D Array programming, array, and up to 16 in 2D architecture. In October 2019, the John M. Martinis, Martinis group, partnered with Google, published an article demonstrating novel quantum supremacy, using a chip composed of 53 superconducting qubits. Background Classical co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sycamore Processor
Sycamore is a transmon superconducting quantum processor created by Google's Artificial Intelligence division. It has 53 qubits. In 2019, Sycamore completed a task in 200 seconds that Google claimed, in a ''Nature'' paper, would take a state-of-the-art supercomputer 10,000 years to finish. Thus, Google claimed to have achieved quantum supremacy. To estimate the time that would be taken by a classical supercomputer, Google ran portions of the quantum circuit simulation on Summit, one of the most powerful classical computers in the world. Later, IBM made a counter-argument, claiming that the task would take only 2.5 days on a classical system like Summit. If Google's claims are upheld, then it would represent a huge leap in computing power. In August 2020, quantum engineers working for Google reported the largest chemical simulation on a quantum computer – a Hartree–Fock approximation with Sycamore paired with a classical computer that analyzed results to provide new paramet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
