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In quantum computing, a qubit is a unit of information analogous to a bit (binary digit) in classical computing, but it is affected by quantum mechanical properties such as superposition and entanglement which allow qubits to be in some ways more powerful than classical bits for some tasks. Qubits are used in quantum circuits and quantum algorithms composed of quantum logic gates to solve computational problems, where they are used for input/output and intermediate computations.
A physical qubit is a physical device that behaves as a two-state quantum system, used as a component of a computer system. [1] [2] A logical qubit is a physical or abstract qubit that performs as specified in a quantum algorithm or quantum circuit [3] subject to unitary transformations, has a long enough coherence time to be usable by quantum logic gates (c.f. propagation delay for classical logic gates). [1] [4] [5]
As of September 2018 [update] , most technologies used to implement qubits face issues of stability, decoherence, [6] [7] fault tolerance [8] [9] and scalability. [6] [9] [10] Because of this, many physical qubits are needed for the purposes of error-correction to produce an entity which behaves logically as a single qubit would in a quantum circuit or algorithm; this is the subject of quantum error correction. [3] [11] Thus, contemporary logical qubits typically consist of many physical qubits to provide stability, error-correction and fault tolerance needed to perform useful computations. [1] [7] [11]
1-bit and 2-bit quantum gate operations have been shown to be universal. [12] [13] [14] [15] A quantum algorithm can be instantiated as a quantum circuit. [16] [17]
A logical qubit specifies how a single qubit should behave in a quantum algorithm, subject to quantum logic operations which can be built out of quantum logic gates. However, issues in current technologies preclude single two-state quantum systems, which can be used as physical qubits, from reliably encoding and retaining this information for long enough to be useful. Therefore, current attempts to produce scalable quantum computers require quantum error correction, and multiple (currently many) physical qubits must be used to create a single, error-tolerant logical qubit. Depending on the error-correction scheme used, and the error rates of each physical qubit, a single logical qubit could be formed of up to 1,000 physical qubits. [18]
The approach of topological qubits, which takes advantage of topological effects in quantum mechanics, has been proposed as needing many fewer or even a single physical qubit per logical qubit. [10] Topological qubits rely on a class of particles called anyons which have spin that is neither half-integral (fermions) nor integral (bosons), and therefore obey neither the Fermi–Dirac statistics nor the Bose–Einstein statistics of particle behavior. [19] Anyons exhibit braid symmetry in their world lines, which has desirable properties for the stability of qubits. Notably, anyons must exist in systems constrained to two spatial dimensions or fewer, according to the spin–statistics theorem, which states that in 3 or more spatial dimensions, only fermions and bosons are possible. [19]
A quantum computer is a computer that takes advantage of quantum mechanical phenomena.
This is a timeline of quantum computing.
In logic circuits, the Toffoli gate, invented by Tommaso Toffoli, is a universal reversible logic gate, which means that any classical reversible circuit can be constructed from Toffoli gates. It is also known as the "controlled-controlled-not" gate, which describes its action. It has 3-bit inputs and outputs; if the first two bits are both set to 1, it inverts the third bit, otherwise all bits stay the same.
In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is usually used for those algorithms which seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement.
Quantum error correction (QEC) is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve fault tolerant quantum computing that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum preparation, and faulty measurements. This would allow algorithms of greater circuit depth.
A topological quantum computer is a theoretical quantum computer proposed by Russian-American physicist Alexei Kitaev in 1997. It employs quasiparticles in two-dimensional systems, called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime. These braids form the logic gates that make up the computer. The advantage of a quantum computer based on quantum braids over using trapped quantum particles is that the former is much more stable. Small, cumulative perturbations can cause quantum states to decohere and introduce errors in the computation, but such small perturbations do not change the braids' topological properties. This is like the effort required to cut a string and reattach the ends to form a different braid, as opposed to a ball bumping into a wall.
In quantum computing, the Gottesman–Knill theorem is a theoretical result by Daniel Gottesman and Emanuel Knill that states that stabilizer circuits, circuits that only consist of gates from the normalizer of the qubit Pauli group, also called Clifford group, can be perfectly simulated in polynomial time on a probabilistic classical computer. The Clifford group can be generated solely by using CNOT, Hadamard, and phase gate S; and therefore stabilizer circuits can be constructed using only these gates.
The one-way or measurement-based quantum computer (MBQC) is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because the resource state is destroyed by the measurements.
In quantum computing, the threshold theorem states that a quantum computer with a physical error rate below a certain threshold can, through application of quantum error correction schemes, suppress the logical error rate to arbitrarily low levels. This shows that quantum computers can be made fault-tolerant, as an analogue to von Neumann's threshold theorem for classical computation. This result was proven by the groups of Dorit Aharanov and Michael Ben-Or; Emanuel Knill, Raymond Laflamme, and Wojciech Zurek; and Alexei Kitaev independently. These results built off a paper of Peter Shor, which proved a weaker version of the threshold theorem.
Daniel Amihud Lidar is the holder of the Viterbi Professorship of Engineering at the University of Southern California, where he is a professor of electrical engineering, chemistry, physics and astronomy. He is the director and co-founder of the USC Center for Quantum Information Science & Technology (CQIST) as well as scientific director of the USC-Lockheed Martin Quantum Computing Center, notable for his research on control of quantum systems and quantum information processing.
The toric code is a topological quantum error correcting code, and an example of a stabilizer code, defined on a two-dimensional spin lattice. It is the simplest and most well studied of the quantum double models. It is also the simplest example of topological order—Z2 topological order (first studied in the context of Z2 spin liquid in 1991). The toric code can also be considered to be a Z2 lattice gauge theory in a particular limit. It was introduced by Alexei Kitaev.
In reversible computing, ancilla bits are extra bits being used to implement irreversible logical operations. In classical computation, any memory bit can be turned on or off at will, requiring no prior knowledge or extra complexity. However, this is not the case in quantum computing or classical reversible computing. In these models of computing, all operations on computer memory must be reversible, and toggling a bit on or off would lose the information about the initial value of that bit. For this reason, in a quantum algorithm there is no way to deterministically put bits in a specific prescribed state unless one is given access to bits whose original state is known in advance. Such bits, whose values are known a priori, are known as ancilla bits in a quantum or reversible computing task.
In quantum many-body physics, topological degeneracy is a phenomenon in which the ground state of a gapped many-body Hamiltonian becomes degenerate in the limit of large system size such that the degeneracy cannot be lifted by any local perturbations.
Quantum machine learning is the integration of quantum algorithms within machine learning programs.
In quantum computing, quantum supremacy or quantum advantage is the goal of demonstrating that a programmable quantum computer can solve a problem that no classical computer can solve in any feasible amount of time, irrespective of the usefulness of the problem. The term was coined by John Preskill in 2012, but the concept dates back to Yuri Manin's 1980 and Richard Feynman's 1981 proposals of quantum computing.
Continuous-variable (CV) quantum information is the area of quantum information science that makes use of physical observables, like the strength of an electromagnetic field, whose numerical values belong to continuous intervals. One primary application is quantum computing. In a sense, continuous-variable quantum computation is "analog", while quantum computation using qubits is "digital." In more technical terms, the former makes use of Hilbert spaces that are infinite-dimensional, while the Hilbert spaces for systems comprising collections of qubits are finite-dimensional. One motivation for studying continuous-variable quantum computation is to understand what resources are necessary to make quantum computers more powerful than classical ones.
Magic state distillation is a method for creating more accurate quantum states from multiple noisy ones, which is important for building fault tolerant quantum computers. It has also been linked to quantum contextuality, a concept thought to contribute to quantum computers' power.
The Eastin–Knill theorem is a no-go theorem that states: "No quantum error correcting code can have a continuous symmetry which acts transversely on physical qubits". In other words, no quantum error correcting code can transversely implement a universal gate set, where a transversal logical gate is one that can be implemented on a logical qubit by the independent action of separate physical gates on corresponding physical qubits.
The current state of quantum computing is referred to as the noisy intermediate-scale quantum (NISQ) era, characterized by quantum processors containing up to 1000 qubits which are not advanced enough yet for fault-tolerance or large enough to achieve quantum supremacy. 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.
This glossary of quantum computing is a list of definitions of terms and concepts used in quantum computing, its sub-disciplines, and related fields.