Universal quantum simulator
Encyclopedia
A universal quantum simulator is a quantum computer
proposed by Richard Feynman
in 1982.
Feynman showed that a classical Turing machine
would presumably experience an exponential slowdown when simulating quantum phenomena, while his hypothetical universal quantum simulator would not. David Deutsch
in 1985, took the ideas further and described a universal quantum computer. In 1996, Seth Lloyd
showed that a standard quantum computer
can be programmed to simulate any local quantum system efficiently.
A quantum system of many particles is described by a Hilbert space
whose dimension is exponentially large in the number of particles. Therefore, the obvious approach to simulate such a system requires exponential time on a classical computer
. However, it is conceivable that a quantum system of many particles could be simulated by a quantum computer using a number of quantum bits
similar to the number of particles in the original system. As shown by Lloyd, this is true for a class of quantum systems known as local quantum systems. This has been extended to much larger classes of quantum systems.
Barreiro et al have created a Universal Open-System Digital Quantum Simulator with trapped ions.
Lanyon et al have created a Universal Digital Quantum Simulation with Trapped Ions.
Quantum computer
A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from traditional computers based on transistors...
proposed by Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
in 1982.
Feynman showed that a classical Turing machine
Turing machine
A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...
would presumably experience an exponential slowdown when simulating quantum phenomena, while his hypothetical universal quantum simulator would not. David Deutsch
David Deutsch
David Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...
in 1985, took the ideas further and described a universal quantum computer. In 1996, Seth Lloyd
Seth Lloyd
Seth Lloyd is a professor of mechanical engineering at the Massachusetts Institute of Technology. He refers to himself as a "quantum mechanic"....
showed that a standard quantum computer
Quantum computer
A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from traditional computers based on transistors...
can be programmed to simulate any local quantum system efficiently.
A quantum system of many particles is described by a Hilbert space
Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...
whose dimension is exponentially large in the number of particles. Therefore, the obvious approach to simulate such a system requires exponential time on a classical computer
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
. However, it is conceivable that a quantum system of many particles could be simulated by a quantum computer using a number of quantum bits
Qubit
In quantum computing, a qubit or quantum bit is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom....
similar to the number of particles in the original system. As shown by Lloyd, this is true for a class of quantum systems known as local quantum systems. This has been extended to much larger classes of quantum systems.
Barreiro et al have created a Universal Open-System Digital Quantum Simulator with trapped ions.
Lanyon et al have created a Universal Digital Quantum Simulation with Trapped Ions.