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Physical Review A

Scheme for reducing decoherence in quantum computer memory

Peter W. Shor

Published Oct 1, 1995• 4,475 citations
Publisher

Abstract

Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest has since been growing in the area of quantum computation. One of the main difficulties of quantum computation is that decoherence destroys the information in a superposition of states contained in a quantum computer, thus making long computations impossible. It is shown how to reduce the effects of decoherence for information stored in quantum memory, assuming that the decoherence process acts independently on each of the bits stored in memory. This involves the use of a quantum analog of errorcorrecting codes.Received 17 May 1995DOI:https://doi.org/10.1103/PhysRevA.52.R2493©1995 American Physical Society

DOI
10.1103/physreva.52.r2493

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Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest has since been growing in the area of quantum computation. One of the main difficulties of quantum computation is that decoherence destroys the information in a superposition of states contained in a quantum computer, thus making long computations impossible. It is shown how to reduce the effects of decoherence for information stored in quantum memory, assuming that the decoherence process acts independently on each of the bits stored in memory. This involves the use of a quantum analog of errorcorrecting codes.Received 17 May 1995DOI:https://doi.org/10.1103/PhysRevA.52.R2493©1995 American Physical Society
It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer making long computations impossible. A further difficulty is that inaccuracies in quantum state transformations throughout the computation accumulate, rendering long computations unreliable. However, these obstacles may not be as formidable as originally believed. For any quantum computation with t gates, we show how to build a polynomial size quantum circuit that tolerates O(1/log/sup c/t) amounts of inaccuracy and decoherence per gate, for some constant c; the previous bound was O(1/t). We do this by showing that operations can be performed on quantum data encoded by quantum error-correcting codes without decoding this data.
As early as 1982 Richard P. Feynman suggested that it might be impossible to simulate quantum mechanical phenomena with a computer without an exponential slowdown the efficiency of computation. He also proposed that this problem may be avoided by allowing the computer to run according to the laws of quantum mechanics, thus implicitely suggesting that a computer based on the quantum mechanical systems, a quantum computer, might have exponentially more computational efficiency than any classical one. A quantum mechanical phenomenon that never occurs classical physics and which actually makes quantum computation interesting and powerful, is the superposition of states, which, loosely speaking, means that instead of being totally one single state, a particle can be in between many states. Compare this to the elements of classical computer, bits. A bit takes values zero or one, but never anything between. In a quantum computer, one is able to store it both values simultaneously one quantum bit, equally weighted or not. Moreover, the classical computer one can store a number from zero to 2n−12^n-12n−1 a register of length nnn, whereas, quantum computation, all the values could be stored simultaneously. The computation, which is performed via unitary transformations the state vector space, then applies to all these values simultaneously. Thus the power of the quantum computation lies not the absolute speed of the hypothetetical quantum computer but the possibility to actually follow many computational path simultaneously, as a nondeterministic automaton does. Alas, the observation of the outcome will yield only one value destroying the rest irreversibly. However, using a procedure smart enough one could obtain some valuable information about the computation.
Decoherence is the process that a quantum particle loses its integrity by interacting with the surrounding environment. The problem of decoherence restricts the time available for implementing a given quantum computation process. This phenomenon has a major impact on the performance of quantum computers. In this paper, we propose a scheme to solve this problem. We use a circuit approach to protect our quantum bits (qubit) from decoherence. This results in a quantum memory that has many applications in quantum information science.
If quantum bits (qubits) couple to the same environment, it has been found the qubits decohere coherently. An interesting result from this phenomenon is that, for a kind of input states, i.e., the coherence-preserving states, coherence of the qubits can be preserved perfectly in quantum memory. In this paper, we propose a feasible scheme to transform an arbitrary unknown input state to the corresponding coherence-preserving state. The transformed state undergoes no decoherence in the noisy memory and, after that, it can be transformed back into the original state with decoherence much reduced. This scheme involves the use of an analogy of the ideas of quantum teleportation.
A new type of uncertainty relation is presented, concerning the information-bearing properties of a discrete quantum system. A natural link is then revealed between basic quantum theory and the linear error correcting codes of classical information theory. A subset of the known codes is described, having properties which are important for error correction in quantum communication. It is shown that a pair of states which are, in a certain sense, "macroscopically different," can form a superposition in which the interference phase between the two parts is measurable. This provides a highly stabilized "Schrödinger cat" state.Received 4 October 1995DOI:https://doi.org/10.1103/PhysRevLett.77.793©1996 American Physical Society