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Chinese Physics Letters

Scheme for Reducing Decoherence in Quantum Computer Memory by Transformation to the Coherence-Preserving States

Duan Lu-ming, Guo Guang-Can

Published Jul 1, 1997• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/14/7/003

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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.
Decoherence in quantum-computer memory due to the inevitable coupling to the external environment is examined. We make the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits decohere collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory, even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of this decoherence model for quantum measurements.
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
Cooperative effects in the loss (the amplitude damping) and decoherence (the phase damping) of the qubits (two-state quantum systems) due to the inevitable coupling to the same environment are investigated. It is found that the qubits undergo the dissipation coherently in this case. In particular, for a special kind of input states (called the coherence-preserving states), whose form depends on the type of the coupling, loss and decoherence in quantum memory are much reduced. Based on this phenomenon, a scheme by encoding the general input states of the qubits into the corresponding coherence-preserving states is proposed for reducing the cooperative loss and decoherence in quantum computation or communication.
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.
We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a lesser number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a non-maximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's lab in terms of the composition of the completely positive maps corresponding to the shared resource state and joint POVM performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is possible perfectly with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with the Werner states and show that even when the Werner states become separable, the amount of teleported coherence is non-zero, implying the possibility of teleportation of coherence without entanglement.
We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a smaller number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a nonmaximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's laboratory in terms of the composition of the completely positive maps corresponding to the shared resource state and a joint positive operator-valued measure (POVM) performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is perfectly possible with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with Werner states and show that even when Werner states become separable, the amount of teleported coherence is nonzero, implying the possibility of teleportation of coherence without entanglement.