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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum memory: write, read, reset, and decoherence

Tai Tsun Wu

Published Aug 5, 2003• 3 citations
Publisher

Abstract

An essential component of any quantum computer is the quantum memory, the content of which is a pure quantum state. A program to study the quantum memory is initiated here, where the spatial variables are of central importance. The presence of the spatial variables makes it possible to apply the powerful and well-developed theory of scattering: The fundamental operations of writing on, reading and resetting the quantum memory are all performed through scattering from the memory. The requirement that the quantum memory must remain in a pure state after scattering implies that the scattering is of a special type, and only certain incident waves are admissible. Models based on the coupled-channel Schrodinger equation for potential scattering are formulated, where there is indeed the required large collection of admissible incident waves. On the basis of these models, certain types of decoherence are unavoidable. Such decoherence and the necessity of using the relativistic Schrodinger equation are discussed. One of the implications of quantum memory is the possible lack of security for the quantum key distribution in quantum cryptography.

DOI
10.1117/12.486028

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An essential component of any quantum computer is the quantum memory, the content of which is a pure quantum state. A program to study the quantum memory is initiated here, where the spatial variables are of central importance. The presence of the spatial variables makes it possible to apply the powerful and well-developed theory of scattering: The fundamental operations of writing on, reading and resetting the quantum memory are all performed through scattering from the memory. The requirement that the quantum memory must remain in a pure state after scattering implies that the scattering is of a special type, and only certain incident waves are admissible. Models based on the coupled-channel Schrodinger equation for potential scattering are formulated, where there is indeed the required large collection of admissible incident waves. On the basis of these models, certain types of decoherence are unavoidable. Such decoherence and the necessity of using the relativistic Schrodinger equation are discussed. One of the implications of quantum memory is the possible lack of security for the quantum key distribution in quantum cryptography.
To a large extent, the power of a quantum computer comes from the possibility of operating on a number of quantum memories simultaneously. For example, if there are n linearly independent quantum states in each of N quantum memories, then the number of linearly independent quantum states is n^N when they are taken together. This exponential increase is the basis of the present interest in quantum computing. In the context of quantum mechanics as described by the Schrodinger equation (which is a partial differential equation), the most explicit model of the quantum memory is one with two linearly independent quantum states described in terms of the Fermi pseudo-potential at one point. In this model, operations on the quantum memory are accomplished through scattering with both symmetrical and anti-symmetrical incident waves. As a first step toward operating on more than one quantum memory, this model is generalized in two directions. (1) With the Fermi pseudo-potential at one point retained, three linearly independent quantum states are used for the quantum memory. This model of the quantum memory requires three external connections. (2) With a more general potential, operations on the quantum memory with two states are accomplished through scattering with either symmetrical or anti-symmetrical incident waves. This second generalization is important because it is not practical to keep the number of external connections equal to the number of linearly independent quantum states.
Quantum computing involves transforming the state of a quantum memory. We view this operation as performed by transmitting nonrelativistic (massive) particles that scatter from the memory. By using a system of (1+1)-dimensional, coupled Schrödinger equations with point interaction and narrow-band incoming pulse wavefunctions, we show how the outgoing pulse becomes entangled with a two-state memory. This effect necessarily induces decoherence, i.e., deviations of the memory content from a pure state. We describe incoming pulses that minimize this decoherence effect under a constraint on the duration of their interaction with the memory.
Quantum memory is a crucial component for the development of quantum computing and quantum communication. However, the primary challenge in building a practical quantum memory lies in mitigating quantum decoherence, the loss of quantum information due to interaction with the environment. This paper proposes a novel quantum memory design leveraging the principle of quantum demixing, a phenomenon where interactions between quantum bits (qubits) can effectively slow down the decoherence rate. The design utilizes a carefully engineered architecture where qubits are coupled in a specific manner to promote entanglement and suppress unwanted dephasing. We explore the theoretical framework for this design, focusing on the mathematical models describing the decoherence process and the impact of qubit interactions. The core claim is that optimized quantum memory structures can significantly reduce decoherence, leading to enhanced storage capacity and read/write rates. This work presents a new approach to quantum memory design, addressing a fundamental limitation in the field. ---
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.
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.
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