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Physical Review A

Combating the effects of disorder in quantum state transfer

Catherine Keele, Alastair Kay

Published Mar 24, 2022• 13 citations
Publisher

Abstract

In this paper we examine disorder (i.e., static imperfections in manufacture) for the fixed-Hamiltonian evolution protocol of quantum state transfer. We improve the performance by optimizing the choice of Hamiltonian and by implementing an encoding and decoding procedure on small regions at either end of the chain. We find that encoding in only the single-excitation subspace is optimal and provides substantial enhancement to the operating regime of these systems.

DOI
10.1103/physreva.105.032612

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In this paper we examine disorder (i.e., static imperfections in manufacture) for the fixed-Hamiltonian evolution protocol of quantum state transfer. We improve the performance by optimizing the choice of Hamiltonian and by implementing an encoding and decoding procedure on small regions at either end of the chain. We find that encoding in only the single-excitation subspace is optimal and provides substantial enhancement to the operating regime of these systems.
In the absence of errors, the dynamics of a spin chain, with a suitably engineered local Hamiltonian, allow the perfect, coherent transfer of a quantum state over large distances. Here, we propose encoding and decoding procedures to recover perfectly from low rates of systematic errors. The encoding and decoding regions, located at opposite ends of the chain, are small compared to the length of the chain, growing linearly with the size of the error. We also describe how these errors can be identified, again by only acting on the encoding and decoding regions.
In the absence of errors, the dynamics of a spin chain, with a suitably engineered local Hamiltonian, allow the perfect, coherent transfer of a quantum state over large distances. Here, we propose encoding and decoding procedures to recover perfectly from low rates of systematic errors. The encoding and decoding regions, located at opposite ends of the chain, are small compared to the length of the chain, growing linearly with the size of the error. We also describe how these errors can be identified, again by only acting on the encoding and decoding regions.
We examine the speed and fidelity of several protocols for state or single excitation transfer in finite spin chains subject to diagonal and off-diagonal disorder. We find that, for a given chain length and maximal achievable interspin exchange (XY\mathit{XY}XY) coupling strength, the optimal static spin-coupling protocol, implementing the fastest state transfer between the two ends of the chain, is more susceptible to off-diagonal (XY\mathit{XY}XY coupling) disorder, as compared to a much slower but robust adiabatic transfer protocol with time-dependent coupling strengths.
We present an encoding technique that reduces the effects of noise on quantum spin systems whose operation is driven by Hamiltonian evolution. This technique is widely applicable, being most relevant to the scenarios where there are insufficient qubits to permit full-scale error correction. Instead, our technique can be implemented over small numbers of qubits and still leads to noticeable improvements in the fidelity of operations. The encoding scheme is easy to implement, flexible with respect to choice of Hamiltonian, and close to optimal.
The transmission of quantum states through spin chains is an important element in the implementation of quantum information technologies. Speed and fidelity of transfer are the main objectives which have to be achieved by the devices even in the presence of imperfections which are unavoidable in any manufacturing process. To reach these goals, several kinds of spin chains have been suggested, which differ in the degree of fine-tuning, or engineering, of the system parameters. In this work we present a systematic study of two important classes of such chains. In one class only the spin couplings at the ends of the chain have to be adjusted to a value different from the bulk coupling constant, while in the other class every coupling has to have a specific value. We demonstrate that configurations from the two different classes may perform similarly when subjected to the same kind of disorder in spite of the large difference in the engineering effort necessary to prepare the system. We identify the system features responsible for these similarities and we perform a detailed study of the transfer fidelity as a function of chain length and disorder strength, yielding empirical scaling laws for the fidelity which are similar for all kinds of chain and all disorder models. These results are helpful in identifying the optimal spin chain for a given quantum information transfer task. In particular, they help in judging whether it is worthwhile to engineer all couplings in the chain as compared to adjusting only the boundary couplings.