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Open Systems & Information Dynamics

Quantum Information Storage in the Localized State of a Spin Chain

Tony J. G. Apollaro, Francesco Plastina

Published Mar 1, 2007• 9 citations
Publisher

Abstract

We describe a chain of qubits with always on exchange interaction in the presence of a spatial inhomogeneity in the qubit level spacing. Similarly to the phenomenon of Anderson localization, this system has a localized eigenstate which can be used to store or trap quantum information. We discuss both the fidelity of storage and the leakage of information from this localized state and show that even a very small defect can be useful.

DOI
10.1007/s11080-007-9027-5

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We describe a chain of qubits with always on exchange interaction in the presence of a spatial inhomogeneity in the qubit level spacing. Similarly to the phenomenon of Anderson localization, this system has a localized eigenstate which can be used to store or trap quantum information. We discuss both the fidelity of storage and the leakage of information from this localized state and show that even a very small defect can be useful.
Anderson localisation is an important phenomenon arising in many areas of physics, and here we explore it in the context of quantum information devices. Finite dimensional spin chains have been demonstrated to be important devices for quantum information transport, and in particular can be engineered to allow for “perfect state transfer” (PST). Here we present extensive investigations of disordered PST spin chains, demonstrating spatial localisation and transport retardation effects, and relate these effects to conventional Anderson localisation. We provide thresholds for Anderson localisation in these finite quantum information systems for both the spatial and the transport domains. Finally, we consider the effect of disorder on the eigenstates and energy spectrum of our Hamiltonian, where results support our conclusions on the presence of Anderson localisation.
We show that, in a system with defects, two-particle states may experience destructive quantum interference, or antiresonance. It prevents an excitation localized on a defect from decaying even where the decay is allowed by energy conservation. The system studied is a qubit chain or an equivalent spin chain with an anisotropic (XXZ)(\mathrm{XXZ})(XXZ) exchange coupling in a magnetic field. The chain has a defect with an excess on-site energy. It corresponds to a qubit with the level spacing different from other qubits. We show that, because of the interaction between excitations, a single defect may lead to multiple localized states. The energy spectra and localization lengths are found for two-excitation states. The localization of excitations facilitates the operation of a quantum computer. Analytical results for strongly anisotropic coupling are confirmed by numerical studies.
We analyze localization of interacting excitations in a system of qubits or spins. The system is modeled by a spin chain with an anisotropic (XXZ) exchange coupling in a magnetic field. Localization occurs on a defect with an excess on-site spin-flip energy. Such a defect corresponds to a qubit with the level spacing different from other qubits. Because of the interaction, a single defect may lead to multiple localized states. We find energy spectra and localization lengths of the two-excitation states. An excitation remains localized on the defect even where energy conservation allows scattering into extended states. This is due to destructive quantum interference in the two-excitation scattering channels, and it facilitates the operation of a quantum computer. Analytical results are obtained for strong anisotropy and are confirmed by numerical studies.
Reliable quantum communication and/or processing links between modules are a necessary building block for various quantum processing architectures. Here we consider a spin-chain system with alternating strength couplings and containing three defects, which impose three domain walls between topologically distinct regions of the chain. We show that---in addition to its useful, high-fidelity, quantum state transfer properties---an entangling protocol can be implemented in this system, with optional localization and storage of the entangled states. We demonstrate both numerically and analytically that, given a suitable initial product-state injection, the natural dynamics of the system produces a maximally entangled state at a given time. We present detailed investigations of the effects of fabrication errors, analyzing random static disorder both in the diagonal and off-diagonal terms of the system Hamiltonian. Our results show that the entangled state formation is very robust against perturbations of up to $\ensuremath{\sim}10%$ the weaker chain coupling, and also robust against timing injection errors. We propose a further protocol, which manipulates the chain in order to localize and store each of the entangled qubits. The engineering of a system with such characteristics would thus provide a useful device for quantum information processing tasks involving the creation and storage of entangled resources.
Spin chains with symmetry-protected edge modes are promising candidates to realize intrinsically robust physical qubits that can be used for the storage and processing of quantum information. In any experimental realization of such physical systems, weak perturbations in the form of induced interactions and disorder are unavoidable and can be detrimental to the stored information. At the same time, the latter may in fact be beneficial; for instance, by deliberately inducing disorder which causes the system to localize. We explore the potential of using an XZX cluster Hamiltonian to encode quantum information into the local edge modes and comprehensively investigate the influence of both many-body interactions and disorder on their stability over time, adding substance to the narrative that many-body localization may stabilize quantum information. We recover the edge state at each time step, allowing us to reconstruct the quantum channel that captures the locally constrained out-of-equilibrium time evolution. With this representation in hand, we analyze how well classical and quantum information are preserved over time as a function of disorder and interactions. We find that the performance of the edge qubits varies dramatically between disorder realizations. Whereas some show a smooth decoherence over time, a sizable fraction is rapidly rendered unusable as memories. We also find that the stability of the classical information-a precursor for the usefulness of the chain as a quantum memory-depends strongly on the direction in which the bit is encoded. When employing the chain as a genuine quantum memory, encoded qubits are most faithfully recovered for low interaction and high disorder.
We propose a quantum-state transfer protocol in a spin chain that requires only the control of the spins at the ends of the quantum wire. The protocol is to a large extent insensitive to inhomogeneity caused by local magnetic fields and perturbation of exchange couplings. Moreover, apart from the free evolution regime, it allows one to induce an adiabatic spin transfer, which provides the possibility of performing the transfer on demand. We also show that the amount of information leaking into the central part of the chain is small throughout the whole transfer process (which protects the information sent from being eavesdropped) and can be controlled by the magnitude of the external magnetic field.