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arXiv:1501.02133 · New Journal of Physics

Optimized dynamical control of state transfer through noisy spin chains

Analía Zwick, Gonzalo A. Álvarez, Guy Bensky, Gershon Kurizki

Published Jun 26, 2014• 52 citations
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Abstract

We propose a method of optimally controlling the tradeoff of speed and fidelity of state transfer through a noisy quantum channel (spin-chain). This process is treated as qubit state-transfer through a fermionic bath. We show that dynamical modulation of the boundary-qubits levels can ensure state transfer with the best tradeoff of speed and fidelity. This is achievable by dynamically optimizing the transmission spectrum of the channel. The resulting optimal control is robust against both static and fluctuating noise in the channelʼs spin–spin couplings. It may also facilitate transfer in the presence of diagonal disorder (on site energy noise) in the channel.

DOI
10.1088/1367-2630/16/6/065021

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We propose a method of optimally controlling the tradeoff of speed and fidelity of state transfer through a noisy quantum channel (spin-chain). This process is treated as qubit state-transfer through a fermionic bath. We show that dynamical modulation of the boundary-qubits levels can ensure state transfer with the best tradeoff of speed and fidelity. This is achievable by dynamically optimizing the transmission spectrum of the channel. The resulting optimal control is robust against both static and fluctuating noise in the channelʼs spin–spin couplings. It may also facilitate transfer in the presence of diagonal disorder (on site energy noise) in the channel.
Existing optimal control methods of open quantum systems rely on extensive numerical simulations of the dynamics in the presence of a bath, or alternatively ignore the exact bath dynamics. If the bath effects are to be treated properly on both Markovian and non-Markovian timescales using numerical simulations, the number of bath modes cannot be large. This may affect the ability to simulate realistic scenarios. Even if realistic, such simulations are hard to interpret physically. An alternative approach advocated here is to resort to a perturbative analysis provided the system–bath coupling is weak. This analysis would allow for the effects of any given bath (finite or infinite, Markovian or non-Markovian) and any control at our disposal. This poses the challenge of constructing a method for the optimization of various operations requiring proper manipulation of the system, based on a general perturbative treatment to second order in the system–bath coupling. This proposed treatment yields a universal tool for optimizing the fidelity of a given operation. It involves a fidelity-control matrix: a construct that allows us to prioritize the use of available control resources so as to maximize the operation fidelity in any given bath. As an analytically solvable example of this general method, we analyse quantum state-transfer optimization, from a ‘noisy’ (write-in) qubit to its ‘quiet’ counterpart (storage qubit). Intriguing interplay is revealed between our ability to avoid bath-induced errors that profoundly depend on the bath-memory time and the limitations imposed by leakage out of the operational subspace. Counterintuitively, under no circumstances is the fastest transfer optimal (for a given transfer energy).
Quantum state transfer in the presence of static disorder and noise is one of the main challenges in building quantum computers. We compare the quantum state transfer properties for two classes of qubit chains under the influence of static disorder. In fully engineered chains all nearest-neighbor couplings are tuned in such a way that a single-qubit state can be transferred perfectly between the ends of the chain, while in chains with modified boundaries only the two couplings between the transmitting and receiving qubits and the remainder of the chain can be optimized. We study how the disorder in the couplings affects the state transfer fidelity depending on the disorder model and strength as well as the chain type and length. We show that the desired level of fidelity and transfer time are important factors in designing a chain. In particular we demonstrate that transfer efficiency comparable or better than that of the most robust engineered systems can also be reached in chains with modified boundaries without the demanding engineering of a large number of couplings.
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 a hybrid variational framework for quantum optimal control aimed at high-fidelity state transfer in spin chains. The system dynamics are discretized and compiled into a parameterized circuit, where deterministic two-qubit blocks implement the drift interactions, while trainable on-site RZ rotations encode the control inputs. We study two parameterizations: a compact global scheme with a small number of shared parameters per slice, and a local scheme with site-wise angles. Using a Sequential Least Squares Quadratic Programming (SLSQP) optimization to minimize infidelity, simulations on XXZ spin chains show that both parameterizations can achieve near-unit fidelities in the noiseless regime. Under depolarizing noise, the global scheme provides improved robustness for comparable circuit depth and iteration budgets. The results make explicit an expressivity-stability trade-off and suggest a scalable route to Noisy Intermediate-Scale Quantum (NISQ) compatible control synthesis.
Spin chains have been widely studied as quantum channels for short-distance communication in quantum devices, where many-body dynamics can mediate quantum-state transfer between distant sites. In finite unmodulated chains, however, dispersion and interference effects associated with the static Hamiltonian often limit the achievable transfer fidelity. Here we investigate the transfer of single-qubit and Bell states in finite XXXXXX spin chains under periodic switching between two Hamiltonians with different boundary couplings. Inspired by Parrondo's paradox, we examine whether alternating between two configurations that individually yield suboptimal transfer fidelities can generate enhanced coherent transmission. Using Floquet theory together with numerical simulations in the single-excitation subspace, we show that periodic driving can outperform static configurations and achieve higher transfer fidelities. This enhancement originates from the noncommutativity of the driven Hamiltonians and reflects a purely coherent interference effect. We further analyze the dependence of the protocol on system size and driving parameters and examine its robustness to asymmetric boundary couplings. Our results show that the transfer fidelity remains stable under moderate disorder, indicating that simple time-dependent control of boundary couplings provides an effective strategy to enhance quantum-state transfer in spin-chain communication channels and optimize quantum information processing in engineered many-body systems.