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arXiv:1005.2571 · Physical Review A

Spin-state transfer in laterally coupled quantum-dot chains with disorders

Song Yang, Abolfazl Bayat, Sougato Bose

Published Aug 31, 2010• 36 citations
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Abstract

Quantum dot arrays are a promising medium for transferring quantum information between two distant points without resorting to mobile qubits. Here we study the two most common disorders, namely hyperfine interaction and exchange coupling fluctuations, in quantum dot arrays and their effects on quantum communication through these chains. Our results show that the hyperfine interaction is more destructive than the exchange coupling fluctuations. The average optimal time for communication is not affected by any disorder in the system and our simulations show that antiferromagnetic chains are much more resistive than the ferromagnetic ones against both kind of disorders. Even when time modulation of a coupling and optimal control is employed to improve the transmission, the antiferromagnetic chain performs much better. We have assumed the quasistatic approximation for hyperfine interaction and time-dependent fluctuations in the exchange couplings. Particularly for studying exchange coupling fluctuations we have considered the static disorder, white noise, and $1/f$ noise.

DOI
10.1103/physreva.82.022336

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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.
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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.
Recent work has demonstrated a new route to discrete time crystal physics in quantum spin chains by periodically driving nearest-neighbor exchange interactions in gate-defined quantum dot arrays [H. Qiao et al., Nat. Commun. 12, 2142 (2021)]. Here, we present a detailed analysis of exchange-driven Floquet physics in small arrays of GaAs quantum dots, including phase diagrams and additional diagnostics. We also show that emergent time-crystalline behavior can benefit the protection and manipulation of multispin states. For typical levels of nuclear spin noise in GaAs, the combination of driving and interactions increases the coherence times of entangled states by orders of magnitude. Similar results can be obtained for other quantum dot systems such as in Si. We further show how to construct a time-crystal-inspired cz gate between singlet-triplet qubits with high fidelity. These results show that periodically driving exchange couplings can enhance the performance of quantum dot spin systems for quantum information applications.
Charge noise remains the primary obstacle to the development of quantum information technologies with semiconductor spin qubits. We use an exact analytical calculation to determine the effects of quasistatic charge noise on a ring of three equally spaced exchange-coupled quantum dots. We calculate the disorder-averaged return probability from a specific initial state and use it to determine the coherence time T2∗{T}_{2}^{*}T2∗​ and show that it depends on only the disorder strength and not the mean interaction strength. We also use a perturbative approach to investigate other arrangements of three or four qubits, finding that the return probability contains multiple oscillation frequencies. These oscillations decay in a Gaussian manner, determined by differences in energy levels of the Hamiltonian. We give quantitative values for gate times resulting in several target fidelities. We find that the decoherence time decreases with an increasing number of qubits. Our work provides useful analytical insight into the charge noise dynamics of coupled spin qubits.