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arXiv:1604.06110 · Physical review. B./Physical review. B

Dynamics of two coupled semiconductor spin qubits in a noisy environment

S. Das Sarma, Robert E. Throckmorton, Yang-Le Wu

Published Jul 27, 2016• 11 citations
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Abstract

We theoretically consider the temporal dynamics of two coupled spin qubits (e.g., semiconductor quantum dots) driven by the interqubit spin-spin coupling. The presence of environmental noise (e.g., charge traps, nuclear spins, random magnetic impurities) is accounted for by including random magnetic field and random interqubit coupling terms in the Hamiltonian. Both Heisenberg coupling and Ising coupling between the spin qubits are considered, corresponding respectively to exchange and capacitive gates as appropriate for single spin and singlet-triplet semiconductor qubit systems, respectively. Both exchange (Heisenberg) and capacitive (Ising) coupling situations can be solved numerically exactly even in the presence of noise, leading to the key findings that (i) the steady-state return probability to the initial state remains close to unity in the presence of strong noise for many, but not all, starting spin configurations, and (ii) the return probability as a function of time is oscillatory with a characteristic noise-controlled decay toward the steady-state value. We also provide results for the magnetization dynamics of the coupled two-qubit system. Our predicted dynamics can be directly tested in the already existing semiconductor spin qubit setups providing insight into their coherent interaction dynamics. Retention of the initial state spin memory even in the presence of strong environmental noise has important implications for quantum computation using spin qubits.

DOI
10.1103/physrevb.94.045435

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We theoretically consider the temporal dynamics of two coupled spin qubits (e.g., semiconductor quantum dots) driven by the interqubit spin-spin coupling. The presence of environmental noise (e.g., charge traps, nuclear spins, random magnetic impurities) is accounted for by including random magnetic field and random interqubit coupling terms in the Hamiltonian. Both Heisenberg coupling and Ising coupling between the spin qubits are considered, corresponding respectively to exchange and capacitive gates as appropriate for single spin and singlet-triplet semiconductor qubit systems, respectively. Both exchange (Heisenberg) and capacitive (Ising) coupling situations can be solved numerically exactly even in the presence of noise, leading to the key findings that (i) the steady-state return probability to the initial state remains close to unity in the presence of strong noise for many, but not all, starting spin configurations, and (ii) the return probability as a function of time is oscillatory with a characteristic noise-controlled decay toward the steady-state value. We also provide results for the magnetization dynamics of the coupled two-qubit system. Our predicted dynamics can be directly tested in the already existing semiconductor spin qubit setups providing insight into their coherent interaction dynamics. Retention of the initial state spin memory even in the presence of strong environmental noise has important implications for quantum computation using spin qubits.
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.
We investigate the effect of magnetic field and charge noise on the generation of entanglement between two Heisenberg exchange-coupled electron spins in a double quantum dot. We focus on exchange-driven evolution that would ideally take an initial unentangled tensor product state to a maximally entangled state in the absence of noise. The presence of noise obviously adversely affects the attainment of maximal entanglement, which we study quantitatively and exactly. To quantify the effects of noise, we calculate two-qubit coherence times and entanglement fidelity, both of which can be extracted from simulations or measurements of the return probability as a function of interaction time, i.e., the time period during which the exchange coupling remains effective between the two spins. We perform these calculations for a broad range of noise strengths that includes the regime of recent experiments. We find that the two types of noise reduce the amount of entanglement in qualitatively distinct ways and that, although charge noise generally leads to faster decoherence, the relative importance of the two types of noise in entanglement creation depends sensitively on the strength of the exchange coupling. Our results can be used to determine the level of noise suppression needed to reach quantum error correction thresholds. We provide quantitative guidance for the requisite noise constraints necessary to eventually reach the >99>99%>99 fidelity consistent with the quantum error correction threshold.
This study presents a numerical investigation of the dynamics of two coupled spin-1/2 quantum systems with emphasis on entanglement, quantum coherence, and state fidelity. The system is described by an isotropic Heisenberg Hamiltonian and investigated for exchange-coupling strengths J=−1, −0.5, 0, 0.5, and 11. Four representative initial states, comprising the Bell state, a partially entangled state with initial concurrence C (0) =0.8, and the separable states ∣01⟩and ∣++⟩are considered. Closed-system evolution is obtained using the unitary propagator, while environmental effects are modelled through a Lindblad master equation with local Markovian pure-dephasing channels for γ=0,0.1,0.5, and 11. The results show that the Bell state maintains maximal concurrence under closed Heisenberg evolution, while the partially entangled state retains its initial concurrence of 0.8 for all tested exchange couplings. In contrast, the initially separable ∣01⟩state develops strong transient entanglement through exchange interaction, reaching concurrence values essentially equal to unity for ∣J∣=0.5 and 11, whereas the ∣++⟩state remains separable to numerical precision. Under pure dephasing, concurrence and coherence decay progressively with increasing dephasing strength, while fidelity decreases toward its asymptotic value. The numerical calculations were further validated through normalization and Hermiticity checks, analytical dephasing benchmarks, and step-refinement convergence tests, with discrepancies remaining at machine-precision levels. The findings demonstrate that the preservation and generation of quantum correlations depend strongly on the initial state, exchange interaction, and environmental decoherence, providing validated numerical benchmarks for the study of coupled qubit dynamics.
Recent work on Ising-coupled double-quantum-dot spin qubits in GaAs with voltage-controlled exchange interaction has shown improved two-qubit gate fidelities from the application of oscillating exchange along with a strong magnetic field gradient between adjacent dots [npj Quantum Inf. 3, 3 (2017)]. By examining how noise propagates in the time-evolution operator of the system, we find an optimal set of parameters that provide passive stroboscopic circumvention of errors in two-qubit gates to first order. We predict over 99% two-qubit gate fidelities in the presence of quasistatic and 1/f1/f1/f noise, which is an order-of-magnitude improvement over the typical unoptimized implementation.
The spin of an electron confined in semiconductor quantum dots is currently a promising candidate for quantum bit (qubit) implementations. Taking advantage of the existing CMOS integration technologies, such devices can offer a platform for large scale quantum computation. However, a quantum mechanical framework bridging a device's physical design and operational parameters to the qubit's energy space is lacking. Furthermore, the spin to charge coupling introduced by intrinsic or induced spin-orbit interaction (SOI) exposes the qubits to charge noise compromising their coherence properties and inducing quantum gate errors. We present here a comodeling framework for double quantum dot (DQD) devices and their charge noise environments. We use a combination of an electrostatic potential solver, full configuration interaction quantum mechanical methods, and two-level-fluctuator models to study the quantum gate performance in realistic device designs and operation conditions. We utilize the developed models together alongside the single electron solutions of the quantum dots to simulate one- and two-qubit gates in the presence of charge noise. We find an inverse correlation between quantum gate errors and quantum dot confinement frequencies. We calculate X-gate fidelities >97>97%>97 in the simulated Si-MOS devices at a typical TLF density of ${10}^{11}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. We also find that exchange driven two-qubit SWAP gates show higher sensitivity to charge noise with fidelities down to 9191%91 in the presence of the same density of TLFs. We further investigate the one- and two-qubit gate fidelities at different TLF densities. We find that given the small size of the quantum dots, sensitivity of a quantum gate to the distance between the noise sources and the quantum dot creates a strong variability in the quantum gate fidelities, which can compromise the device yields in scaled qubit technologies.