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arXiv:1610.02032 · Physical review. B./Physical review. B

Environmental noise effects on entanglement fidelity of exchange-coupled semiconductor spin qubits

Robert E. Throckmorton, Edwin Barnes, S. Das Sarma

Published Feb 6, 2017• 21 citations
arXivHTMLPDF

Abstract

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 $>99%$ fidelity consistent with the quantum error correction threshold.

DOI
10.1103/physrevb.95.085405

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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.
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.
Abstract The electron exchange interaction is a promising medium for the entanglement of single-spin qubits in semiconductors as it results in high-speed two-qubit gates. The quality of such entangling gates is reduced by the presence of noise caused by nearby defects acting as two-level fluctuators. To date, the effect of charge noise has been calculated assuming a Gaussian distribution of exchange interaction frequencies between the qubits equivalent to a linear coupling of charge noise with the exchange interaction. In reality the coupling can differ significantly from this linear-coupling approximation depending on the inter-qubit tunnel coupling, detuning of the qubit system, and the magnitude of charge noise. We derive analytical expressions for the frequency spectra of exchange oscillations that encompasses both linear and non-linear coupling to charge-noise. The resulting decoherence times and decay profiles of the exchange oscillations vary considerably. When compared with recent experiments our model shows that non-linear charge-noise coupling is significant and requires consideration to characterise and optimise exchange-based entangling gates.
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.
We determine the interqubit crosstalk- and charge-noise-induced decoherence time T2∗{T}_{2}^{*}T2∗​ for a system of LLL exchange-coupled electronic spin qubits in arrays of size L=3L=3L=3--14 for a number of different multiqubit geometries by directly calculating the return probability. We compare the behavior of the return probability to other quantities, namely, the average spin, the Hamming distance, and the entanglement entropy. In all cases, we use a starting state with alternating spins, $|{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}=|\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\cdots}\ensuremath{\rangle}$. We show that a power law behavior, ${T}_{2}^{*}\ensuremath{\propto}{L}^{\ensuremath{-}\ensuremath{\gamma}}$, is a good fit to the results for the chain and ring geometries as a function of the number of qubits and provide numerical results for the exponent $\ensuremath{\gamma}$. We find that T2∗{T}_{2}^{*}T2∗​ depends crucially on the multiqubit geometry of the system. We also calculate the expectation value of one of the spins, the Hamming distance, and the entanglement entropy and show that they are good proxies for the return probability for measuring T2∗{T}_{2}^{*}T2∗​. A key finding is that T2∗{T}_{2}^{*}T2∗​ decreases with increasing LLL. We also demonstrate that these results may be understood in terms of perturbation theory and its breakdown.
Quantum dot-based quantum computation employs extensively the exchange interaction between nearby electronic spins in order to manipulate and couple different qubits. The exchange interaction, however, couples the qubit states to charge noise, which reduces the fidelity of the quantum gates that employ it. The effect of charge noise can be mitigated by working at noise sweetspots in which the sensitivity to charge variations is reduced. In this work we study the response to charge noise of a double quantum dot based qubit in the presence of ac gates, with arbitrary driving amplitudes, applied either to the dot levels or to the tunneling barrier. Tuning with an ac driving allows to manipulate the sign and strength of the exchange interaction as well as its coupling to environmental electric noise. Moreover, we show the possibility of inducing a second-order sweetspot in the resonant spin-triplet qubit in which the dephasing time is significantly increased.