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arXiv:1901.00851 · Physical review. B./Physical review. B

High-fidelity gate set for exchange-coupled singlet-triplet qubits

Pascal Cerfontaine, René Otten, M. A. Wolfe, Patrick Bethke, Hendrik Bluhm

Published Apr 28, 2020• 27 citations
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Abstract

In order to enable semiconductor-based quantum computing with many qubits, issues like residual interqubit coupling and constraints from scalable control hardware need to be tackled to retain the high gate fidelities demonstrated in current single-qubit devices. Here we focus on two exchange-coupled singlet-triplet spin qubits, considering realistic control hardware as well as Coulomb and exchange coupling that cannot be fully turned off. Using measured noise spectra, we optimize realistic control pulses and show that two-qubit (single-qubit) gate fidelities of 99.90% ($\ensuremath{\ge}99.69%$) can be reached in GaAs, while 99.99% ($\ensuremath{\ge}99.95%$) can be achieved in Si.

DOI
10.1103/physrevb.101.155311

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A key ingredient for fault-tolerant quantum computers are sufficiently accurate logic gates on single and multiple qubits in the presence of decohering noise. In this thesis, we theoretically develop and experimentally demonstrate such high-fidelity quantum gates for semiconductor-based quantum computing. Specifically, we consider a qubit encoded in the singlet and one triplet state of two electron spins in GaAs. While its potential for optical coupling makes GaAs an attractive material, highly auto-correlated magnetic field noise from fluctuating nuclear spins leads to considerably lower coherence times than for Si-based devices, where nuclear spins can be removed by isotopic purification. In addition to noise, the control methods used in earlier experiments are based on unrealistic approximations. For these reasons, fidelities well above 99 %, as required by current quantum error correction (QEC) schemes, have not been obtained before this thesis. To tackle these issues, we extend the filter function formalism to describe quantum gates and processes in the presence of experimentally relevant non-Markovian noise. Since this formalism can consider all relevant noise sources in a computationally efficient manner, it can be used to find optimal control pulses by numerical optimization, leading to predicted single-qubit gate fidelities of 99.9 %. Furthermore, we deal with the considerable control challenges associated with this qubit type by experimental calibration of the optimized control pulses. To this end, we extend our previous experimental gate set calibration (GSC) routine to remove systematic gate errors on an arbitrary number of qubits. We apply the numerically optimized single-qubit control pulses to our GaAs sample and experimentally calibrate them with GSC. This procedure yields an average gate fidelity of 99.50 ± 0.04 % and a low leakage rate of 0.13 ± 0.03 % out of the computational subspace, characterized by randomized benchmarking. We also optimize realistic two-qubit control pulses, considering current control hardware as well as interqubit Coulomb and exchange coupling that cannot be fully turned off. Using measured noise spectra, we show that two-qubit gate fidelities of 99.90 % can be reached in GaAs, while 99.99 % can be achieved in Si. These results demonstrate that high-fidelity gates can be realized even in the presence of nuclear spins as in GaAs.
Several logical qubits and quantum gates have been proposed for semiconductor quantum dots controlled by voltages applied to top gates. The different schemes can be difficult to compare meaningfully. Here we develop a theoretical framework to evaluate disparate qubit-gating schemes on an equal footing. We apply the procedure to two types of double-dot qubits: the singlet-triplet and the semiconducting quantum dot hybrid qubit. We investigate three quantum gates that flip the qubit state: a DC pulsed gate, an AC gate based on logical qubit resonance, and a gate-like process known as stimulated Raman adiabatic passage. These gates are all mediated by an exchange interaction that is controlled experimentally using the interdot tunnel coupling g and the detuning [Symbol: see text], which sets the energy difference between the dots. Our procedure has two steps. First, we optimize the gate fidelity (f) for fixed g as a function of the other control parameters; this yields an f(opt)(g) that is universal for different types of gates. Next, we identify physical constraints on the control parameters; this yields an upper bound f(max) that is specific to the qubit-gate combination. We show that similar gate fidelities (~99:5%) should be attainable for singlet-triplet qubits in isotopically purified Si, and for hybrid qubits in natural Si. Considerably lower fidelities are obtained for GaAs devices, due to the fluctuating magnetic fields ΔB produced by nuclear spins.
Single-qubit operations on singlet-triplet qubits in GaAs double quantum dots have not yet reached the fidelities required for fault-tolerant quantum information processing. Considering experimentally important constraints and using measured noise spectra, we numerically minimize the effect of decoherence (including high-frequency 1/f-like noise) and show, theoretically, that quantum gates with fidelities higher than 99.9% are achievable. We also present a self-consistent tuning protocol which should allow the elimination of individual systematic gate errors directly in an experiment.
Singlet-triplet qubits in lateral quantum dots in semiconductor heterostructures exhibit high-fidelity single-qubit gates via exchange interactions and magnetic field gradients. High-fidelity two-qubit entangling gates are challenging to generate since weak interqubit interactions result in slow gates that accumulate error in the presence of noise. However, the interqubit electrostatic interaction also produces a shift in the local double well detunings, effectively changing the dependence of exchange on the gate voltages. We consider an operating point where the effective exchange is first-order insensitive to charge fluctuations while maintaining nonzero interactions. This ``sweet spot'' exists only in the presence of interactions. We show that working at the interacting sweet spot can directly produce maximally entangling gates, and we simulate the gate evolution under realistic 1/f1/f1/f noise. We report theoretical two-qubit gate fidelities above 99% in GaAs and Si systems.
We analyze a simple exchange-based two-qubit gate for singlet-triplet qubits in gate-defined semiconductor quantum dots that can be implemented in a single exchange pulse. Excitations from the logical subspace are suppressed by a magnetic field gradient that causes spin-flip transitions to be non-energy-conserving. We show that the use of adiabatic pulses greatly reduces leakage processes comapred to square pulses. We also characterize the effect of charge noise on the entanglement fidelity of the gate both analytically and in simulations; demonstrating high entanglement fidelities for physically realistic experimental parameters. Specifically we find that it is possible to achieve fidelities and gate times that are comparable to single-qubit states using realistic magnetic field gradients.
We propose methods to mitigate single- and two-qubit control errors due to residual exchange coupling in systems of exchange-coupled resonant singlet-triplet qubits. Commensurate driving, where the pulse length is an integer multiple of the drive period, can mitigate errors from residual intra-qubit exchange, including effects from counter rotating terms and off-axis rotations, as well as leakage errors during two-qubit operations. Residual inter-qubit exchange creates crosstalk errors that reduce single-qubit control fidelities. We show that using a single-spin coupler between two resonant singlet-triplet qubits can reduce this crosstalk error by an order of magnitude. Assuming perfect coupler state preparation and realistic charge and hyperfine noise, we predict that coupler-assisted two-qubit gate errors can be below 3×10−33\times10^{-3}3×10−3 for gate times as short as 66 ns66~\text{ns}66 ns, even in the presence of residual exchange levels exceeding several hundred kHz. Our results suggest the potential of utilizing coupler-based architectures for large scale fault-tolerant spin qubit processors based on resonant singlet-triplet qubits.