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arXiv:1301.0826 · Physical Review Letters

Noise-Resistant Control for a Spin Qubit Array

J. P. Kestner, Xin Wang, Lev S. Bishop, Edwin Barnes, S. Das Sarma

Published Apr 5, 2013• 102 citations
arXivHTMLPDF

Abstract

We develop a systematic method of performing corrected gate operations on an array of exchange-coupled singlet-triplet qubits in the presence of both fluctuating nuclear Overhauser field gradients and charge noise. The single-qubit control sequences we present have a simple form, are relatively short, and form the building blocks of a corrected cnot gate when also implemented on the interqubit exchange link. This is a key step towards enabling large-scale quantum computation in a semiconductor-based architecture by facilitating error reduction below the quantum error correction threshold for both single-qubit and multiqubit gate operations.

DOI
10.1103/physrevlett.110.140502

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We develop a systematic method of performing corrected gate operations on an array of exchange-coupled singlet-triplet qubits in the presence of both fluctuating nuclear Overhauser field gradients and charge noise. The single-qubit control sequences we present have a simple form, are relatively short, and form the building blocks of a corrected cnot gate when also implemented on the interqubit exchange link. This is a key step towards enabling large-scale quantum computation in a semiconductor-based architecture by facilitating error reduction below the quantum error correction threshold for both single-qubit and multiqubit gate operations.
In addition to magnetic field and electric charge noise adversely affecting spin-qubit operations, performing single-qubit gates on one of multiple coupled singlet-triplet qubits presents a new challenge: crosstalk, which is inevitable (and must be minimized) in any multiqubit quantum computing architecture. We develop a set of dynamically corrected pulse sequences that are designed to cancel the effects of both types of noise (i.e., field and charge) as well as crosstalk to leading order, and provide parameters for these corrected sequences for all 24 of the single-qubit Clifford gates. We then provide an estimate of the error as a function of the noise and capacitive coupling to compare the fidelity of our corrected gates to their uncorrected versions. Dynamical error correction protocols presented in this work are important for the next generation of singlet-triplet qubit devices where coupling among many qubits will become relevant.
We present a comprehensive theoretical treatment of supcode, a method for generating dynamically corrected quantum gate operations, which are immune to random noise in the environment, by using carefully designed sequences of soft pulses. supcode enables dynamical error suppression even when the control field is constrained to be positive and uniaxial, making it particularly suited to counteracting the effects of noise in systems subject to these constraints such as singlet-triplet qubits. We describe and explain in detail how to generate supcode pulse sequences for arbitrary single-qubit gates and provide several explicit examples of sequences that implement commonly used gates, including the single-qubit Clifford gates. We develop sequences for noise-resistant two-qubit gates for two exchange-coupled singlet-triplet qubits by cascading robust single-qubit gates, leading to a 35% reduction in gate time compared to previous works. This cascade approach can be scaled up to produce gates for an arbitrary-length spin qubit array and is thus relevant to scalable quantum computing architectures. To more accurately describe real spin qubit experiments, we show how to design sequences that incorporate additional features and practical constraints such as sample-specific charge noise models and finite pulse rise times. We provide a detailed analysis based on randomized benchmarking to show how supcode gates perform under realistic $1/{f}^{\ensuremath{\alpha}}$ noise and find a strong dependence of gate fidelity on the exponent $\ensuremath{\alpha}$, with best performance for $\ensuremath{\alpha}>1$. Our supcode sequences can therefore be used to implement robust universal quantum computation while accommodating the fundamental constraints and experimental realities of singlet-triplet qubits.
Abstract Capacitively coupled semiconductor spin qubits hold promise as the building blocks of a scalable quantum computing architecture with long-range coupling between distant qubits. However, the two-qubit gate fidelities achieved in experiments to date have been severely limited by decoherence originating from charge noise and hyperfine interactions with nuclear spins, and are currently unacceptably low for any conceivable multi-qubit gate operations. Here, we present control protocols that implement two-qubit entangling gates while substantially suppressing errors due to both types of noise. These protocols are obtained by making simple modifications to control sequences already used in the laboratory and should thus be easy enough for immediate experimental realisation. Together with existing control protocols for robust single-qubit gates, our results constitute an important step toward scalable quantum computation using spin qubits in semiconductor platforms.
Optimal control of qubits requires the ability to adapt continuously to their ever-changing environment. We demonstrate a real-time control protocol for a two-electron singlet-triplet qubit with two fluctuating Hamiltonian parameters. Our approach leverages single-shot readout classification and dynamic waveform generation, allowing full Hamiltonian estimation to dynamically stabilize and optimize the qubit performance. Powered by a field-programmable gate array (FPGA), the quantum control electronics estimates the Overhauser field gradient between the two electrons in real time, enabling controlled Overhauser-driven spin rotations and thus bypassing the need for micromagnets or nuclear polarization protocols. It also estimates the exchange interaction between the two electrons and adjusts their detuning, resulting in extended coherence of Hadamard rotations when correcting for fluctuations of both qubit axes. Our study highlights the role of feedback in enhancing the performance and stability of quantum devices affected by quasistatic noise.
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.
We present a scheme for correcting for crosstalk- and noise-induced errors in exchange-coupled singlet-triplet semiconductor double quantum dot qubits. While exchange coupling allows the coupling strength to be controlled independently of the intraqubit exchange couplings, there is also the problem of leakage, which must be addressed. We show that, if a large magnetic field difference is present between the two qubits, leakage is suppressed. We then develop pulse sequences that correct for crosstalk- and noise-induced errors and present parameters describing them for the 24 Clifford gates. We determine the infidelity for both the uncorrected and corrected gates as a function of the error-inducing terms and show that our corrected pulse sequences reduce the error by several orders of magnitude.