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

Abstract

Qubit arrays with access to high-fidelity single-and two-qubit gates are a key ingredient for building a quantum computer. As semiconductor-based devices with several qubits become available, issues like residual interqubit coupling and additional constraints from scalable control hardware need to be tackled to retain the high gate fidelities demonstrated in single-qubit devices. Focusing on two exchange-coupled singlet-triplet spin qubits, we address these issues by considering realistic control hardware as well as Coulomb and interqubit exchange coupling that cannot be fully turned off. We use measured noise spectra for charge and magnetic field noise to numerically optimize experimentally realistic pulse sequences and show that two-qubit (single-qubit) gate fidelities of 99.90% (≥ 99.69%) can be reached in GaAs, while 99.99% (≥ 99.95%) can be achieved with vanishing magnetic field noise as in Si.

Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory

“…This milestone-making a 1D array which realizes the repetition code and demonstrating that the logical error decreases with increasing code distance-has been reached for superconducting devices in [2]. While challenging, we will show that such a device would be currently experimentally feasible for singlet-triplet qubits, even in GaAs, in terms of fabrication and operation, assuming the two-qubit device performance as investigated by [13], without the need for additional elements. We show this by numerically running decoders on repeated error-correcting cycles of the phase-flip code, subject to phenomenological and circuit-level noise, as well as realistic device-specific noise, which we simulate using full-density-matrix simulations.…”

“…In the other extreme, very high coherence times are limited by the gate noise induced by the gates that are employed for the echoing pulses themselves. Two-qubit gates are the focus of the current research effort and recent results of accurately modeling the two-qubit operation analogous to the single-qubit case suggest operability at the same high fidelities as the single-qubit gates [13].…”

“…For gate operations, one typically moves to smaller detuning. The gates done in [13], which will be explained in the subsequent section, assume an incoming small detuning baseline at the start of the pulse sequence in order to deal with pulse transients caused by the finite bandwidth of the voltage pulses used for qubit control (for details see [13]). In order to reach this qubit operation point after the singlet initialization, one can adiabatically decrease the detuning, such that the singlet hybridizes with the triplet state |T 0 = 1 √ 2 (|↑↓ + |↓↑ ) into the state |↑↓ = |0 (or, respectively, |↓↑ depending on the direction of the magnetic field gradient).…”

“…Note that we only describe the dynamics of the dots involved in the respective quantum gate, which implicitly assumes negligible cross-talk to other qubits, i.e., we can execute gates in parallel on disjoint sets of qubits. Finding optimal pulse sequences is a challenging optimization problem; we refer the reader to [13], where the average gate fidelity was used as the target function of a numerical optimization routine in order to find good composite pulse sequences for single-and two-qubit gates. The gate unitary coming out of such a pulse sequence is given by the timeevolution operator over a time duration, namely, the gate execution time t gate , which is divided into N intervals of length t. During each individual interval the couplings are kept approximately constant, such that the total time-evolution operator is of the form…”

“…Detailed two-qubit gate simulations [13] predict very low leakage rates (≈10 −4 ), which is why we focus on control noise errors in the present paper, deferring leakage to Sec. IV F, where we explain how leakage can be incorporated into error correction via leakage reduction.…”