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arXiv:2405.15148 · Physical Review Applied

Dynamically corrected gates in silicon singlet-triplet spin qubits

Habitamu Y. Walelign, Xinxin Cai, Bikun Li, Edwin Barnes, John M. Nichol

Published Dec 10, 2024• 12 citations
arXivHTMLPDF

Abstract

Quantum computers are sensitive to sources of noise in their surroundings. In this work the authors design, implement, and demonstrate a technique that can overcome noise from the nuclei of the atoms hosting a semiconductor spin qubit. The team uses the geometrical properties of qubits to design noise-canceling control sequences and experimentally demonstrate high-fidelity quantum operations.

DOI
10.1103/physrevapplied.22.064029

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Quantum computers are sensitive to sources of noise in their surroundings. In this work the authors design, implement, and demonstrate a technique that can overcome noise from the nuclei of the atoms hosting a semiconductor spin qubit. The team uses the geometrical properties of qubits to design noise-canceling control sequences and experimentally demonstrate high-fidelity quantum operations.
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.
Dynamically corrected gates are extended to non-Markovian open quantum systems where limitations on the available controls and/or the presence of control noise make existing analytical approaches unfeasible. A computational framework for the synthesis of dynamically corrected gates is formalized that allows sensitivity against non-Markovian decoherence and control errors to be perturbatively minimized via numerical search, resulting in robust gate implementations. Explicit sequences for achieving universal high-fidelity control in a singlet-triplet spin qubit subject to realistic system and control constraint are provided, which simultaneously cancel to the leading order the dephasing due to non-Markovian nuclear-bath dynamics and voltage noise affecting the control fields. Substantially improved gate fidelities are predicted for current laboratory devices.
There is a huge, worldwide effort to build a quantum computer due to its potential to perform chemical and materials simulations and to break current cryptography schemes. While there has been incredible progress in recent years, each potential platform still faces meaningful obstacles. The singlet-triplet qubit in gallium arsenide, which is based on electric spin, boasts several advantages, including fast single-gate times and readout, long lifetimes, and a clear path to large-scale integration using current semiconductor manufacturing techniques. However, it also suffers from electric and magnetic field noise that limits coherence time and weak two-qubit interactions, which have prevented the construction of multi-qubit systems so far. In this thesis, I will discuss my research measuring and working to improve noise and entangling gates in singlet-triplet qubits and will examine the viability of the singlet-triplet qubit as the building block for a quantum computer. \nBy measuring the dynamics of the electric and magnetic field noise that the singlet-triplet experiences, we can develop an understanding of their origins and how to reduce their impact. The singlet-triplet can be operated rapidly enough to use it as a sensor and directly measure the fluctuating magnetic field arising from the nuclear spins in the semiconductor heterostructure surrounding it. We use Hamiltonian parameter estimation, a technique that maximizes the rate at which we learn information, given the strange properties of quantum measurement, to measure magnetic noise to within 15 μT at a rate of 2 kHz, and we use these measurements to provide real-time feedback to system controls, increasing the coherence time by a factor of 30. Charge noise has much larger high-frequency components than magnetic noise, and thus requires use of dynamical decoupling methods borrowed from NMR to measure it. We measure its power spectrum up to 1 MHz and find that it has a 1/f spectrum. We perform these measurements for several different devices and have begun to determine how our growth and fabrication processes affect dephasing. \nPlacing a high-impedance resonator between two singlet-triplet qubits to mediate their interaction shows promise as way to create long-distance entanglement and to increase the speed of the entangling gate. We analyze this gate theoretically, finding that we expect the fidelity to be over 95%, with a straightforward path to increasing it to above 99% with improved resonator parameters. However, because the singlet-triplet qubit is extremely sensitive to changes in its electrostatic environment, which can be affected both by the resonator’s fabrication process and the presence of the proximal resonator gate, implementing this gate experimentally is challenging. We have developed processes for fabricating narrow, thin, NbN resonators directly adjacent to the double quantum dots that compose singlet-triplet qubits. These processes yield quantum dots that can be tuned into low-noise, stable singlet-triplet qubits, and superconducting resonators with impedances over 1 kOhm.
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.
Nuclear spin qubits in silicon are well-isolated from their environment. Consequently, they have very long lifetimes and low sensitivity to noise, but this also suggests that control and measurement is challenging. We introduce electron pair interferometry (EPI), a protocol to overcome this challenge and maintain robustness to noise. EPI is implemented using an array of quantum dots with isoelectronic nuclear spin qubits located in the dots. A pair of electrons are initialized into a singlet ground state, split apart, and shuttled to the dots containing nuclear spin qubits. We show it is possible to coherently transfer the parity of the nuclei onto the measurable state of singlet/triplet-encoded electrons. Global nuclear magnetic resonance (NMR) can be used to change bases and implement dynamical decoupling (DD). Combined with selective hyperfine-induced ZπZ_πZπ​ rotations, our gate set is complete for universal quantum computation, tailored to Calderbank-Shor-Steane (CSS) quantum error correction, and robust to noise. We discuss very low sensitivity to charge noise and study the sensitivity to both DC and AC magnetic field inhomogeneity which depends strongly on their relative strengths.