Full-Permutation Dynamical Decoupling in Triple-Quantum-Dot Spin Qubits
Bo Sun, T. Brecht, Bryan H. Fong, Moonmoon Akmal, Jacob Blumoff, Tyler A. Cain, Faustin W. Carter, Dylan H. Finestone, Micha N. Fireman, Wonill Ha, Anthony T. Hatke, Ryan M. Hickey, Clayton A. C. Jackson, Ian D. Jenkins, Aaron M. Jones, Andrew Pan, Daniel R. Ward, Aaron Weinstein, Samuel J. Whiteley, Parker J. Williams, Matthew Borselli, Matthew T. Rakher, Thaddeus D. Ladd
Dynamical decoupling of spin qubits in silicon can increase fidelity and can be used to extract the frequency spectra of noise processes. We demonstrate a full-permutation dynamical decoupling technique that cyclically exchanges the spins in a triple-quantum-dot qubit. This sequence not only suppresses both low-frequency charge-noise-induced and magnetic-noise-induced errors; it also refocuses leakage errors to first order, which is particularly interesting for encoded exchange-only qubits. For a specific construction, which we call “NZ1y,” the qubit is isolated from error sources to such a degree that we measure a remarkable exchange pulse error of 2.8×10−5 . This sequence maintains a quantum state for roughly 18,000 exchange pulses, extending the qubit coherence from T2∗=2μs to T2=720μs . We experimentally validate an error model that includes 1/f charge noise and 1/f magnetic noise in two ways: by direct exchange-qubit simulation and by integration of the assumed noise spectra with derived filter functions, both of which reproduce the measured error and leakage with respect to a change of the repetition rate. Published by the American Physical Society 2024
Dynamical decoupling of spin qubits in silicon can increase fidelity and can be used to extract the frequency spectra of noise processes. We demonstrate a full-permutation dynamical decoupling technique that cyclically exchanges the spins in a triple-quantum-dot qubit. This sequence not only suppresses both low-frequency charge-noise-induced and magnetic-noise-induced errors; it also refocuses leakage errors to first order, which is particularly interesting for encoded exchange-only qubits. For a specific construction, which we call “NZ1y,” the qubit is isolated from error sources to such a degree that we measure a remarkable exchange pulse error of 2.8×10−5 . This sequence maintains a quantum state for roughly 18,000 exchange pulses, extending the qubit coherence from T2∗=2μs to T2=720μs . We experimentally validate an error model that includes 1/f charge noise and 1/f magnetic noise in two ways: by direct exchange-qubit simulation and by integration of the assumed noise spectra with derived filter functions, both of which reproduce the measured error and leakage with respect to a change of the repetition rate. Published by the American Physical Society 2024
We provide analytical composite pulse sequences that perform dynamical decoupling concurrently with arbitrary rotations for a qubit coded in the spin state of a triple quantum dot. The sequences are designed to respect realistic experimental constraints such as strictly nonnegative couplings. Logical errors and leakage errors are simultaneously corrected. A short pulse sequence is presented to compensate nuclear noise and a longer sequence is presented to simultaneously compensate nuclear and charge noise. The capability developed in this work provides a clear prescription for combatting the relevant sources of noise that currently hinder exchange-only qubit experiments.
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 Zπ 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.
The resonant exchange (RX) qubit is a promising variant of the exchange-only spin qubit in a triple quantum dot which responds to a narrow-band resonant frequency. But the advantage of a permanently applied exchange splitting for spin control generally entails an increased susceptibility to charge noise. We have investigated the influence of electrical charge noise on a resonant exchange (RX) qubit by taking into account uncorrelated noise in each quantum dot, giving rise to two independent noisy bias parameters e and ∆ [1]. Calculating the energy splitting of the two qubit states as a function of these two bias detuning parameters, we have identified sweet spots, where the qubit is least susceptible to noise. Our investigation shows that the sweet spots exist within the low-bias regime, in which the bias detuning parameters have the same magnitude as the hopping parameters between the dots. By calculating and comparing the charge dephasing rates at the various operating points of the RX qubit, we identify a new favorable operating regime for the RX qubit in the case of weak noise, based on these double sweet spots. In contrast, spin noise can be mitigated using exchange-based dynamical decoupling sequences that have been optimized using two different strategies, Uhrig dynamical decoupling (UDD) and optimized filter function dynamical decoupling (OFDD) [2]. Finally, we give a brief outlook towards the possibility of long-distance coupling between resonant exchange qubits mediated by a microwave cavity [3]. [1] M. Russ and G. Burkard, Phys. Rev. B 91, 235411 (2015). [2] N. Rohling and G. Burkard, arXiv:1510.04098. [3] M. Russ and G. Burkard, Phys. Rev. B (accepted) [arXiv:1508.07122].
Semiconductor quantum dot spin qubits are promising candidates for quantum computing. In these systems, the dynamically corrected gates offer considerable reduction of gate errors and are therefore of great interest both theoretically and experimentally. They are, however, designed under the static-noise model and may be considered as low-frequency filters. In this work, we perform a comprehensive theoretical study of the response of a type of dynamically corrected gates, namely the supcode for singlet-triplet qubits, to realistic 1/f noises with frequency spectra 1/ω(α). Through randomized benchmarking, we have found that supcode offers improvement of the gate fidelity for α 1 and the improvement becomes exponentially more pronounced with the increase of the noise exponent in the range 1 α ≤ 3 studied. On the other hand, for small α, supcode will not offer any improvement. The δJ-supcode, specifically designed for systems where the nuclear noise is absent, is found to offer additional error reduction than the full supcode for charge noises. The computed filter transfer functions of the supcode gates are also presented.
A triple-quantum-dot system can be operated as either an exchange-only qubit or a resonant-exchange qubit. While it is generally believed that the decisive advantage of the resonant-exchange qubit is the suppression of charge noise because it is operated at a sweet spot, we show that the leakage is also an important factor. Through molecular-orbital-theoretic calculations, we show that when the system is operated in the exchange-only scheme, the leakage to states with double electron occupancy in quantum dots is severe when rotations around the axis ${120}^{\ensuremath{\circ}}$ from $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ is performed. While this leakage can be reduced by either shrinking the dots or separating them further, the exchange interactions are also suppressed at the same time, making the gate operations unfavorably slow. When the system is operated as a resonant-exchange qubit, the leakage is three to five orders of magnitude smaller. We have also calculated the optimal detuning point which minimizes the leakage for the resonant-exchange qubit, and have found that although it does not coincide with the double sweet spot for the charge noise, they are rather close. Our results suggest that the resonant-exchange qubit has another advantage, that leakage can be greatly suppressed compared to the exchange-only qubit, and operating at the double sweet spot point should be optimal both for reducing charge noise and suppressing leakage.
Encoding quantum information in d-dimensional systems (qudits) with d>2 offers appealing new directions for resource-efficient quantum computing. However, protecting the coherence of nonclassical qudit resource states remains an open challenge. Dynamical decoupling (DD) is a well-established technique for extending coherence, but its application to qudits is hindered by the quadratic scaling of the decoupling sequence overhead with the dimension d. As a result, demonstrations of qudit DD have so far been limited to low-dimensional qudits. Here, we show that noise-biased qudits enable a nontrivial reduction of this overhead, for example, from quadratic to linear. We perform qudit DD on a model d=8 qudit, the nuclear spin of an antimony donor in silicon. We benchmark DD performance on highly nonclassical states such as uniform superpositions, cat states, and Haar random states and measure coherence improvements up to a factor 5 to 10. For a spin-cat error correction code, continuous DD extends the coherence time of the logical superposition ∣+⟩L to 225~ms, compared to 19~ms under free evolution and 85~ms with a Hahn echo. This improvement shows that DD sequences tailored to a system's noise bias can significantly enhance the lifetime of encoded logical qubits.