Suppressing Counter-Rotating Errors for Fast Single-Qubit Gates with Fluxonium
David A. Rower, Leon Ding, Helin Zhang, Max Hays, Junyoung An, P. M. Harrington, Ilan T. Rosen, Jeffrey Gertler, Thomas Hazard, Bethany M. Niedzielski, Mollie E. Schwartz, Simon Gustavsson, Kyle Serniak, Jeffrey A. Grover, William D. Oliver
Qubit decoherence unavoidably degrades the fidelity of quantum logic gates. Accordingly, realizing gates that are as fast as possible is a guiding principle for qubit control, necessitating protocols for mitigating error channels that become significant as gate time is decreased. One such error channel arises from the counter-rotating component of strong, linearly polarized drives. This error channel is particularly important when gate times approach the qubit Larmor period and represents the dominant source of infidelity for sufficiently fast single-qubit gates with low-frequency qubits such as fluxonium. In this work, we develop and demonstrate two complementary protocols for mitigating this error channel. The first protocol realizes circularly polarized driving in circuit QED through simultaneous charge and flux control. The second protocol—commensurate pulses—leverages the coherent and periodic nature of counter-rotating fields to regularize their contributions to gates, enabling single-qubit gate fidelities reliably exceeding 99.997%. This protocol is platform independent and requires no additional calibration overhead. This work establishes straightforward strategies for mitigating counter-rotating effects from strong drives in circuit QED and other platforms, which we expect to be helpful in the effort to realize high-fidelity control for fault-tolerant quantum computing. Published by the American Physical Society 2024
Qubit decoherence unavoidably degrades the fidelity of quantum logic gates. Accordingly, realizing gates that are as fast as possible is a guiding principle for qubit control, necessitating protocols for mitigating error channels that become significant as gate time is decreased. One such error channel arises from the counter-rotating component of strong, linearly polarized drives. This error channel is particularly important when gate times approach the qubit Larmor period and represents the dominant source of infidelity for sufficiently fast single-qubit gates with low-frequency qubits such as fluxonium. In this work, we develop and demonstrate two complementary protocols for mitigating this error channel. The first protocol realizes circularly polarized driving in circuit QED through simultaneous charge and flux control. The second protocol—commensurate pulses—leverages the coherent and periodic nature of counter-rotating fields to regularize their contributions to gates, enabling single-qubit gate fidelities reliably exceeding 99.997%. This protocol is platform independent and requires no additional calibration overhead. This work establishes straightforward strategies for mitigating counter-rotating effects from strong drives in circuit QED and other platforms, which we expect to be helpful in the effort to realize high-fidelity control for fault-tolerant quantum computing. Published by the American Physical Society 2024
In many quantum platforms, single-qubit gates are applied using a linear drive resonant with the qubit transition frequency, which is often theoretically described within the rotating-wave approximation (RWA). However, for fast gates on low-frequency qubits, the RWA may not hold and we need to consider the contribution from counterrotating terms to the qubit dynamics. The inclusion of counterrotating terms into the theoretical description gives rise to two challenges. First, it becomes challenging to analytically calculate the time evolution as the Hamiltonian is no longer self-commuting. Moreover, the time evolution now depends on the carrier phase such that, in general, every operation in a sequence of gates is different. In this work, we derive and verify a correction to the drive pulses that minimizes the effect of these counterrotating terms in a two-level system. We then derive a second correction term that arises from noncomputational levels for a strongly anharmonic system. We experimentally implement these correction terms on a fluxonium superconducting qubit, which is an example of a strongly anharmonic, low-frequency qubit for which the RWA may not hold, and demonstrate how fast, high-fidelity single-qubit gates can be achieved without the need for additional hardware and calibration complexities.
Quantum gates based on resonant Rabi oscillations are inherently slow for small-frequency qubits. They are also prone to errors due to counter-rotating terms. However, when the anharmonicity is sufficiently high, as in the fluxonium architecture, alternative manipulation protocols can outperform standard resonant driving. In this work, we implement fast, high-fidelity quantum gates based on a one-period Landau-Zener-Stückelberg-Majorana (LZSM) driving protocol. We derive analytical expressions that simplify the exploration of the parameter space while accounting for the multi-level structure of the circuit. Furthermore, we analyze the role of leakage, discussing strategies to mitigate it and identifying regimes in which it becomes the dominant source of error. Finally, to evaluate the impact of dissipation on gate fidelity, we develop a robust formalism suitable for analyzing the open-system performance of quantum gates in the strong driving regime.
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 3×10−3 for gate times as short as 66ns, 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.
The heavy-fluxonium circuit is a promising building block for superconducting quantum processors due to its long relaxation and dephasing time at the flux-frustration point. However, the suppressed charge matrix elements and low transition frequency make it challenging to perform fast single-qubit gates using standard protocols. We report on new protocols for reset, fast coherent control,and readout that allow high-quality operation of the qubit with a 14 MHz transition frequency, an order of magnitude lower in energy than the ambient thermal energy scale. We utilize higher levels of the fluxonium to read out the qubit state and to initialize the qubit with 97% fidelity corresponding to cooling it to 190 μK. Instead of using standard microwave pulses, we control the qubit only with fast-flux pulses, generating control fields much larger than the qubit frequency. We develop a universal set of gates based on nonadiabatic Landau-Zener transitions that act in 20-60 ns, less than the single-qubit Larmor period. We measure qubit coherence of T1,T2e∼300 μs for a fluxonium in a 2D architecture and realize single-qubit gates with an average gate fidelity of 99.8% as characterized by randomized benchmarking.
Achieving very fast gates that undercut the natural limits set by decoherence requires going into the strong driving limit. Realizing single-qubit control predicted beyond semi-classical, time-dependent modeling has yet to be experimentally realized on superconducting and most other computing platforms. In this regime, the common model of dynamics within a three-level manifold breaks down, and instead, we see new quantum error channels growing abruptly with decreasing time. To identify these error processes we systematically calculate the effect of multi-photon transitions that occur out of the computational space. We then derive analytical formulas to suppress these effects, as well as amplitude and phase errors on the qubit space; we term these R1D for suppressing the ∣0⟩−∣2⟩ transition and R2D when also suppressing ∣1⟩−∣3⟩ leakage. We also answer long-standing questions about the optimal values of the DRAG prefactor as well as constant detuning, when accounting for time-ordering, and also show how to calibrate other prefactors for further performance improvement. Upon correcting these varied sources of error, we numerically demonstrate gate infidelities below 10−5 for a 7ns π-rotation when incorporating existing decoherence rates.
High-coherence qubits, which can store and manipulate quantum states for long times with low error rates, are necessary building blocks for quantum computers. Here we propose a driven superconducting erasure qubit, the Floquet fluxonium molecule, which minimizes bit-flip rates through disjoint support of its qubit states and suppresses phase flips by a novel second-order insensitivity to flux-noise dephasing. We estimate the bit-flip, phase-flip, and erasure rates through numerical simulations, with predicted coherence times of approximately 50 ms in the computational subspace and erasure lifetimes of about 500 μ s . We also present a protocol for performing high-fidelity single-qubit rotation gates via additional flux modulation, on timescales of roughly 500 ns, and propose a scheme for erasure detection and logical readout. Our results demonstrate the utility of drives for building new qubits that can outperform their static counterparts. Published by the American Physical Society 2024