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Extending the computational reach of a noisy superconducting quantum processor
Abhinav Kandala, Kristan Temme, Antonio D. Corcoles, Antonio Mezzacapo, Jerry M. Chow, Jay M. Gambetta
TL;DR
The paper develops error mitigation for noisy superconducting quantum processors by extrapolating results from experiments with varied noise levels. It demonstrates that carefully calibrated gate stretching and Richardson extrapolation can improve mitigated estimates, while nonlinearities and coherence-time fluctuations constrain the protocol.
Problem
Noisy superconducting processors require error mitigation because reliable quantum computation otherwise demands extremely low operation errors and substantial physical-qubit overhead.
Method
The method stretches gate evolutions, calibrates cross-resonance pulses for each stretch factor, and obtains mitigated estimates using Richardson extrapolation.
Results
Weaker drive amplitudes keep extrapolated estimates within bounds, whereas fast nonlinear gates can drive them severely out of bounds.
Takeaways & Limitations
Error mitigation can access computational accuracies otherwise inaccessible with faster gates, but requires calibration tailored to the mitigation protocol and slower gate operation.
Takeaways & Limitations
The protocol assumes time-translation-invariant noise, so measurements at different stretch factors should be performed shortly after one another when coherence times fluctuate.
Abstract
from arXiv · showhide
Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems. Yet, because of the inherent fragile nature of the physical computing elements, qubits, achieving quantum advantages over classical computation requires extremely low error rates for qubit operations as well as a significant overhead of physical qubits, in order to realize fault-tolerance via quantum error correction. However, recent theoretical work has shown that the accuracy of computation based off expectation values of quantum observables can be enhanced through an extrapolation of results from a collection of varying noisy experiments. Here, we demonstrate this error mitigation protocol on a superconducting quantum processor, enhancing its computational capability, with no additional hardware modifications. We apply the protocol to mitigate errors on canonical single- and two-qubit experiments and then extend its application to the variational optimization of Hamiltonians for quantum chemistry and magnetism. We effectively demonstrate that the suppression of incoherent errors helps unearth otherwise inaccessible accuracies to the variational solutions using our noisy processor. These results demonstrate that error mitigation techniques will be critical to significantly enhance the capabilities of near-term quantum computing hardware.
I. DEVICE AND GATES
The processor uses five fixed-frequency transmon qubits with microwave control, and implements error-mitigation experiments by stretching calibrated single-qubit pulses and hardware-efficient entanglers.
- The device uses five fixed-frequency transmon qubits with superconducting resonators for coupling, control, and readout.
- Single-qubit operations use software Z gates or DRAG-style 4σ Gaussian microwave pulses whose durations, buffers, amplitudes, and parameters are rescaled by ci.
- Gate fidelities across stretch factors are characterized for both single-qubit and two-qubit gates using randomized benchmarking.
- Hardware-efficient trial states use entanglers built from pairwise ZXπ/4 gates implemented through echoed cross-resonance pulses.
II. COHERENCE TIME FLUCTUATIONS IN SUPERCONDUCTING QUBITS
Zero-noise extrapolation requires time-translation-invariant noise, so measurements at different stretch factors must be acquired closely together when superconducting coherence times fluctuate.
- The rescaled-state interpretation of amplified noise is valid only when the noise is time-translation invariant.
- Measurements for different stretch factors must be performed shortly after one another because superconducting T1 and T2 times fluctuate over time.
- When stretch-factor measurements are grouped over the full averaging period, their average decay times match for typical T1 and echo T2 sequences with ci=1,2.
- Separately sampled stretched experiments can have different decays, potentially producing Richardson-extrapolated expectation values outside physical bounds.
III. STRETCHING OF TWO-QUBIT GATES
Two-qubit stretching uses cross-resonance gates whose interaction strengths can be nonlinear in drive amplitude, requiring calibrated, lower-power operation to keep extrapolation reliable.
- The cross-resonance drive contains several interactions, with ZX and IX predicted to dominate and additional terms including IY, IZ, ZY, ZZ, and ZI.
- The CR interaction exhibits amplitude-dependent nonlinearities that must be considered when implementing error mitigation.
- The modeled ZX interaction combines linear and cubic drive-amplitude terms, with fixed amplitude-damping and dephasing noise added to each qubit.
- Stretch factors ci=1,2 are applied by scaling drive time and amplitude, while first-order Richardson extrapolation produces the mitigated estimates.
- Fast, high-power gates can drive mitigated estimates severely out of bounds, whereas weaker drives keep them within bounds at the cost of slower gates.
- The experiment calibrates CR amplitudes separately for ZXπ/2 at each stretch factor and uses echoed pulses to isolate ZX in a lower-power regime.
IV. SAMPLING AND BOOTSTRAPPING
The analysis corrects readout assignment errors and estimates uncertainty in mitigated expectation values through bootstrap resampling of measured distributions.
- Measured expectation values are particularly sensitive to readout assignment infidelity for large-weight Pauli operators.
- Variational-eigensolver expectation values are corrected using readout calibration at every optimization iteration.
- Bootstrapping resamples readout calibrations and quantum-state measurements to simulate finite-sampling variability in mitigated estimates.
- Repeating the bootstrapping protocol 50-100 times yields a distribution of numerical outcomes for the mitigated expectation value.