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Physical Review A

Fragility of gate-error metrics in simulation models of flux-tunable transmon quantum computers

Hannes Lagemann, Dennis Willsch, Madita Willsch, Fengping Jin, Hans A. De Raedt, Kristel F. L. Michielsen

Published Aug 8, 2023• 3 citations
Publisher

Abstract

Constructing a quantum computer requires immensely precise control over a quantum system. A lack of precision is often quantified by gate-error metrics, such as the average infidelity or the diamond distance. However, usually such gate-error metrics are only considered for individual gates and not the errors that accumulate over consecutive gates. Furthermore, it is not well known how susceptible the metrics are to the assumptions which make up the model. Here we investigate these issues using realistic simulation models of quantum computers with flux-tunable transmons and coupling resonators. Our main findings reveal that (i) gate-error metrics are indeed affected by the many assumptions of the model, (ii) consecutive gate errors do not accumulate linearly, and (iii) gate-error metrics are poor predictors for the performance of consecutive gates. Additionally, we discuss a potential limitation in the scalability of the studied device architecture.

DOI
10.1103/physreva.108.022604

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Constructing a quantum computer requires immensely precise control over a quantum system. A lack of precision is often quantified by gate-error metrics, such as the average infidelity or the diamond distance. However, usually such gate-error metrics are only considered for individual gates and not the errors that accumulate over consecutive gates. Furthermore, it is not well known how susceptible the metrics are to the assumptions which make up the model. Here we investigate these issues using realistic simulation models of quantum computers with flux-tunable transmons and coupling resonators. Our main findings reveal that (i) gate-error metrics are indeed affected by the many assumptions of the model, (ii) consecutive gate errors do not accumulate linearly, and (iii) gate-error metrics are poor predictors for the performance of consecutive gates. Additionally, we discuss a potential limitation in the scalability of the studied device architecture.
Constructing a quantum computer requires immensely precise control over a quantum system. A lack of precision is often quantified by gate-error metrics, such as the average infidelity or the diamond distance. However, usually such gate-error metrics are only considered for individual gates, and not the errors that accumulate over consecutive gates. Furthermore, it is not well known how susceptible the metrics are to the assumptions which make up the model. Here, we investigate these issues using realistic simulation models of quantum computers with flux-tunable transmons and coupling resonators. Our main findings reveal that (1) gate-error metrics are indeed affected by the many assumptions of the model, (2) consecutive gate errors do not accumulate linearly, and (3) gate-error metrics are poor predictors for the performance of consecutive gates. Additionally, we discuss a potential limitation in the scalability of the studied device architecture.
Over the past decades, tremendous effort has gone into building a universal quantum computer. In theory, such a device can solve certain problems such as factoring exponentially faster than digital computers. The leading technological prototypes are based on superconducting circuits and contain about 10-50 qubits. Controlling these fragile systems requires an enormous amount of precision, posing a difficult challenge for the experimentalists. We study such quantum systems in detail by solving the time-dependent Schrödinger equation for a generic model Hamiltonian. For this purpose, we have developed efficient product-formula algorithms that are tailored to key features of the model Hamiltonian. This allows us to simulate each individual voltage pulse that is used in experiments to realize a certain quantum gate, as dictated by the computational model of a quantum computer. By optimizing the pulse parameters, we find that even in the ideal case, the best pulses still contain undesirable errors in the realization of the intended quantum gate. The common gate metrics measured and reported in experiments or computed in theory are shown to provide insufficient practical information about the significance of these errors.
We develop a simulator for quantum computers composed of superconducting transmon qubits. The simulation model supports an arbitrary number of transmons and resonators. Quantum gates are implemented by time-dependent pulses. Nontrivial effects such as crosstalk, leakage to non-computational states, entanglement between transmons and resonators, and control errors due to the pulses are inherently included. The time evolution of the quantum computer is obtained by solving the time-dependent Schrödinger equation. The simulation algorithm shows excellent scalability on high-performance supercomputers. We present results for the simulation of up to 16 transmons and resonators. Additionally, the model can be used to simulate environments, and we demonstrate the transition from an isolated system to an open quantum system governed by a Lindblad master equation. We also describe a procedure to extract model parameters from electromagnetic simulations or experiments. We compare simulation results to experiments on several NISQ processors of the IBM Q Experience. We find nearly perfect agreement between simulation and experiment for quantum circuits designed to probe crosstalk in transmon systems. By studying common gate metrics such as the fidelity or the diamond distance, we find that they cannot reliably predict the performance of repeated gate applications or practical quantum algorithms. As an alternative, we find that the results from two-transmon gate set tomography have an exceptional predictive power. Finally, we test a protocol from the theory of quantum error correction and fault tolerance. We find that the protocol systematically improves the performance of transmon quantum computers in the presence of characteristic control and measurement errors.
To scale up the number of qubits in a quantum processor, it is important that each qubit, or pair of qubits, can be controlled individually. Flux crosstalk between frequency-tunable superconducting qubits means that assumptions about addressability may no longer be valid. In this study, the authors detail several methods for measuring flux crosstalk between transmon qubits. These crosstalk metrics can then be used to predict $s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}s$ performance of two-qubit gates, and thus employed as engineering milestones on the path to truly scalable quantum computers.
In the companion paper (Part I), we developed an optimal-control framework to suppress intrinsic and decoherence-induced errors in controlled-Z (CZ) gates between directly coupled, frequency-tunable transmons. Here, we extend this framework to incorporate uncertainties in coupling strength, anharmonicities, and zero-flux qubit frequencies, enabling the design of high-fidelity gates robust against noise and parameter uncertainties. We classify these uncertainties by whether they perturb the off-diagonal coupling strengths or the diagonal detunings of the Hamiltonian, and we identify distinct suppression mechanisms for each class. Coupling errors are mitigated through dynamical decoupling induced by strong detuning modulation. For a 30-ns gate, this strategy reduces the coupling error to 6.21×10−76.21\times10^{-7}6.21×10−7 and tolerates coupling-strength uncertainties up to 2π×42π\times42π×4 MHz while keeping total gate infidelity below 10−310^{-3}10−3. Detuning errors are minimized near a symmetric-detuning operating point that balances the two dominant leakage-mediated interactions. A 24-ns gate operated near this point tolerates individual uncertainties of up to 2π×52π\times52π×5 MHz in each relevant diagonal parameter under the same infidelity threshold. We further optimize gate performance under realistic conditions where intrinsic errors, decoherence, and parameter uncertainties coexist across six representative stages of progressively improving hardware performance. The resulting stage-specific controls achieve lower infidelity and greater robustness. Together with the companion study (Part I), this framework offers a practical approach to balance speed, fidelity, and robustness while reducing the need for exhaustive characterization and frequent recalibration in large-scale superconducting quantum processors.
Fault-tolerant quantum computing requires quantum gates that combine short duration, high fidelity, and robustness to noise. As quantum processors scale, robustness becomes increasingly important because exhaustive characterization and frequent recalibration of individual gates become impractical. We present a comprehensive optimal-control framework for controlled-Z (CZ) gates between directly coupled, frequency-tunable transmons that systematically accounts for intrinsic Hamiltonian errors and realistic decoherence mechanisms, including energy relaxation and dephasing. Using smooth, single-shot flux pulses, we obtain 12-ns CZ gates---close to the theoretical speed limit of 11.6 ns---with intrinsic errors suppressed to the 2×10−52\times10^{-5}2×10−5 level. We construct dephasing noise models, calibrated against published experimental measurements, that capture fast dephasing from room-temperature control electronics and slow dephasing from 1/f1/f1/f flux noise. Using these models, we identify dephasing sweet spots that suppress sensitivity to dephasing noise. We further exploit transmon asymmetry as a design parameter to access distinct noise-resilient operating regimes. These results establish an experimentally applicable framework for balancing gate speed, fidelity, and noise robustness while reducing characterization and recalibration overhead.