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arXiv:2307.09031 · npj Quantum Information

Hamiltonian phase error in resonantly driven CNOT gate above the fault-tolerant threshold

Yi-Hsien Wu, Leon C. Camenzind, Akito Noiri, Kenta Takeda, Takashi Nakajima, Takashi Kobayashi, C. Y. Chang, Amir Sammak, Giordano Scappucci, Hsi‐Sheng Goan, Seigo Tarucha

Published Jan 11, 2024• 11 citations
arXivHTMLPDF

Abstract

Abstract Because of their long coherence time and compatibility with industrial foundry processes, electron spin qubits are a promising platform for scalable quantum processors. A full-fledged quantum computer will need quantum error correction, which requires high-fidelity quantum gates. Analyzing and mitigating gate errors are useful to improve gate fidelity. Here, we demonstrate a simple yet reliable calibration procedure for a high-fidelity controlled-rotation gate in an exchange-always-on Silicon quantum processor, allowing operation above the fault-tolerance threshold of quantum error correction. We find that the fidelity of our uncalibrated controlled-rotation gate is limited by coherent errors in the form of controlled phases and present a method to measure and correct these phase errors. We then verify the improvement in our gate fidelities by randomized benchmark and gate-set tomography protocols. Finally, we use our phase correction protocol to implement a virtual, high-fidelity, controlled-phase gate.

DOI
10.1038/s41534-023-00802-9

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•Jan 1, 2019•155 citations
Abstract Because of their long coherence time and compatibility with industrial foundry processes, electron spin qubits are a promising platform for scalable quantum processors. A full-fledged quantum computer will need quantum error correction, which requires high-fidelity quantum gates. Analyzing and mitigating gate errors are useful to improve gate fidelity. Here, we demonstrate a simple yet reliable calibration procedure for a high-fidelity controlled-rotation gate in an exchange-always-on Silicon quantum processor, allowing operation above the fault-tolerance threshold of quantum error correction. We find that the fidelity of our uncalibrated controlled-rotation gate is limited by coherent errors in the form of controlled phases and present a method to measure and correct these phase errors. We then verify the improvement in our gate fidelities by randomized benchmark and gate-set tomography protocols. Finally, we use our phase correction protocol to implement a virtual, high-fidelity, controlled-phase gate.
Single-qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. Although high-fidelity single-qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT gate has been challenging because of rapid nuclear spin dephasing and charge noise. We demonstrate an efficient resonantly driven CNOT gate for electron spins in silicon. Our platform achieves single-qubit rotations with fidelities greater than 99%, as verified by randomized benchmarking. Gate control of the exchange coupling allows a quantum CNOT gate to be implemented with resonant driving in ~200 nanoseconds. We used the CNOT gate to generate a Bell state with 78% fidelity (corrected for errors in state preparation and measurement). Our quantum dot device architecture enables multi-qubit algorithms in silicon.
Abstract High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault tolerance—the ability to correct errors faster than they occur 1 . The central requirement for fault tolerance is expressed in terms of an error threshold. Whereas the actual threshold depends on many details, a common target is the approximately 1% error threshold of the well-known surface code 2,3 . Reaching two-qubit gate fidelities above 99% has been a long-standing major goal for semiconductor spin qubits. These qubits are promising for scaling, as they can leverage advanced semiconductor technology 4 . Here we report a spin-based quantum processor in silicon with single-qubit and two-qubit gate fidelities, all of which are above 99.5%, extracted from gate-set tomography. The average single-qubit gate fidelities remain above 99% when including crosstalk and idling errors on the neighbouring qubit. Using this high-fidelity gate set, we execute the demanding task of calculating molecular ground-state energies using a variational quantum eigensolver algorithm 5 . Having surpassed the 99% barrier for the two-qubit gate fidelity, semiconductor qubits are well positioned on the path to fault tolerance and to possible applications in the era of noisy intermediate-scale quantum devices.
The calibration of high-quality two-qubit entangling gates is an essential component in engineering large-scale, fault-tolerant quantum computers. However, many standard calibration techniques are based on randomized circuits that are only quadratically sensitive to calibration errors. As a result, these approaches are inefficient, requiring many experimental shots to achieve acceptable performance. In this work, we demonstrate that robust phase estimation can enable high-precision, Heisenberg-limited estimates of coherent errors in multi-qubit gates. Equipped with an efficient estimator, the calibration problem may be reduced to a simple optimization loop that minimizes the estimated coherent error. We experimentally demonstrate our calibration protocols by improving the operation of a two-qubit controlled-Z gate on a superconducting processor, and we validate the improved performance with gate set tomography. Our methods are applicable to gates in other quantum hardware platforms such as ion traps and neutral atoms, and on other multi-qubit gates, such as CNOT or iSWAP.
A two-qubit controlled-not (cnot) gate, realized by a controlled-phase (C-phase) gate combined with single-qubit gates, has been experimentally implemented recently for quantum-dot spin qubits in isotopically enriched silicon, a promising solid-state system for practical quantum computation. In the experiments, the single-qubit gates have been demonstrated with fault-tolerant control fidelity, but the infidelity of the two-qubit C-phase gate is, primarily due to the electrical noise, still higher than the required error threshold for fault-tolerant quantum computation (FTQC). Here, by taking the realistic system parameters and the experimental constraints on the control pulses into account, we construct experimentally realizable high-fidelity cnot gates robust against electrical noise with the experimentally measured 1/f1.011/{f}^{1.01}1/f1.01 noise spectrum and also against the uncertainty in the interdot tunnel coupling amplitude. Our fine-tuned optimal cnot gate has about two orders of magnitude improvement in gate infidelity over the ideal C-phase gate constructed without considering any noise effect. Furthermore, within the same control framework, high-fidelity and robust single-qubit gates can also be constructed, paving the way for large-scale FTQC.
Abstract Silicon spin qubits offer a promising path to scalable quantum computing due to their compatibility with industrial semiconductor manufacturing. A key requirement for scaling quantum processors is the ability to perform high-fidelity operations in parallel across many qubits. However, simultaneous control remains a major challenge in silicon devices, as fidelities typically degrade under parallel operation. Here we identify microwave-drive-induced a.c.-Stark shifts as the dominant source of this degradation in a five-qubit silicon spin array. We address this by introducing a scalable mitigation protocol based solely on pairwise phase calibrations. Using tailored control pulses on a shared control line, we achieve primitive X and Y gate fidelities well above 99.99% for each qubit individually, with some approaching 99.999%. Furthermore, these fidelities are preserved above 99.99% during simultaneous operation of up to three qubits. During parallel five-qubit operation, fidelities remain above the widely targeted fault-tolerant threshold of 99.9%. By maintaining high-fidelity control during simultaneous operation, shared qubit-control lines can support the development of large-scale semiconductor quantum processors.
Abstract Universal quantum computation will require qubit technology based on a scalable platform1, together with quantum error correction protocols that place strict limits on the maximum infidelities for one- and two-qubit gate operations2, 3. Although various qubit systems have shown high fidelities at the one-qubit level4–10, the only solid-state qubits manufactured using standard lithographic techniques that have demonstrated two-qubit fidelities near the fault-tolerance threshold6 have been in superconductor systems. Silicon-based quantum dot qubits are also amenable to large-scale fabrication and can achieve high single-qubit gate fidelities (exceeding 99.9 per cent) using isotopically enriched silicon11, 12. Two-qubit gates have now been demonstrated in a number of systems13–15, but as yet an accurate assessment of their fidelities using Clifford-based randomized benchmarking, which uses sequences of randomly chosen gates to measure the error, has not been achieved. Here, for qubits encoded on the electron spin states of gate-defined quantum dots, we demonstrate Bell state tomography with fidelities ranging from 80 to 89 per cent, and two-qubit randomized benchmarking with an average Clifford gate fidelity of 94.7 per cent and an average controlled-rotation fidelity of 98 per cent. These fidelities are found to be limited by the relatively long gate times used here compared with the decoherence times of the qubits. Silicon qubit designs employing fast gate operations with high Rabi frequencies16, 17, together with advanced pulsing techniques18, should therefore enable much higher fidelities in the near future.