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arXiv:quant-ph/0701165 · Physical Review A

Robust controlled-NOT gate in the presence of large fabrication-induced variations of the exchange interaction strength

Matthew J. Testolin, Charles D. Hill, Cameron J. Wellard, Lloyd C. L. Hollenberg

Published Jul 3, 2007• 30 citations
arXivHTMLPDF

Abstract

We demonstrate how using two-qubit composite rotations a high fidelity controlled-NOT (CNOT) gate can be constructed, even when the strength of the interaction between qubits is not accurately known. We focus on the exchange interaction oscillation in silicon based solid-state architectures with a Heisenberg Hamiltonian. This method easily applies to a general two-qubit Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity when a single application of the composite rotations is combined with a modest level of Hamiltonian characterization. Operating the robust CNOT gate in a suitably characterized system means concatenation of the composite pulse is unnecessary, hence reducing operation time, and ensuring the gate operates below the threshold required for fault-tolerant quantum computation.

DOI
10.1103/physreva.76.012302

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We demonstrate how using two-qubit composite rotations a high fidelity controlled-NOT (CNOT) gate can be constructed, even when the strength of the interaction between qubits is not accurately known. We focus on the exchange interaction oscillation in silicon based solid-state architectures with a Heisenberg Hamiltonian. This method easily applies to a general two-qubit Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity when a single application of the composite rotations is combined with a modest level of Hamiltonian characterization. Operating the robust CNOT gate in a suitably characterized system means concatenation of the composite pulse is unnecessary, hence reducing operation time, and ensuring the gate operates below the threshold required for fault-tolerant quantum computation.
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Abstract Robust two-qubit gates are essential for scalable silicon spin qubits, but their fidelities are limited by microwave-control imperfections and charge-noise-induced exchange fluctuations. We propose a practical scheme for robust controlled-Z (CZ) and controlled-NOT (CNOT) gates in a silicon double quantum dot. By applying a transverse microwave drive, the effective Hamiltonian can be decomposed into two driven subspaces. In the subspace mainly controlled by the microwave field, a Broadband 1 (BB1) composite pulse is used to suppress errors in the microwave amplitude. In the exchange-assisted subspace, the microwave phases and durations are kept fixed, while a few piecewise-constant exchange amplitudes are optimized by a GRAPE-like procedure. This design reduces the sensitivity to both microwave-amplitude and exchange-amplitude errors while keeping the control waveform simple and experimentally friendly. Numerical simulations show that the optimized CNOT gate reaches a fidelity above 99.99% under experimentally relevant noise strengths, and the CZ gate also maintains a fidelity above 99.9%. These results indicate that combining composite pulses with optimized exchange control provides an experimentally feasible route to robust two-qubit gates in silicon spin qubits.
A self-contained approach to studying the unitary evolution of coupled qubits is introduced, capable of addressing a variety of physical systems described by exchange Hamiltonians containing Rabi terms. The method automatically determines both the Weyl chamber steering trajectory and the accompanying local rotations. Particular attention is paid to the case of anisotropic exchange with tracking controls, which is solved analytically. It is shown that, if computational subspace is well isolated, any exchange interaction can always generate high fidelity, single-step controlled-NOT (CNOT) logic, provided that both qubits can be individually manipulated. The results are then applied to superconducting qubit architectures, for which several CNOT gate implementations are identified. The paper concludes with consideration of two CNOT gate designs having high efficiency and operating with no significant leakage to higher-lying noncomputational states.
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.