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arXiv:1805.03569 · New Journal of Physics

Quantum control for high-fidelity multi-qubit gates

Raymond J. Spiteri, Marina Schmidt, Joydip Ghosh, Ehsan Zahedinejad, Barry C. Sanders

Published Oct 11, 2018• 24 citations
arXivHTMLPDF

Abstract

Quantum control for error correction is critical for the practical use of quantum computers. We address quantum optimal control for single-shot multi-qubit gates by framing it as a feasibility problem for the Hamiltonian model that is then solved with standard global optimization software. Our approach yields faster high-fidelity (>99.99%) single-shot three-qubit-gate control than obtained previously, and it has also enabled us to solve the quantum-control problem for a fast high-fidelity four-qubit gate.

DOI
10.1088/1367-2630/aae79a

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Quantum control for error correction is critical for the practical use of quantum computers. We address quantum optimal control for single-shot multi-qubit gates by framing it as a feasibility problem for the Hamiltonian model that is then solved with standard global optimization software. Our approach yields faster high-fidelity (>99.99%) single-shot three-qubit-gate control than obtained previously, and it has also enabled us to solve the quantum-control problem for a fast high-fidelity four-qubit gate.
A single-shot Toffoli, or controlled-controlled-not, gate is desirable for classical and quantum information processing. The Toffoli gate alone is universal for reversible computing and, accompanied by the Hadamard gate, forms a universal gate set for quantum computing. The Toffoli gate is also a key ingredient for (nontopological) quantum error correction. Currently Toffoli gates are achieved by decomposing into sequentially implemented single- and two-qubit gates, which require much longer times and yields lower overall fidelities compared to a single-shot implementation. We develop a quantum-control procedure to construct a single-shot Toffoli gate for three nearest-neighbor-coupled superconducting transmon systems such that the fidelity is 99.9% and is as fast as an entangling two-qubit gate under the same realistic conditions. The gate is achieved by a nongreedy quantum control procedure using our enhanced version of the differential evolution algorithm.
Flip-flop qubits, encoded in the antiparallel spin states of electron and nuclear spins in phosphorus donors in silicon, are promising for quantum processors due to their long coherence times, long-range two-qubit coupling, and CMOS compatibility. However, the large Hilbert space complicates understanding and controlling the dynamics. In this work, the authors use sophisticated techniques to derive effective flip-flop qubit Hamiltonians and design optimal control pulses that implement high-fidelity single-qubit gates that are much faster and more robust than previous proposals.
Quantum optimal control for gate optimization aims to provide accurate, robust, and fast pulse sequences to achieve gate fidelities on quantum systems below the error correction threshold. Many methods have been developed and successfully applied in simulation and on quantum hardware. In this paper, we establish a connection between the iterative linear quadratic regulator and quantum optimal control by adapting it to gate optimization of quantum systems. We include constraints on the controls and their derivatives to enable smoother pulses. We achieve high-fidelity simulation results forX\mathbf{X}Xand cross-resonance gates on one- and two-qubit fixed-frequency transmons simulated with two and three levels.
To build a quantum computer, one can simplify the design of multi-qubit elements (logic gates) by treating them as series of well known one- and two-qubit gates---at the price of a slower processor. What if there were a handy means for $d\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}t$ multi-qubit design? The authors show numerically that, under existing experimental constraints, their recently developed SuSSADE scheme can yield three-qubit gates for single-shot entangling operations with fidelity greater than 99.9%. This powerful approach brings us that much closer to a fault-tolerant solid-state quantum computer.
In two and three coupled Josephson charge qubits, we exemplify how to take pulses for realizing quantum gates from fidelity-limited pioneering stages to the decoherence limit of near time optimal high-fidelity controls. Thus, a CNOT gate can be obtained with a fidelity >1>1>1--${10}^{\ensuremath{-}9}$ for the two qubits. Even when including higher charge states, the leakage is below 11%1, although the pulses are nonadiabatic. The controls are five times faster than the pioneering experiment [Nature (London) 425, 941 (2003)] for otherwise identical parameters---i.e., a progress towards the error-correction threshold by a factor of 100. We outline schemes to generate these shaped pulses by Cauer synthesis, or more generally by few LCR circuits. The approach generalizes to larger systems: e.g., directly realizing a TOFFOLI gate in three linearly coupled charge qubits is shown to be 13 times faster than decomposing it into a circuit of nine CNOT gates of the above experimental work. In view of the next generation of fast pulse shapers, the combination of methods is designed to find wide application in quantum control of pseudospin and macroscopic quantum systems.
Implementing fast and high-fidelity quantum operations using open-loop quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as the presence of spurious modes or pulse distortions, can degrade the performance of optimal controls in practice. Here, we propose an experimentally simple approach to realize optimal quantum controls tailored to the device parameters and environment while specifically characterizing this quantum system. Concretely, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimentally available data and then optimize our experimental controls on this trained model. We show the power and feasibility of this approach by optimizing arbitrary single-qubit operations on a superconducting transmon qubit, using detailed numerical simulations. We demonstrate that this framework produces an accurate description of the device dynamics under arbitrary controls, together with the precise pulses achieving arbitrary single-qubit gates with a high fidelity of about 99.99%.