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.

Quantum control is valuable for various quantum technologies such as highfidelity gates for universal quantum computing, adaptive quantum-enhanced metrology, and ultra-cold atom manipulation. Although supervised machine learning and reinforcement learning are widely used for optimizing control parameters in classical systems, quantum control for parameter optimization is mainly pursued via gradient-based greedy algorithms. Although the quantum fitness landscape is often compatible with greedy algorithms, sometimes arXiv:1607.03428v3 [cs.LG]

Although quantum control typically relies on greedy (local) optimization, traps (irregular critical points) in the control landscape can make optimization hard by foiling local search strategies. We demonstrate the failure of greedy algorithms as well as the (non greedy) genetic-algorithm method to realize two fast quantum computing gates: a qutrit phase gate and a controlled-NOT gate. We show that our evolutionary algorithm circumvents the trap to deliver effective quantum control in both instances. Even when greedy algorithms succeed, our evolutionary algorithm can deliver a superior control procedure, for example, reducing the need for high time resolution.

Three-qubit quantum gates are key ingredients for quantum error correction and quantum-information processing. We generate quantum-control procedures to design three types of three-qubit gates, namely Toffoli, controlled-NOT-NOT, and Fredkin gates. The design procedures are applicable to a system comprising three nearest-neighbor-coupled superconducting artificial atoms. For each three-qubit gate, the numerical simulation of the proposed scheme achieves 99.9% fidelity, which is an accepted threshold fidelity for fault-tolerant quantum computing. We test our procedure in the presence of decoherenceinduced noise and show its robustness against random external noise generated by the control electronics. The three-qubit gates are designed via the machine-learning algorithm called subspace-selective selfadaptive differential evolution.

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.