Feasibility of single-shot realizations of conditional three-qubit gates in exchange-coupled qubit arrays with local control

Abstract

We investigate the feasibility of single-shot Toffoli- and Fredkin-gate realizations in qubit arrays with Heisenberg-type exchange interactions between adjacent qubits. As follows from the Lie-algebraic criteria of controllability, such an array is rendered completely controllable -- equivalent to allowing universal quantum computation -- by a Zeeman-like control field with two orthogonal components acting on a single "actuator" qubit. Adopting this local-control setting, we start our analysis with piecewise-constant control fields and determine the global maxima of the relevant figure of merit (target-gate fidelity) by combining the multistart-based clustering algorithm and quasi-Newton type local optimization. We subsequently introduce important practical considerations, such as finite frequency bandwidth of realistic fields and their leakage away from the actuator. We find the shortest times required for high-fidelity Toffoli- and Fredkin-gate realizations and provide comparisons to their respective two-qubit counterparts -- controlled-NOT and exponential-SWAP. In particular, the Toffoli-gate time compares much more favorably to that of controlled-NOT than in the standard decomposition-based approach. This study indicates that the use of the single-shot approach can alleviate the burden on control-generating hardware in future experimental realizations of multi-qubit gates.

project started in 2016 and completed -- after a long interruption -- in 2018

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Cited by in corpus (6)

• Conversion from $W$ to Greenberger-Horne-Zeilinger states in the Rydberg-blockade regime of neutral-atom systems: Dynamical-symmetry-based approach
• Dicke-state preparation through global transverse control of Ising-coupled qubits
• Quantum-brachistochrone approach to the conversion from $W$ to Greenberger-Horne-Zeilinger states for Rydberg-atom qubits
• Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control
• Digital Quantum Simulation of Scalar Yukawa Coupling
• Harnessing subspace controllability: Dynamical generation of Dicke states in Heisenberg-coupled qubit arrays with a single local control