Optimal control for fast and high-fidelity quantum gates in coupled superconducting flux qubits

TL;DR

This paper demonstrates a quantum optimal control approach to implement fast, high-fidelity single- and two-qubit gates in superconducting flux qubits without additional couplers, achieving operation times much shorter than decoherence times.

Contribution

It introduces a control scheme that uses fixed qubit parameters and optimal control theory to realize high-fidelity quantum gates efficiently in superconducting flux qubits.

Findings

Single-qubit gates < 1 ns

CNOT gates ~ 2 ns

High fidelity with minimal leakage and decoherence effects

Abstract

We apply the quantum optimal control theory based on the Krotov method to implement single-qubit $X$ and $Z$ gates and two-qubit CNOT gates for inductively coupled superconducting flux qubits with fixed qubit transition frequencies and fixed off-diagonal qubit-qubit coupling. Our scheme that shares the same advantage of other directly coupling schemes requires no additional coupler subcircuit and control lines. The control lines needed are only for the manipulation of individual qubits (e.g., a time-dependent magnetic flux or field applied on each qubit). The qubits are operated at the optimal coherence points and the gate operation times (single-qubit gates $< 1$ ns; CNOT gates $\sim 2$ ns) are much shorter than the corresponding qubit decoherence time. A CNOT gate or other general quantum gates can be implemented in a single run of pulse sequence rather than being decomposed into several single-qubit and some entangled two-qubit operations in series by composite pulse sequences. Quantum gates constructed via our scheme are all with very high fidelity (very low error) as our optimal control scheme takes into account the fixed qubit detuning and fixed two-qubit interaction as well as all other time-dependent magnetic-field-induced single-qubit interactions and two-qubit couplings. The effect of leakage to higher energy-level states and the effect of qubit decoherence on the quantum gate operations are also discussed.