Effect of Ohmic environment on optimally controlled flux-biased phase qubit

TL;DR

This paper investigates how an Ohmic environment impacts the performance of flux-biased phase qubits during gate operations, using numerical solutions of the master equation to evaluate errors and compare pulse strategies.

Contribution

It introduces a detailed analysis of environmental effects on flux-biased phase qubits using the Caldeira-Leggett model and compares single- and two-quadrature control pulses.

Findings

Two-quadrature pulses reduce gate error more effectively than single-quadrature pulses.

Environmental effects increase gate error but do not negate the advantage of two-quadrature control.

Numerical results highlight the importance of considering environment in qubit control strategies.

Abstract

We analyze the effect of environment on the gate operation of flux-biased phase qubits. We employ the master equation for a reduced density matrix of the qubit system coupled to an Ohmic environment, described by the Caldeira-Leggett model. Numerically solving this equation, we evaluate the gate error as a function of energy splitting between qubit states, junction capacitance, and temperature. The analysis is presented for single-quadrature microwave (control) pulses as well as for two-quadrature pulses, which lower the gate error significantly for idealized systems in the absence of environment. Our results indicate that two-quadrature pulses outperform single quadrature pulses even in the presence of environment.