Pulse variational quantum eigensolver on cross-resonance based hardware

TL;DR

This paper introduces a pulse-based variational quantum eigensolver that encodes parameters directly into hardware pulses, significantly reducing circuit duration and improving energy estimates on noisy cross-resonance quantum hardware.

Contribution

The authors develop a pulse-parameter encoding method for variational algorithms, achieving shorter circuit durations and better energy results on IBM cross-resonance hardware.

Findings

Up to 5x reduction in schedule duration compared to CNOT-based ansatzes.

Improved energy estimates for hydrogen molecules, especially H3.

Demonstrated feasibility of pulse-encoded variational algorithms on real hardware.

Abstract

State-of-the-art noisy digital quantum computers can only execute short-depth quantum circuits. Variational algorithms are a promising route to unlock the potential of noisy quantum computers since the depth of the corresponding circuits can be kept well below hardware-imposed limits. Typically, the variational parameters correspond to virtual $R_Z$ gate angles, implemented by phase changes of calibrated pulses. By encoding the variational parameters directly as hardware pulse amplitudes and durations we succeed in further shortening the pulse schedule and overall circuit duration. This decreases the impact of qubit decoherence and gate noise. As a demonstration, we apply our pulse-based variational algorithm to the calculation of the ground state of different hydrogen-based molecules (H$_2$, H$_3$ and H$_4$) using IBM cross-resonance-based hardware. We observe a reduction in schedule duration of up to $5\times$ compared to CNOT-based Ans\"atze, while also reducing the measured energy. In particular, we observe a sizable improvement of the minimal energy configuration of H$_3$ compared to a CNOT-based variational form. Finally, we discuss possible future developments including error mitigation schemes and schedule optimizations, which will enable further improvements of our approach paving the way towards the simulation of larger systems on noisy quantum devices.