A proposal for charge basis tomography of superconducting qubits

TL;DR

This paper presents a novel protocol called charge basis tomography for reconstructing the density matrix of superconducting qubits, enabling better validation of quantum models and potential detection of complex quantum phases.

Contribution

The paper introduces a new charge basis tomography protocol combining Josephson pulses and projective charge readout for superconducting qubits.

Findings

Simulated ground state reconstruction of a transmon using the protocol.

Hilbert-Schmidt distance detects deviations from the model Hamiltonian.

Protocol enables validation of quantum models and exploration of topological phases.

Abstract

We introduce a general protocol for obtaining the charge basis density matrix of a superconducting quantum circuit. Inspired by cavity state tomography, our protocol combines Josephson-energy pulse sequences and projective charge-basis readout to access the off-diagonal elements of the density matrix, a scheme we thus dub charge basis tomography. We simulate the reconstruction of the ground state of a target transmon using the Aharonov-Casher effect in a probe qubit to realise projective readout and show the Hilbert-Schmidt distance can detect deviations from the correct model Hamiltonian. Unlocking this ability to validate models using the ground state sets the stage for using transmons to detect interacting and topological phases, particularly in materials where time-domain and spectroscopic probes can be limited by intrinsic noise.