# Quantum eigenstate tomography with qubit tunneling spectroscopy

## TL;DR

This paper extends qubit tunneling spectroscopy to perform quantum eigenstate tomography on multi-qubit systems by coupling a probe qubit to multiple qubits, enabling measurement of energy eigenstates in arbitrary bases.

## Contribution

It introduces a generalized QTS method that allows projective measurements of multi-qubit eigenstates, advancing quantum state tomography techniques.

## Key findings

- Demonstrates how to perform eigenstate tomography using generalized QTS.
- Shows application to probing eigenstates of a kink in a frustrated transverse Ising chain.
- Provides a practical scheme for multi-qubit state measurement in quantum systems.

## Abstract

Measurement of the energy eigenvalues (spectrum) of a multi-qubit system has recently become possible by qubit tunneling spectroscopy (QTS). In the standard QTS experiments, an incoherent probe qubit is strongly coupled to one of the qubits of the system in such a way that its incoherent tunneling rate provides information about the energy eigenvalues of the original (source) system. In this paper, we generalize QTS by coupling the probe qubit to many source qubits. We show that by properly choosing the couplings, one can perform projective measurements of the source system energy eigenstates in an arbitrary basis, thus performing quantum eigenstate tomography. As a practical example of a limited tomography, we apply our scheme to probe the eigenstates of a kink in a frustrated transverse Ising chain.