Tomography scheme for two spin-1/2 qubits in a double quantum dot

TL;DR

This paper proposes a comprehensive quantum state tomography method for two spin-1/2 qubits in a double quantum dot, utilizing charge measurements and quantum gates, including exchange and ESR, to determine the two-qubit density matrix.

Contribution

It introduces a tomography scheme based on mutually unbiased bases, representing projections via charge measurements and specific quantum gate operations, with a focus on practical ESR limitations.

Findings

15 quantum states enable full density matrix reconstruction.

Charge measurements after spin-to-charge conversion are sufficient.

ESR gates are limited to a pi/2 rotation per measurement.

Abstract

We present a scheme for full quantum state tomography tailored for two spin qubits in a double quantum dot. A set of 15 quantum states allows to determine the density matrix in this two-qubit space by projective measurement. In this paper we choose a set gained from mutually unbiased bases. We determine how those 15 projections can be represented by charge measurements after a spin-to-charge conversion and the application of quantum gates. The quantum gates include exchange-based gates as well as rotations by electron spin resonance (ESR). We assume the experimental realization of ESR operations to be more difficult than the exchange gate operation. Therefore, it is an important result that the ESR gates are limited by a pi/2 rotation for one of the electron spins per measurement.