Quantum State and Process Tomography via Adaptive Measurements

TL;DR

This paper introduces an adaptive measurement protocol for efficient quantum state and process tomography, significantly reducing experimental requirements while maintaining high fidelity, demonstrated through NMR experiments on key quantum gates.

Contribution

The paper presents novel adaptive protocols for quantum state and process tomography that require fewer measurements than traditional methods, applicable to all pure states and unitary channels.

Findings

A 2d-1 measurement outcome protocol for pure state tomography.

A d^2+d-1 measurement outcome protocol for unitary process tomography.

Experimental validation on NMR system showing reduced measurements with high fidelity.

Abstract

We investigate quantum state tomography (QST) for pure states and quantum process tomography (QPT) for unitary channels via $adaptive$ measurements. For a quantum system with a $d$-dimensional Hilbert space, we first propose an adaptive protocol where only $2d-1$ measurement outcomes are used to accomplish the QST for $all$ pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography (AUPT) protocol of $d^2+d-1$ measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, $T$ gate ($\pi/8$ phase gate), and controlled-NOT gate, respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.