Quantum-state texture and gate identification

TL;DR

This paper introduces the concept of quantum-state texture, develops a resource theory around it, and demonstrates its utility in efficiently characterizing quantum gates without tomography.

Contribution

It presents a new resource theory for quantum-state texture, an easily measurable monotone, and shows how textures can be used to identify quantum gates in circuit layers.

Findings

Textures are useful for characterizing unknown quantum gates.

The method works with randomized inputs and does not require tomography.

It can fully characterize circuit layers with at least one CNOT gate.

Abstract

We introduce and explore the notion of texture of an arbitrary quantum state, in a selected basis. In the first part of this letter we develop a resource theory and show that state texture is adequately described by an easily computable monotone, which is also directly measurable. It is shown that textures are useful in the characterization of unknown quantum gates in universal circuit layers. By using randomized input states and recording the textures of the output qubits we are able to fully characterize the circuit layer, whenever it contains at least one CNOT gate. This can be done without the need of tomographic protocols and the use of ancillary systems.