Experimental learning of quantum states

TL;DR

This paper experimentally demonstrates that quantum states of up to 6 qubits can be approximately learned with a number of measurements that scales linearly with the number of qubits, challenging traditional exponential scaling assumptions.

Contribution

It provides the first experimental validation that quantum states can be

Findings

Quantum states of up to 6 qubits can be learned with linear measurements.

Supports the application of computational learning theory to quantum information.

Shows potential for scaling quantum state analysis to larger systems.

Abstract

The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling clearly limits our ability to do tomography to systems with no more than a few qubits and has been used to argue against the universal validity of quantum mechanics itself. However, from a computational learning theory perspective, it can be shown that, in a probabilistic setting, quantum states can be approximately learned using only a linear number of measurements. Here we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales.