Verification of Many-Qubit States

TL;DR

This paper introduces protocols for verifying complex many-qubit quantum states using only sequential single-qubit measurements, applicable to ground states, states from certain circuits, and hypergraph states, without assuming i.i.d. copies.

Contribution

It presents novel verification protocols for a wide class of many-qubit states, including hypergraph states and states from IQP circuits, without relying on i.i.d. assumptions.

Findings

Protocols verify ground states of Hamiltonians.

Verification of states generated by specific quantum circuits.

Applicable to states used in quantum supremacy and blind quantum computing.

Abstract

Verification is a task to check whether a given quantum state is close to an ideal state or not. In this paper, we show that a variety of many-qubit quantum states can be verified with only sequential single-qubit measurements of Pauli operators. First, we introduce a protocol for verifying ground states of Hamiltonians. We next explain how to verify quantum states generated by a certain class of quantum circuits. We finally propose an adaptive test of stabilizers that enables the verification of all polynomial-time-generated hypergraph states, which include output states of the Bremner-Montanaro-Shepherd-type instantaneous quantum polynomial time (IQP) circuits. Importantly, we do not make any assumption that the identically and independently distributed copies of the same states are given: Our protocols work even if some highly complicated entanglement is created among copies in any artificial way. As applications, we consider the verification of the quantum computational supremacy demonstration with IQP models, and verifiable blind quantum computing.