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.
Highlights
Quantum computing is expected to solve several problems exponentially faster than classical computing, and realizing universal quantum computers is one of the most central goals in modern quantum information science
We explain how to verify quantum states generated by a certain class of quantum circuits
We show a protocol for verifying quantum states generated by a certain class of quantum circuits
Summary
Quantum computing is expected to solve several problems exponentially faster than classical computing, and realizing universal quantum computers is one of the most central goals in modern quantum information science. Can we verify ground states of Hamiltonians and states generated by general quantum circuits with sequential single-qubit measurements of Pauli operators?. (2) Can we verify hypergraph states with high connectivity by using only sequential single-qubit measurements of Pauli operators?. High connectivity means that Eq (1) is polynomial with respect to jVj. The second open problem is important for the verification of the quantum computational supremacy demonstration because output states of the Bremner-MontanaroShepherd-type IQP circuits [12] are hypergraph states with high connectivity. With respect to the boson sampling model [4], a verification protocol has already been proposed [58], but this protocol requires at most exponentially many copies of a verified quantum state. At this moment, we do not know which approach is better
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