Verification of Many-Qubit States

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.

Efficient Verification of Pure Quantum States in the Adversarial Scenario

“…This bound on the number of tests is much smaller than previous results based on quantum de Finetti theorem [23,24]. Nevertheless, the scaling with 1/δ is still suboptimal, and this behavior cannot be changed if Ω is singular; cf.…”

“…To verify hypergraph states with recent approaches in Refs. [23,24] for example, the number of required tests is enormous even in the simplest nontrivial cases. An outstanding problem underlying this deadlock is that, even for a given verification strategy, no efficient method is known for deter-mining the minimal number of tests required to achieve a given precision, as characterized by the infidelity and significance level [24,25].…”

Efficient verification of bosonic quantum channels via benchmarking

“…Verification, along with validation that determines whether an implementation is qualified to accomplish a certain task, is important for assessing the credibility of a product or a system. Here quantum-state verification [18][19][20][21][22][23] aims to check whether an implementation of certain quantum state meets the specifications of a target quantum state or not. While [18,19,21] use 'certification' to refer to the process of verification, in this paper, we use the phrase 'quantum-state verification' rather than 'certification'.…”

Verifying commuting quantum computations via fidelity estimation of weighted graph states

“…In fact, the verification of quantum computer has been actively studied as quantum characterization, verification, and validation 6 . From this importance, several efficient verification protocols have been proposed for various sub-universal quantum computing models [29][30][31][32][33]. However, there is a possibility that conjectures making classical simulations of these verifiable sub-universal models intractable will be rejected.…”

“…The first one is based on hypergraph states [37], which are generalizations of graph states. For this type of IQP circuits, verification protocols have already been proposed via the efficient fidelity estimation of hypergraph states [29][30][31][32]. On the other hand, in the second type of IQP circuits, we generate a weighted graph state up to local unitary transformations and measure it with Z-basis, where weighted graph states are another generalizations of graph states (for the definition, see section 2).…”