Verifiable fault-tolerance in measurement-based quantum computation

Abstract

Quantum systems, in general, output data that cannot be simulated efficiently by a classical computer, and hence is useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately, that verification of the output of the quantum systems is not so trivial, since predicting the output is exponentially hard. As another problem, quantum system is very delicate for noise and thus needs error correction. Here we propose a framework for verification of the output of fault-tolerant quantum computation in the measurement-based model. Contrast to existing analyses on fault-tolerance, we do not assume any noise model on the resource state, but an arbitrary resource state is tested by using only single-qubit measurements to verify whether the output of measurement-based quantum computation on it is correct or not. The overhead for verification including classical processing is linear in the size of quantum computation. Since full characterization of quantum noise is exponentially hard for large-scale quantum computing systems, our framework provides an efficient way of practical verification of experimental quantum error correction. Moreover, the proposed verification scheme is also compatible to measurement-only blind quantum computation, where a client can accept the delegated quantum computation even when a quantum sever makes deviation, as long as the output is correct.

7 pages, 3 figures

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• Efficient Verification of Hypergraph States
• General framework for verifying pure quantum states in the adversarial scenario
• Self-guaranteed measurement-based quantum computation
• Resource-efficient verification of quantum computing using Serfling's bound
• Accrediting outputs of noisy intermediate-scale quantum computing devices
• Verifying commuting quantum computations via fidelity estimation of weighted graph states
• Robust and efficient verification of graph states in blind measurement-based quantum computation
• Quantum verification and estimation with few copies
• Blind quantum computation for a user who only performs single-qubit gates
• A Hybrid and Universal Blind Quantum Computation
• Nonadaptive fault-tolerant verification of quantum supremacy with noise
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
• Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Verifiable Quantum Secure Modulo Summation
• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• A Specification Format and a Verification Method of Fault-Tolerant Quantum Circuits
• Role of Hypothesis Testing in Quantum Information
• Public verifiable measurement-only blind quantum computation based on entanglement witnesses
• Passive verification protocol for thermal graph states
• Quantum subspace verification for error correction codes
• Experimental Verification of Entangled States in the Adversarial Scenario
• Parallel remote state preparation for fully device-independent verifiable blind quantum computation
• Blind quantum computing can always be made verifiable
• Phase Transitions and Noise Robustness of Quantum Graph States
• Maximally nonlocal subspaces
• Universal and Efficient Quantum State Verification via Schmidt Decomposition and Mutually Unbiased Bases