Resource-efficient verification of quantum computing using Serfling's bound

Abstract

Verifying quantum states is central to certifying the correct operation of various quantum information processing tasks. In particular, in measurement-based quantum computing, checking whether correct graph states are generated is essential for reliable quantum computing. Several verification protocols for graph states have been proposed, but none of these are particularly resource efficient: multiple copies are required to extract a single state that is guaranteed to be close to the ideal one. The best protocol currently known requires $O(n^{15})$ copies of the state, where $n$ is the size of the graph state. In this paper, we construct a significantly more resource-efficient verification protocol for graph states that only requires $O(n^5\log n)$ copies. The key idea is to employ Serfling's bound, which is a probability inequality in classical statistics. Utilizing Serfling's bound also enables us to generalize our protocol for qudit and continuous-variable graph states. Constructing a resource-efficient verification protocol for them is non-trivial. For example, the previous verification protocols for qubit graph states that use the quantum de Finetti theorem cannot be generalized to qudit and continuous-variable graph states without tremendously increasing the resource overhead. This is because the overhead caused by the quantum de Finetti theorem depends on the local dimension. On the other hand, in our protocol, the resource overhead is independent of the local dimension, and therefore generalizing to qudit or continuous-variable graph states does not increase the overhead. The flexibility of Serfling's bound also makes our protocol robust: our protocol accepts slightly noisy but still useful graph states.

arXiv comment29 pages, 2 figures, close to published version. Theorem 1, Theorem 2, and related parts are revised from the previous version in arXiv

References in corpus (29)

• Measurement-based quantum computation with cluster states
• Encoding a qubit in an oscillator
• Multi-party entanglement in graph states
• Universal Quantum Computation with Continuous-Variable Cluster States
• Experimental high-dimensional two-photon entanglement and violations of generalised Bell inequalities
• Topological fault-tolerance in cluster state quantum computation
• Ultra-Large-Scale Continuous-Variable Cluster States Multiplexed in the Time Domain
• Universal blind quantum computation
• One-Way Quantum Computing in the Optical Frequency Comb
• Unconditionally verifiable blind computation
• Novel schemes for measurement-based quantum computation
• Verifiable measurement-only blind quantum computing with stabilizer testing
• Blind quantum computation protocol in which Alice only makes measurements
• Quantum computation based on d-level cluster states
• A largely self-contained and complete security proof for quantum key distribution
• 16-qubit IBM universal quantum computer can be fully entangled
• Post hoc verification of quantum computation
• Post hoc verification with a single prover
• Hierarchy of universal entanglement in 2D measurement-based quantum computation
• Interactive proofs for BQP via self-tested graph states
• Continuous-variable blind quantum computation
• Efficient Verification of Hypergraph States
• Device-Independent Quantum Key Distribution with Local Bell Test
• Verified measurement-based quantum computing with hypergraph states
• Self-guaranteed measurement-based quantum computation
• Verifiable fault-tolerance in measurement-based quantum computation
• Quantum de Finetti theorem under fully-one-way adaptive measurements
• Capacity estimation and verification of quantum channels with arbitrarily correlated errors
• Efficient and Effective Quantum Compiling for Entanglement-based Machine Learning on IBM Q Devices

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