We present verification protocols to gain confidence in the correct performance of a device implementing an arbitrary quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are classically efficiently simulable, become universal if supplemented with additional resources. We combine tools from weak simulation, randomized compiling, and statistics to derive verification circuits that (i) strongly resemble the original circuit and (ii) can be classically efficiently simulated not only in the ideal, i.e., error free scenario, but also in the realistic situation where errors are present. In fact, in one of the protocols we apply exactly the same circuit as in the original computation, however, to a slightly modified input state. Published by the American Physical Society 2024
We present verification protocols to gain confidence in the correct performance of a device implementing an arbitrary quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are classically efficiently simulable, become universal if supplemented with additional resources. We combine tools from weak simulation, randomized compiling, and statistics to derive verification circuits that (i) strongly resemble the original circuit and (ii) can be classically efficiently simulated not only in the ideal, i.e., error free scenario, but also in the realistic situation where errors are present. In fact, in one of the protocols we apply exactly the same circuit as in the original computation, however, to a slightly modified input state. Published by the American Physical Society 2024
We present verification protocols to gain confidence in the correct performance of the realization of an arbitrary universal quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are classically efficiently simulable, become universal if supplemented with additional resources. We combine tools from weak simulation, randomized compiling, and classical statistics to derive verification circuits. These circuits have the property that (i) they strongly resemble the original circuit and (ii) cannot only be classically efficiently simulated in the ideal, i.e. error free, scenario, but also in the realistic situation where errors are present. In fact, in one of the protocols we apply exactly the same circuit as in the original computation, however, to a slightly modified input state.
Recently proposed schemes for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers, have been based on adaptations of the classical theory of interactive proof systems (IP). These schemes remarkably provide confidence against arbitrarily malicious adversarial behaviour in the misfunctioning of the quantum computing device in the course of the verification protocol. Here we propose a different verification scheme which although not secure against arbitrarily adversarial behaviour, may nevertheless be sufficiently acceptable in many practical situations. Our scheme is far simpler than the IP based schemes, and in contrast to them, our verifier is entirely classical. It is based on the fact that adaptive Clifford circuits on general product state inputs provide universal quantum computation, while the same processes without adaptation are always classically efficiently simulatable.
We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious adversarial behaviour in the misfunctioning of the quantum computing device. Our scheme is not secure against arbitrarily adversarial behaviour, but may nevertheless be sufficiently acceptable in many practical situations. With this concession we gain in manifest simplicity and transparency, and in contrast to previous schemes, our verifier is entirely classical. It is based on the fact that adaptive Clifford circuits on general product state inputs provide universal quantum computation, while the same processes without adaptation are always classically efficiently simulatable.
This research paper provides an in-depth examination of verification and testing approaches for quantum circuits, focusing on methodologies essential for ensuring the correctness, reliability and operational efficiency of quantum computing systems. Since quantum circuits function on the fundamental principles of superposition and entanglement, they present verification challenges that cannot be effectively addressed using conventional classical testing techniques. As a result, the development of specialized quantum-specific verification strategies has become critically important. The study highlights simulation-based verification as a foundational technique, wherein the outcomes of quantum circuit simulations are systematically compared with results obtained from physical quantum hardware. This process enables the identification of functional inconsistencies and supports iterative refinement of circuit designs. In addition, randomized benchmarking is examined as a key evaluation method for estimating circuit fidelity and quantifying error rates through the application of random gate sequences and performance comparisons against established benchmarks. To further improve system robustness, the research investigates fault-tolerant mechanisms, particularly quantum error correction codes, which play a vital role in minimizing the effects of noise, decoherence and hardware imperfections. The integration of advanced quantum metrology and characterization techniques is also explored, enabling precise measurement and detailed analysis of quantum system behavior. These techniques provide deeper insights into circuit performance and contribute significantly to validation processes. By combining simulation-based verification, randomized benchmarking, fault-tolerant protocols and quantum metrology, this study proposes a comprehensive and reliable framework for quantum circuit verification and testing. The findings contribute to the advancement of dependable quantum technologies and support their growing applications in areas such as cryptography, materials science and other emerging domains.
The promise of scalable quantum technology appears more realistic, after recent advances in both theory and experiment. Assuming a quantum computer is developed, the task of verifying the correctness of its outcome becomes crucial. Unfortunately, for a system that involves many particles, predicting its evolution via classical simulation becomes intractable. Moreover, verification of the outcome by computational methods, i.e. involving a classical witness, is believed inefficient for the hardest problems solvable by a quantum computer. A feasible alternative to verify quantum computation is via cryptographic methods, where an untrusted prover has to convince a weak verifier for the correctness of his outcome. This is the approach we take in this thesis. In the most standard configuration the prover is capable of computing all polynomial-time quantum circuits and the verifier is restricted to classical with very modest quantum power. The goal of existing verification protocols is to reduce the quantum requirements for the verifier - ideally making it purely classical - and reduce the communication complexity. In Part II we propose a composition of two existing verification protocols [Fitzsimons and Kashefi, 2012], [Aharonov et al., 2010] that achieves quadratic improvement in communication complexity, while keeping the quantum requirements for the verifier modest. Along this result, several new techniques are proposed, including the generalization of [Fitzsimons and Kashefi, 2012] to prime dimensions. In Part III we discuss the idea of model-specific quantum verification, where the prover is restricted to intermediate quantum power, i.e. between full-fledged quantum and purely classical, thus more feasible experimentally. As a proof of principle we propose a verification protocol for the One-Pure-Qubit computer [Knill and Laflamme, 1998], which tolerates noise and is capable of computing hard problems such as large matrix trace estimation. The verification protocol is an adaptation of [Fitzsimons and Kashefi, 2012] running on Measurement-Based Quantum Computing with newly proved properties of the underlying resources. Connections of quantum verification to other security primitives are considered in Part IV. Authenticated quantum communication has been already proved to relate to quantum verification. We expand this by proposing a quantum authentication protocol derived from [Fitzsimons and Kashefi, 2012] and discuss implications to verification with purely classical verifier. Connections between quantum security primitives, namely blindness - prover does not learn the computation -, and classical security are considered in Part V. We introduce a protocol where a client with restricted classical resources computes blindly a universal classical gate with the help of an untrusted server, by adding modest quantum capabilities to both client and server. This example of quantum-enhanced classical security we prove to be a task classically impossible.
How can a user with limited quantum resources verify the output of an untrusted, fully quantum server? This manuscript provides a conceptual synthesis of some recent developments toward answering this question under statistical (information-theoretic) security. Rather than duplicating the dense technical proofs of the underlying publications, our focus here is on the physical motivations, the structural connections between different protocols, and the path toward hardware-efficient implementation.
We begin by introducing a modular, composable framework that partitions verification into three distinct, independent primitives: remote state preparation, trap-based deviation detection, and error-correcting embedding. Using this framework, we show how the demanding hardware requirements of early protocols can be systematically relaxed. We review schemes that eliminate the spatial overhead, remove the need to prepare computational-basis dummy states, and replace single-photon sources with trusted local rotations or weak coherent pulses. Finally, we examine how these techniques scale, both to asymmetric multi-party settings and to the delegation of fully fault-tolerant computations in the presence of gate-level noise. This document is intended as a guide to the architectural principles of practical quantum verification.