Classical Verification of Quantum Computation with Quasilinear Resources, from Compiled Nonlocal Games

arXiv:2609.38060 · quant-ph, cs.CR · Submitted 2026-09-29 · Read on arXiv

quant-ph, cs.CR

Submitted: 2026-09-29

Updated: 2026-09-29

Terminology

• Verifier — 83× in this paper · explained in 2 episodes
• Consistency — 79× in this paper · explained in 3 episodes
• Self-consistency — 35× in this paper · explained in 2 episodes
• Verification — 35× in this paper · explained in 2 episodes
• Hilbert Space — 27× in this paper · explained in 2 episodes
• Trace — 26× in this paper · explained in 2 episodes
• Entanglement — 22× in this paper · explained in 4 episodes
• BQP — 19× in this paper · explained in 2 episodes
• Robustness — 10× in this paper · explained in 5 episodes
• Block Encoding — 7× in this paper · explained in 4 episodes
• Foundations of Computer Science — 5× in this paper
• Quantum Circuits — 5× in this paper · explained in 2 episodes
• Ancilla Qubits — 3× in this paper · explained in 1 episode
• BQP-complete — 2× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes
• Trace Distance — 1× in this paper · explained in 3 episodes
• Verifiability — 1× in this paper · explained in 2 episodes

Sources

• The Quantum PCP Conjecture
• Improved Simulation of Stabilizer Circuits
• An inequality for the trace of matrix products, using absolute values
• Analysis and limitations of modified circuit-to-Hamiltonian constructions
• A Cryptographic Test of Quantumness and Certifiable Randomness from a Single Quantum Device
• Universal Quantum Circuits
• On the Power of Oblivious State Preparation
• How to Verify a Quantum Computation
• Self-testing of Pauli observables for device-independent entanglement certification
• Verifier-on-a-Leash: new schemes for verifiable delegated quantum computation, with quasilinear resources
• Consequences and Limits of Nonlocal Strategies
• A Computational Tsirelson's Theorem for the Value of Compiled XOR Games
• Operator algebraic approach to inverse and stability theorems for amenable groups
• Spectral gap and stability for groups and non-local games
• Reducing resources for verification of quantum computations
• Parallel self-testing of EPR pairs under computational assumptions
• Inverse and stability theorems for approximate representations of finite groups
• Robustness and device independence of verifiable blind quantum computing
• Quantum cryptography with classical communication: parallel remote state preparation for copy-protection, verification, and more
• A simple protocol for verifiable delegation of quantum computation in one round

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity