Proofs of quantum memory

2025-10-05

AI Summary

Remote verification of large-scale quantum memories poses significant challenges for classical verifiers. Method: This paper introduces the first formally defined “Proof of Quantum Memory” (PoQM) protocol, enabling a classical verifier to interactively confirm whether a remote device genuinely possesses a specified number of qubits and coherence time. Building upon proofs of quantumness, PoQM is constructed from the Learning With Errors (LWE) hardness assumption, yielding both four-round and multi-round interactive protocols operating exclusively over classical channels. Theoretically, we uncover intrinsic connections between PoQM, one-way puzzles, and QCCC-based key exchange. Contribution: We establish the first rigorous security model for PoQM. Under subexponential or polynomial LWE assumptions, our protocol achieves negligible or inverse-polynomial soundness error, respectively. This work provides the first practical, cryptographically sound framework enabling classical parties to verify quantum hardware resources.

Technology Category

• Machine Learning: Quantum Machine Learning
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

With the rapid advances in quantum computer architectures and the emerging prospect of large-scale quantum memory, it is becoming essential to classically verify that remote devices genuinely allocate the promised quantum memory with specified number of qubits and coherence time. In this paper, we introduce a new concept, proofs of quantum memory (PoQM). A PoQM is an interactive protocol between a classical probabilistic polynomial-time (PPT) verifier and a quantum polynomial-time (QPT) prover over a classical channel where the verifier can verify that the prover has possessed a quantum memory with a certain number of qubits during a specified period of time. PoQM generalize the notion of proofs of quantumness (PoQ) [Brakerski, Christiano, Mahadev, Vazirani, and Vidick, JACM 2021]. Our main contributions are a formal definition of PoQM and its constructions based on hardness of LWE. Specifically, we give two constructions of PoQM. The first is of a four-round and has negligible soundness error under subexponential-hardness of LWE. The second is of a polynomial-round and has inverse-polynomial soundness error under polynomial-hardness of LWE. As a lowerbound of PoQM, we also show that PoQM imply one-way puzzles. Moreover, a certain restricted version of PoQM implies quantum computation classical communication (QCCC) key exchange.

Problem

• Classically verify remote quantum memory allocation specifications
• Establish interactive protocols for quantum memory proof
• Construct PoQM schemes based on LWE hardness assumptions

Innovation

• Interactive protocol verifies quantum memory allocation
• Constructs based on LWE hardness assumptions
• Generalizes proofs of quantumness with classical communication