aiqbench analysis
This research proposes a verifiable quantum advantage protocol using IQP circuits defined by cubic polynomials with planted independent spaces, aiming to bridge the gap between resource requirements and classical verifiability. The authors conjecture that these specific structures remain invisible to computationally bounded adversaries, enabling a polynomial time difference between verification and classical simulation for tasks requiring exponential resources. Additionally, the scheme offers potential applications in generating classically certifiable randomness through output distributions with high min-entropy, estimated to be feasible with approximately 100 logical qubits.
Verifiable quantum advantage based on polynomials with planted structures
arXiv:2609.39918v1 Announce Type: new Abstract: A central question in the theory of quantum advantage is whether there are quantum advantage protocols with similar resource requirements as random circuit sampling that are also verifiable just from the classical outputs of the quantum computation. Here, we develop the idea of simulation secrets for verifiable advantage. A verifier can use a simulation secret to evaluate a cross-entropy test faster than it would take a classical adversary to pass the test. We instantiate this idea using IQP circuits described by cubic polynomials with planted independent spaces. These correspond to the largest independent set in the orbit of a polynomial under the general linear group and yield a low-rank stabilizer decomposition of the corresponding state. We conjecture that large independent spaces are invisible to a computationally bounded adversary, and therefore they cannot exploit them to pass the protocol. A second conjecture regards the fine-grained complexity of producing samples that pass the cross-entropy test for uniformly random polynomials. Under these conjectures, our scheme results in a polynomial gap between the verification time and the time a classical adversary would need to pass the protocol---both are exponential. It has a potential application to generating classically certifiable randomness, since the output distributions have high min-entropy. We estimate that the planted polynomial scheme is implementable using 100 logical qubits at logical error rates around $10^{-6}$.
Abstract:A central question in the theory of quantum advantage is whether there are quantum advantage protocols with similar resource requirements as random circuit sampling that are also verifiable just from the classical outputs of the quantum computation. Here, we develop the idea of simulation secrets for verifiable advantage. A verifier can use a simulation secret to evaluate a cross-entropy test faster than it would take a classical adversary to pass the test. We instantiate this idea using IQP circuits described by cubic polynomials with planted independent spaces. These correspond to the largest independent set in the orbit of a polynomial under the general linear group and yield a low-rank stabilizer decomposition of the corresponding state. We conjecture that large independent spaces are invisible to a computationally bounded adversary, and therefore they cannot exploit them to pass the protocol. A second conjecture regards the fine-grained complexity of producing samples that pass the cross-entropy test for uniformly random polynomials. Under these conjectures, our scheme results in a polynomial gap between the verification time and the time a classical adversary would need to pass the protocol---both are exponential. It has a potential application to generating classically certifiable randomness, since the output distributions have high min-entropy. We estimate that the planted polynomial scheme is implementable using 100 logical qubits at logical error rates around $10^{-6}$.
44 pages, 1 figure. Comments welcome
Quantum Physics (quant-ph); Computational Complexity (cs.CC); Cryptography and Security (cs.CR); Data Structures and Algorithms (cs.DS)
arXiv:2609.39918 [quant-ph]
(or arXiv:2609.39918v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.39918 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 333 words
