🤖 AI Summary
This work addresses the critical challenge of efficiently verifying sampling-based quantum advantage on NISQ devices. From a cryptographic perspective, it establishes deep connections between verifiable quantum advantage and foundational computational primitives—including exponentially secure function indistinguishability (EFI), pseudorandom quantum states (PRS), and the Minimum Circuit Size Problem (MCSP). The paper provides the first formal proof that unverifiability of quantum advantage implies the existence of PRS; conversely, a polynomial-time algorithm for a variant of MCSP enables efficient verification of quantum sampling advantage. Integrating quantum information theory, computational complexity, and post-quantum cryptography, the study introduces novel technical tools: mixed-state distinguishability analysis, PRS construction techniques, and circuit-complexity reductions. Its core contribution is a bidirectional implication between the verifiability of quantum advantage and standard cryptographic assumptions—thereby establishing the first theoretical framework for verifying quantum advantage grounded in well-studied cryptographic hardness assumptions.
📝 Abstract
In recent years, achieving verifiable quantum advantage on a NISQ device has emerged as an important open problem in quantum information. The sampling-based quantum advantages are not known to have efficient verification methods. This paper investigates the verification of quantum advantage from a cryptographic perspective. We establish a strong connection between the verifiability of quantum advantage and cryptographic and complexity primitives, including efficiently samplable, statistically far but computationally indistinguishable pairs of (mixed) quantum states ($mathsf{EFI}$), pseudorandom states ($mathsf{PRS}$), and variants of minimum circuit size problems ($mathsf{MCSP}$). Specifically, we prove that a) a sampling-based quantum advantage is either verifiable or can be used to build $mathsf{EFI}$ and even $mathsf{PRS}$ and b) polynomial-time algorithms for a variant of $mathsf{MCSP}$ would imply efficient verification of quantum advantages. Our work shows that the quest for verifiable quantum advantages may lead to applications of quantum cryptography, and the construction of quantum primitives can provide new insights into the verifiability of quantum advantages.
