Efficiently Verifiable Quantum Advantage on Near-Term Analog Quantum Simulators

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on verification of an analog quantum simulation, in which the verifier need only run an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>O</a:mi><a:mo stretchy="false">(</a:mo><a:msup><a:mi>λ</a:mi><a:mn>2</a:mn></a:msup><a:mo stretchy="false">)</a:mo></a:math>-time classical computation, and the prover need only prepare <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><f:mi>O</f:mi><f:mo stretchy="false">(</f:mo><f:mn>1</f:mn><f:mo stretchy="false">)</f:mo></f:math> samples of a history state and perform <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><k:mi>O</k:mi><k:mo stretchy="false">(</k:mo><k:msup><k:mi>λ</k:mi><k:mn>2</k:mn></k:msup><k:mo stretchy="false">)</k:mo></k:math> single-qubit measurements, for a security parameter <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><p:mi>λ</p:mi></p:math>. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.