A game of quantum advantage: linking verification and simulation

  title={A game of quantum advantage: linking verification and simulation},
  author={Daniel Stilck França and Ra{\'u}l Garc{\'i}a-Patr{\'o}n},
We present a formalism that captures the process of proving quantum superiority to skeptics as an interactive game between two agents, supervised by a referee. Bob, is sampling from a classical distribution on a quantum device that is supposed to demonstrate a quantum advantage. The other player, the skeptical Alice, is then allowed to propose mock distributions supposed to reproduce Bob's device's statistics. He then needs to provide witness functions to prove that Alice's proposed mock… 

Exponentially tighter bounds on limitations of quantum error mitigation

Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing by classically post-processing outcomes of multiple quantum circuits. It



On the complexity and verification of quantum random circuit sampling

Evidence is provided that quantum random circuit sampling, a near-term quantum computational task, is classically hard but verifiable, making it a leading proposal for achieving quantum supremacy.

Simpler Proofs of Quantumness

A two-message (challenge-response) proof of quantumness based on any trapdoor claw-free function is given, which allows the use of smaller security parameters and more diverse computational assumptions, significantly reducing the quantum computational effort required for a successful demonstration.

Complexity-Theoretic Foundations of Quantum Supremacy Experiments

General theoretical foundations are laid for how to use special-purpose quantum computers with 40--50 high-quality qubits to demonstrate "quantum supremacy": that is, a clear quantum speedup for some task, motivated by the goal of overturning the Extended Church-Turing Thesis as confidently as possible.

Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

  • M. BremnerR. JozsaD. Shepherd
  • Computer Science, Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2010
The class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection is introduced, and it is proved first that post- IQP equals the classical class PP, and that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, then the infinite tower of classical complexity classes known as the polynomial hierarchy would collapse to its third level.

Constant-round Blind Classical Verification of Quantum Sampling

A simple yet powerful generic compiler is provided that transforms any CVQC protocol to a blind one while preserving its completeness and soundness errors as well as the number of rounds.

Classical Simulation of Quantum Supremacy Circuits

It is shown that achieving quantum supremacy may require a period of continuing quantum hardware developments without an unequivocal first demonstration, and an orders-of-magnitude reduction in classical simulation time is indicated.

Limitations of Linear Cross-Entropy as a Measure for Quantum Advantage

The results demonstrate that XEB’s utility as a proxy for fidelity hinges on several conditions, which should be independently checked in the benign setting, but cannot be assumed in the general adversarial setting, and therefore, the XEB on its own has a limited Utility as a benchmark for quantum advantage.

Sample Complexity of Device-Independently Certified "Quantum Supremacy".

It is shown that any noninteractive certification from classical samples and a description of the target distribution requires exponentially many uses of the device, and that the sampling distributions, as random variables depending on the random unitaries defining the problem instances, have small second moments.

Characterizing quantum supremacy in near-term devices

A critical question for quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of

Closing Gaps of a Quantum Advantage with Short-Time Hamiltonian Dynamics.

This work provides the strongest theoretical evidence to date that Hamiltonian quantum simulators are classically intractable, building upon recently developed techniques for random circuit sampling.