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Trading Locality for Time: Certifiable Randomness from Low-Depth Circuits.

Matthew Coudron1, Jalex Stark2, Thomas Vidick3

  • 1National Institute of Standards and Technology/QuICS, University of Maryland, College Park, USA.

Communications in Mathematical Physics
|March 22, 2021
PubMed
Summary
This summary is machine-generated.

We present a new quantum protocol for generating certified random bits using a single quantum device. This method offers robust randomness expansion with efficient classical verification, demonstrating a quantum advantage without relying on complexity-theoretic conjectures.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Information Theory

Background:

  • Certifiable randomness generation is a key differentiator between quantum and classical devices.
  • Existing randomness certification methods often rely on Bell inequality violations or computational assumptions.
  • There is a need for robust quantum advantage demonstrations with practical verification.

Purpose of the Study:

  • To propose a protocol for exponential certified randomness expansion using a single quantum device.
  • To establish a new framework for robust randomness expansion inspired by relational problems.
  • To offer a quantum advantage proposal with advantages in verification and noise tolerance.

Main Methods:

  • Implementing a simple quantum circuit of constant depth on a 2D lattice of qubits.
  • Verifying the output classically in linear time.
  • Leveraging a relational problem solvable by constant-depth quantum circuits but not sub-logarithmic depth classical circuits.

Main Results:

  • The protocol guarantees a polynomial number of certified random bits under a sub-logarithmic depth assumption for the device.
  • Demonstrates randomness generation by sampling from the ideal output distribution within constant statistical distance.
  • Achieves robustness against noise, allowing for a small constant additive error in total variation distance.

Conclusions:

  • The proposed protocol offers a novel approach to demonstrated quantum advantage.
  • It relies on a physical assumption (sub-logarithmic depth) rather than complexity-theoretic conjectures.
  • The method provides efficient classical verification and enhanced noise tolerance compared to existing proposals.