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This study introduces a novel measurement-driven quantum circuit approach for efficient sampling. It demonstrates quantum advantage using midcircuit measurements on bounded-degree hardware, offering speedups for complex quantum dynamics.

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Area of Science:

  • Quantum Computing and Information Theory
  • Computational Complexity

Background:

  • Quantum advantage schemes explore the limits of classical simulation for quantum dynamics.
  • Midcircuit measurements are crucial for enhancing the computational power of quantum circuits.

Purpose of the Study:

  • To investigate the impact of midcircuit measurements on quantum circuit computational power.
  • To develop an efficient, constant-depth, measurement-driven approach for quantum sampling.

Main Methods:

  • Introduced a constant-depth measurement-driven circuit for sampling commuting diagonal quantum circuits.
  • Utilized randomized 'fan-out staircases' with midcircuit measurements and feedforward.
  • Demonstrated measurement-driven feature maps for quantum machine learning benchmarks.

Main Results:

  • Achieved efficient sampling from structured phase states previously requiring polynomial-depth unitary circuits.
  • Generated phase states with random-matrix statistics and anticoncentration properties.
  • Successfully distinguished phases of an extended Su-Schrieffer-Heeger model in a reservoir computing benchmark.

Conclusions:

  • Midcircuit measurements enable quantum advantage on bounded-degree hardware with favorable topology.
  • This approach bypasses Lieb-Robinson light-cone constraints, allowing global entanglement.
  • Provides complexity-theoretic evidence for quantum speedups enabled by midcircuit measurements.