Measurement-Driven Quantum Advantages in Shallow Circuits

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.