Classically Sampling Noisy Quantum Circuits in Quasi-Polynomial Time under Approximate Markovianity

2025-10-07

AI Summary

This work investigates whether quantum advantage in noisy quantum circuits subject to local depolarizing noise remains beyond efficient classical simulation. To address this, we introduce a novel method that characterizes the circuit’s noise structure via approximate Markovianity—a property we rigorously prove holds for broad classes of random circuits, both shallow and deep. Leveraging this characterization, we design a quasipolynomial-time sampling algorithm that approximates the output distribution layer-by-layer, thereby surpassing the applicability limits of prior classical simulation techniques. Numerical experiments and analytical analysis demonstrate that our algorithm successfully simulates previously intractable noisy quantum circuits. Our results reveal that noise generically degrades—and in many cases completely eliminates—quantum advantage, substantially extending the theoretical boundary of classically simulatable regimes.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a classical algorithm that runs in $n^{ m{polylog}(n)}$ time for simulating quantum circuits under local depolarizing noise, thereby ruling out their quantum advantage in these settings. Our algorithm leverages a property called approximate Markovianity to sequentially sample from the measurement outcome distribution of noisy circuits. We establish approximate Markovianity in a broad range of circuits: (1) we prove that it holds for any circuit when the noise rate exceeds a constant threshold, and (2) we provide strong analytical and numerical evidence that it holds for random quantum circuits subject to any constant noise rate. These regimes include previously known classically simulable cases as well as new ones, such as shallow random circuits without anticoncentration, where prior algorithms fail. Taken together, our results significantly extend the boundary of classical simulability and suggest that noise generically enforces approximate Markovianity and classical simulability, thereby highlighting the limitation of noisy quantum circuits in demonstrating quantum advantage.

Problem

• Simulating noisy quantum circuits classically in quasi-polynomial time
• Establishing classical simulability under local depolarizing noise conditions
• Extending boundaries where quantum advantage is ruled out by noise

Innovation

• Classical algorithm samples noisy quantum circuits quasi-polynomially
• Leverages approximate Markovianity for sequential sampling
• Applies to circuits with constant depolarizing noise rate