[Paper Review] Classical Simulation of Intermediate-Size Quantum Circuits

Jianxin Chen, Fang Zhang+3 more|arXiv (Cornell University)|May 3, 2018

Quantum Computing Algorithms and ArchitectureComputer Science75 citations

TL;DR

The paper presents a distributed classical simulator for general quantum circuits, achieving new barriers in simulating intermediate-size circuits and providing evidence that quantum supremacy may be difficult to achieve in low-depth random circuits. It demonstrates speedups on Alibaba’s cluster and analyzes implications for quantum advantage under realistic noise.

ABSTRACT

We introduce a distributed classical simulation algorithm for general quantum circuits, and present numerical results for calculating the output probabilities of universal random circuits. We find that we can simulate more qubits to greater depth than previously reported using the cluster supported by the Data Infrastructure and Search Technology Division of the Alibaba Group. For example, computing a single amplitude of an $8 imes 8$ qubit circuit with depth $40$ was previously beyond the reach of supercomputers. Our algorithm can compute this within $2$ minutes using a small portion ($\approx$ 14% of the nodes) of the cluster. Furthermore, by successfully simulating quantum supremacy circuits of size $9 imes 9 imes 40$, $10 imes 10 imes 35 $, $11 imes 11 imes 31$, and $12 imes 12 imes 27 $, we give evidence that noisy random circuits with realistic physical parameters may be simulated classically. This suggests that either harder circuits or error-correction may be vital for achieving quantum supremacy from random circuit sampling.

Motivation & Objective

• Motivate and enable verification of quantum processors by pushing classical simulation boundaries in the NISQ era.
• Develop a cluster-friendly tensor-network–based simulator that computes single amplitudes efficiently.
• Explore how graph-based treewidth and parallelization over key variables impact simulation feasibility.
• Assess implications for quantum supremacy by testing random circuit sampling under realistic noise assumptions.

Proposed method

• Adapt variable-elimination-based tensor-network contraction to a cluster setting, focusing on treewidth as the main complexity factor.
• Construct an undirected graphical model representation of an arbitrary circuit’s amplitude with diagonal gates simplifying the graph.
• Parallelize by fixing values of high-impact variables to create subtasks that can be evaluated concurrently.
• Use QuickBB to estimate elimination orderings and treewidth to guide both graph simplification and subtask allocation.
• Partition tasks into subtasks to balance memory and compute across many nodes, using a greedy strategy to select vertices for removal based on estimated base algorithm cost.

Experimental results

Research questions

• RQ1 Can a distributed classical simulator compute single amplitudes for intermediate-size quantum circuits efficiently on a large cluster?
• RQ2 How can graph-based contraction and parallelization over key variables push the practical limits of classical simulation for quantum circuits?
• RQ3 Do noisy random circuits with realistic gate fidelities remain classically simulable under the proposed framework, challenging quantum supremacy in the low-depth regime?

Key findings

• The simulator can compute a single amplitude for an 8x8 qubit circuit with depth 40 in about 2 minutes using roughly 14% of the cluster.
• Simulations of quantum supremacy circuits of sizes up to 9x9x40, 10x10x35, 11x11x31, and 12x12x27 were demonstrated, providing evidence that noisy random circuits may be simulable classically under plausible physical parameters.
• The approach pushes the boundary of what can be simulated on a cluster with 10,000 machines, each with substantial CPU cores and memory, highlighting the role of treewidth and parallelization in feasibility.
• The results support the view that quantum supremacy in this specific framework may require either harder circuits or error correction to be achievable.