[Paper Review] Fast classical simulation of evidence for the utility of quantum computing before fault tolerance

Tomislav Begušić, Garnet Kin‐Lic Chan|arXiv (Cornell University)|Jun 28, 2023

Quantum Computing Algorithms and Architecture15 citations

TL;DR

The paper presents a sparse Pauli dynamics method that classically simulates 127-qubit quantum circuits more efficiently than the quantum hardware experiments, matching zero-noise extrapolated results and outperforming prior MPS approaches.

ABSTRACT

We show that a classical algorithm based on sparse Pauli dynamics can efficiently simulate quantum circuits studied in a recent experiment on 127 qubits of IBM's Eagle processor [Nature 618, 500 (2023)]. Our classical simulations on a single core of a laptop are orders of magnitude faster than the reported walltime of the quantum simulations, as well as faster than the estimated quantum hardware runtime without classical processing, and are in good agreement with the zero-noise extrapolated experimental results.

Motivation & Objective

• Motivate the need to assess quantum advantage before fault tolerance using classical simulations.
• Develop and apply a Clifford-perturbation-theory-based method to simulate non-Clifford quantum circuits.
• Demonstrate that sparse Pauli dynamics can reproduce or approximate results from recent large-quircuit experiments.
• Compare classical SPD results with exact, quantum hardware, and MPS/isoTNS simulations to establish accuracy and efficiency.

Proposed method

• Transform the circuit to express non-Clifford rotations in terms of rotated Pauli operators via Clifford transformations.
• Rewrite non-Clifford Pauli rotations to isolate near-Clifford structure and apply angle transformations to simplify into single-qubit Pauli operators when possible.
• Execute Heisenberg evolution of observables in the Pauli basis under the sparse Pauli dynamics expansion, truncating the growing Pauli set at a chosen order K.
• Represent the evolved observable as a weighted sum of Pauli terms and update coefficients using a recurrence that accounts for commutation with new gates.
• Discard Pauli terms with index greater than K to control computational cost and approximate the expectation value efficiently.
• Implement a Python (Qiskit) implementation to compute observables such as magnetization and weight-10/weight-17 observables for circuits with multiple Trotter steps.

Experimental results

Research questions

• RQ1 Can sparse Pauli dynamics (SPD) faithfully approximate expectation values of large, near-Clifford quantum circuits before fault tolerance?
• RQ2 How does SPD compare in accuracy and efficiency to exact methods, tensor-network simulations, and quantum hardware results for IBM Eagle-like circuits?
• RQ3 What is the impact of truncation order K on accuracy and runtime in simulating non-Clifford gate layers?
• RQ4 To what extent do near-Clifford structures in realistic circuits permit efficient classical simulation without exploiting device connectivity?

Key findings

• SPD simulations on a single laptop core reproduce zero-noise extrapolated quantum results within controlled truncation errors.
• Each data point in the study takes about 1–2 minutes on a single CPU core, far faster than the quantum wallclock times reported in the referenced experiments.
• SPD is two orders of magnitude faster than the reported quantum wallclock run times and faster than the hypothesized classical runtime without processing, for the presented figures.
• With truncation orders K=10 (for some observables) and K=6 (for others), SPD results are generally within the estimated quantum-experiment errors and surpass the prior MPS results in accuracy.
• The method does not rely on specific qubit connectivity and does not require low entanglement, illustrating a broader potential for classical approximation methods.
• The results corroborate that classical SPD can faithfully simulate the quantum experiments on IBM’s Eagle processor, offering a competitive alternative to tensor-network approaches for these circuits.