[Paper Review] Recursive Multi-Tensor Contraction for XEB Verification of Quantum Circuits

Gleb Kalachev, Pavel Panteleev+1 more|arXiv (Cornell University)|Aug 12, 2021

Parallel Computing and Optimization Techniques3 references4 citations

TL;DR

This paper introduces a recursive multi-tensor contraction algorithm that dramatically reduces the computational cost of calculating linear cross-entropy (XEB) fidelities for quantum circuits, enabling exact XEB verification up to 16 cycles on the 53-qubit Sycamore chip using only moderate GPU resources. When scaled to the Summit supercomputer, the method estimates XEB computation for 20-cycle circuits in just 7.5 days—orders of magnitude faster than prior estimates.

ABSTRACT

The computational advantage of noisy quantum computers have been demonstrated by sampling the bitstrings of quantum random circuits. An important issue is how the performance of quantum devices could be quantified in the so-called regime. The standard approach is through the linear cross entropy (XEB), where the theoretical value of the probability is required for each bitstring. However, the computational cost of XEB grows exponentially. So far, random circuits of the 53-qubit Sycamore chip was verified up to 10 cycles of gates only; the XEB fidelities of deeper circuits were approximated with simplified circuits instead. Here we present a multi-tensor contraction algorithm for speeding up the calculations of XEB of quantum circuits, where the computational cost can be significantly reduced through a recursive manner with some form of memoization. As a demonstration, we analyzed the experimental data of the 53-qubit Sycamore chip and obtained the exact values of the corresponding XEB fidelities up to 16 cycles using only moderate computing resources (few GPUs). If the algorithm was implemented on the Summit supercomputer, we estimate that for the 20-cycles supremacy circuits, it would only cost 7.5 days, which is several orders of magnitudes lower than previously estimated in the literature.

Motivation & Objective

• To address the exponential computational cost of exact XEB fidelity evaluation for deep quantum circuits.
• To enable precise verification of quantum supremacy circuits beyond the 10-cycle limit previously achievable.
• To reduce the resource requirements for XEB calculations using tensor network optimization techniques.
• To provide a scalable and efficient method for benchmarking noisy intermediate-scale quantum (NISQ) devices.

Proposed method

• The method employs recursive multi-tensor contraction to compute the XEB fidelity by systematically contracting tensor networks representing quantum circuits.
• It incorporates memoization to avoid redundant computation during tensor contractions, significantly reducing time complexity.
• The algorithm is designed to exploit structural symmetries and sparsity in quantum circuit tensors to accelerate evaluation.
• It leverages GPU-accelerated tensor operations to achieve high performance on moderate-scale hardware.
• The approach enables exact computation of XEB values without relying on approximations or simplified circuit models.
• The method is benchmarked on the 53-qubit Sycamore circuit, extending fidelity verification beyond prior limits.

Experimental results

Research questions

• RQ1 Can XEB fidelity be computed exactly for deeper quantum circuits beyond the 10-cycle threshold?
• RQ2 How much can recursive tensor contraction with memoization reduce the computational cost of XEB evaluation?
• RQ3 What is the practical feasibility of computing XEB for 20-cycle Sycamore circuits using current high-performance hardware?
• RQ4 To what extent can GPU-accelerated tensor network methods outperform prior classical simulation approaches for XEB?
• RQ5 Can exact XEB values be obtained for experimental data without relying on circuit simplifications?

Key findings

• The proposed algorithm enables exact XEB fidelity computation for the 53-qubit Sycamore circuit up to 16 cycles using only moderate computing resources, including a few GPUs.
• The method reduces the estimated time to compute XEB for 20-cycle circuits to 7.5 days when run on the Summit supercomputer, a significant improvement over prior estimates.
• The use of recursive contraction with memoization leads to a substantial reduction in computational cost compared to naive tensor contraction approaches.
• The algorithm achieves exact XEB values without relying on approximations or simplified circuit models, improving fidelity verification accuracy.
• The results demonstrate that exact XEB evaluation for deep quantum circuits is feasible with optimized tensor network techniques and modern HPC infrastructure.