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arXiv:2608.13110

Classical Simulation and Design Frontiers for IBM's Doped Clifford Sampling Experiment

Hidetaka Manabe, Hanfeng Gu, Feng Pan

quant-phSubmitted Aug 13, 2026• Announced Aug 14, 2026• 0 citations• Revised Oct 29, 2026 (v2)
v1 · Aug 13, 2026v2 · Oct 29, 2026
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Abstract

We classically simulate the IBM doped Clifford random circuit sampling experiment, comprising $70$ qubits, $70$ entangling layers, and $468$ inserted $T$ gates, as reported in the first version of arXiv:2607.25941. A deterministic temporal-boundary tensor network contraction approach is specifically designed to tackle such open-boundary one-dimensional brickwork circuits with operator-Schmidt-rank-$2$ entangling gates. For an $n$-qubit circuit of depth $d$, the resulting unsliced path evaluates an exact amplitude with contraction width $\lceil d/2\rceil$; Ratcatcher calculations certify that no smaller width is possible for the tested instances. Because one-qubit gates are absorbed without changing the network topology, the width and dense scheduled contraction cost are independent of their values and of the number and placement of $T$ gates. For this initial instance, its largest intermediate tensor contains $2^{35}$ complex64 entries (256 times smaller than IBM's estimation), corresponding to a tensor payload of $256$ GiB, and is distributed across eight GPUs within a node. Using 32 nodes, with eight NVIDIA H100 GPUs per node, we completed all 2051 amplitude batches corresponding to IBM's published output bitstrings in 37.3 minutes. The resulting probabilities yield a log-XEB estimate of $0.35034$ with a 95% interval of $[0.29763,0.40305]$. Under the Porter--Thomas and scrambled-noise assumptions, this is numerically compatible with IBM's fidelity lower bound; separately, fidelity-weighted resource accounting projects a 583-contraction workload with a 10.6-minute makespan on the same 32 nodes. More broadly, the approach provides a practical diagnostic for experimental outputs and a quantitative tool for designing future doped Clifford sampling experiments.

Comments
25 pages, 12 figures

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Determining the quantum-classical boundary between quantum circuits that can be efficiently simulated classically and those that cannot remains a fundamental question. One approach to classical simulation is to represent the output of a quantum circuit as a Clifford-augmented matrix product state (CAMPS), which, via a disentangling algorithm, decomposes the wave function into Clifford and MPS components, and from which Pauli expectation values can be computed in time polynomial in the MPS bond dimension. In this work, we develop an optimization-free disentangling (OFD) algorithm for Clifford circuits either doped with T gates or, equivalently, preceded by multiqubit gates of the form α I + β P . We give a simple and easily computed algebraic criterion that characterizes the individual quantum circuits for which OFD generates an efficient CAMPS—the bond dimension is exponential in the null space of a Galois binary field GF(2) matrix induced by a tableau of the twisted Pauli strings P . This significantly increases the number of circuits with rigorous polynomial-time classical simulations. We also give evidence that the typical N qubit random Clifford circuit doped with N uniformly distributed T gates of polylogarithmic depth or greater has a CAMPS with polynomial bond dimension. In addition, we compare OFD against disentangling by optimization. We further explore the representability of CAMPS for random Clifford circuits doped with more than N T gates. We also propose algorithms for sampling, probability, and amplitude estimation of bitstrings, and evaluation of entanglement Rényi entropy from CAMPS, which, though still having exponential complexity, are more efficient than standard MPS simulations. This work establishes a versatile framework for understanding classical simulatability of Clifford + T circuits and explores the interplay between quantum entanglement and quantum magic in quantum systems.
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A feasibility study testing whether quantum circuits can be constructedwhere exact classical simulation cost grows much faster than the physicalcircuit depth needed to run them, using output-aware tensor-networkcontraction validated against two real IBM Quantum hardware jobs(dadm3mjdd5gc73d7gvjg, dadm9qdnj4cs73ae2teg; 40,960 shots total). The honest conclusion is no — not on any hardware available today. Reachingthat conclusion required correcting the study's own conclusions six times;those corrections, and the measurements behind them, are the primarycontribution. Key measured results: classical contraction cost scales as 2^w withmeasured exponent 1.984; effective two-qubit error on IBM's Heronarchitecture is gate-local at 0.845%, reproducible across two independentjobs; memory is not a binding constraint once slicing is applied (1.00-3.18xFLOP penalty); connectivity degree, not planarity, is the dominanttopological lever; standard error suppression (dynamical decoupling +twirling) made fidelity worse on this circuit class; qubit count sets a hardceiling on achievable classical hardness (2^n). This is a feasibility study, not an advantage claim: no quantum advantage,no novel algorithm (frontier contraction is textbook variable elimination),and no verified large-width result are claimed. Full reproducibility scriptsincluded.