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arXiv:2511.05433

Quantum advantage from effective 200200200-qubit holographic random circuit sampling

Bingzhi Zhang, Quntao Zhuang

quant-phcs.CCSubmitted Nov 7, 2025• Announced Nov 10, 2025• 0 citations
v1 · Nov 7, 2025v2 · Apr 14, 2026
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Abstract

Quantum computers hold the promise of outperforming classical computers in solving certain problems. While large-scale quantum algorithms will require fault-tolerant devices, near-term demonstrations of quantum advantage on existing devices can provide important milestones. Random circuit sampling has emerged as a leading candidate for such demonstrations. However, existing implementations often underutilize circuit depth, limiting the achievable advantage. We introduce a holographic random circuit sampling algorithm that substantially increases the sampling complexity by leveraging repeated interactions and mid-circuit measurements. This approach scales the effective sampling dimension with the circuit depth, ultimately leading to an exponential growth in sampling complexity. With merely 20 physical qubits on IBM quantum devices, we experimentally demonstrate the effective sampling of up to 200 qubits, with a cross-entropy benchmark fidelity of $0.0593$, establishing a new route to scalable quantum advantage through the combined use of spatial and temporal quantum resources.

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9+23 pages, 4+7 figures

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Quantum computers hold the promise of outperforming classical computers in solving certain problems. While large-scale quantum algorithms will require fault-tolerant devices, near-term demonstrations of quantum advantage on existing devices can provide important milestones. Random circuit sampling has emerged as a leading candidate for such demonstrations. However, existing implementations often underutilize circuit depth, limiting the achievable advantage. We introduce a holographic random circuit sampling algorithm that substantially increases the sampling complexity by leveraging repeated interactions and mid-circuit measurements. This approach scales the effective sampling dimension with the circuit depth, ultimately leading to an exponential growth in sampling complexity. With merely 20 physical qubits on IBM quantum devices, we experimentally demonstrate the effective sampling of up to 200 qubits, with a cross-entropy benchmark fidelity of 0.05930.05930.0593, establishing a new route to scalable quantum advantage through the combined use of spatial and temporal quantum resources.
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Sampling problems give some of the clearest conditional separations between quantum and classical computation. In Fermion Sampling, passive linear optics acts on a non-Gaussian magic input. Globally Haar-random transformations give anticoncentration and high-precision average-case hardness, but require linear depth and quadratically many gates. A natural open question is whether linear depth is necessary? We show that logarithmic depth suffices for both guarantees in the same ensemble. For fresh uniform matchings with independent Haar two-mode gates, the collision reaches the passive-Haar scale at a sharp threshold of log⁡n/log⁡(9/4)≈0.855log⁡2n\log n/\log(9/4)\approx0.855\log_2 nlogn/log(9/4)≈0.855log2​n layers, with an explicit limiting transition profile and a matching lower bound from two-particle correlations. The mechanism is input-dependent: the magic input suppresses the extensive weight of the slowest relaxation mode, leaving the next to set the scale. An occupation-basis input retains large collision even under full Haar randomness. At a larger logarithmic depth, we prove, in the real-RAM model, average-case #P\#\mathsf{P}#P-hardness of estimating output probabilities to additive error 2−O(nlog⁡2n)2^{-O(n\log^2 n)}2−O(nlog2n) on any fixed fraction of instances above 3/43/43/4. We construct hard instances in four native layers, embed them in typical schedules, and interpolate along Cayley paths using a rational linear-program decoder. A finite 192192192-gate alphabet preserves the collision law exactly. Both guarantees use logarithmic native fermionic depth between arbitrary mode pairs and O(nlog⁡n)O(n\log n)O(nlogn) gates, replacing the global-Haar construction's quadratic budget. The accuracy proved is finer than the 1/N1/N1/N scale, where N=(nn/2)N=\binom{n}{n/2}N=(n/2n​), required by sampling-to-counting; hardness of sampling within constant total-variation distance remains open.
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