Efficient implementation of randomized quantum algorithms with dynamic circuits

Ikko Hamamura; Naoki Yamamoto; Qi Gao; Rudy Raymond; Shu Kanno

arxiv: 2503.17833 · v2 · submitted 2025-03-22 · 🪐 quant-ph

Efficient implementation of randomized quantum algorithms with dynamic circuits

Shu Kanno , Ikko Hamamura , Rudy Raymond , Qi Gao , Naoki Yamamoto This is my paper

Pith reviewed 2026-05-22 22:51 UTC · model grok-4.3

classification 🪐 quant-ph

keywords dynamic circuitsrandomized quantum algorithmsclassical shadowmid-circuit measurementquantum hardwarePauli measurementshydrogen chain

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The pith

Dynamic circuits let quantum hardware generate its own random selections for randomized algorithms instead of relying on classical precomputation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes an engineering method to implement randomized quantum algorithms using dynamic circuits that incorporate intermediate measurements and classical feedback. The core idea is to generate the required probability distribution directly on the quantum device, so that many different static circuits can be realized through a single dynamic circuit with repeated measurements. This approach was demonstrated on an IBM superconducting processor for random Pauli measurements on one qubit, yielding a 14,000-fold reduction in execution time compared with the conventional static-circuit method. The same technique enabled classical shadow estimation for 28- and 40-qubit hydrogen chain models using 10 million random circuits, the largest such demonstration reported. The method thereby removes the practical bottleneck of preparing and loading large numbers of distinct circuits from a classical host.

Core claim

By generating the probability distribution that defines a target randomized algorithm on the quantum computer itself rather than on a classical computer, a variety of static circuits can be realized on a single dynamic circuit containing many measurements, which produces large reductions in total execution time on real hardware.

What carries the argument

Dynamic circuit with intermediate measurements and classical feedback that samples the target probability distribution on the device during execution.

If this is right

Randomized algorithms that previously required prohibitive numbers of distinct circuit uploads become feasible on near-term devices.
Classical shadow protocols can be executed at scales of millions of random circuits for systems up to at least 40 qubits.
Execution overhead for tasks such as random Pauli measurements drops by four orders of magnitude.
The classical pre-processing step of enumerating and compiling many circuits is largely eliminated.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The technique could be applied to other randomized subroutines such as randomized compiling or variational algorithms that rely on ensembles of circuits.
Further gains would follow from hardware that supports faster mid-circuit readout and feedback.
The method reduces dependence on classical control electronics for circuit selection, which may ease scaling to larger qubit counts.

Load-bearing premise

The intermediate measurements and classical feedback in the dynamic circuit must sample the intended probability distribution without hardware biases or decoherence that would break the statistical guarantees of the randomized algorithm.

What would settle it

Running the dynamic-circuit implementation and the conventional static-circuit implementation of the same randomized algorithm on identical hardware and finding that the output statistics or runtime speedup deviate substantially from the claimed distribution or acceleration factor.

Figures

Figures reproduced from arXiv: 2503.17833 by Ikko Hamamura, Naoki Yamamoto, Qi Gao, Rudy Raymond, Shu Kanno.

**Figure 2.** Figure 2: FIG. 2. Depictions of the proposed method. Single lines and double lines represent quantum and classical registers, respectively. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. One qubit test for the random Pauli measurement. (a) Circuit for the verification. The single line and double lines [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Results of expectation values for the hydrogen chain model with Hartree–Fock state. (a) and (b) [(c) and (d)] are [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Device topology of the Eagle devices. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Circuit example in the 28 qubit model. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Circuit example in the 40 qubit model. [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Results of expectation values for the hydrogen chain model with Hartree–Fock state including the readout error [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗

read the original abstract

Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an engineering method to reduce the executing time for randomized algorithms using dynamic circuits, i.e., quantum circuits involving intermediate measurement and feedback processes. The main idea is to generate the probability distribution defining a target randomized algorithm on a quantum computer, instead of a classical computer, which enables us to implement a variety of static circuits on a single dynamic circuit with many measurements. We applied the proposed method to the task of random Pauli measurement for one qubit on an IBM superconducting device, showing that a 14,000-fold acceleration of executing time was observed compared with a conventional method using static circuits. Additionally, for the problem of estimating expectation values of 28- and 40-qubit hydrogen chain models, we successfully applied the proposed method to realize the classical shadow with 10 million random circuits, which is the largest demonstration of classical shadow. This work significantly simplifies the execution of randomized algorithms on real quantum hardware.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Dynamic circuits move the sampling step for randomized algorithms onto the hardware itself, which produced the reported speedups and large-scale classical-shadow runs, but leaves the fidelity of the generated distribution unverified.

read the letter

The central move is to use mid-circuit measurements and classical feedback inside a single dynamic circuit to draw the random choices (Pauli bases or unitaries) directly on the device instead of loading a new static circuit for each sample. That removes the classical loading overhead and is what lets them claim the 14,000-fold speedup on one-qubit random Pauli measurements and the 10-million-circuit classical-shadow runs on 28- and 40-qubit hydrogen chains on IBM hardware. Those numbers are the concrete engineering result the paper delivers. The scale they reached is larger than most prior shadow demonstrations, so the technique clearly works at the level of raw execution time. The soft spot is exactly the one flagged in the stress test: there is no reported check that the empirical distribution over the chosen circuits matches the intended target distribution. Readout errors, reset infidelity, and feedback latency can in principle bias the sampled bases or add outcome-dependent decoherence. Without a direct fidelity comparison or an error budget on the sampling step, it is not yet clear whether the statistical guarantees of the randomized algorithm survive the hardware implementation. This paper is for experimental groups that already run or want to run large numbers of randomized circuits on superconducting hardware. It has enough experimental reach and a distinct engineering idea to deserve peer review, even though the validation of the sampling distribution will need tightening.

Referee Report

2 major / 2 minor

Summary. The paper proposes an engineering approach to implement randomized quantum algorithms via dynamic circuits, generating the required probability distributions on the quantum device through intermediate measurements and classical feedback rather than classically. This enables executing many distinct static circuits as variants of a single dynamic circuit. Demonstrations on IBM superconducting hardware include a claimed 14,000-fold reduction in execution time for single-qubit random Pauli measurements versus static-circuit methods, plus application to classical shadow estimation of expectation values for 28- and 40-qubit hydrogen chains using 10 million random circuits—the largest such demonstration reported.

Significance. If the sampling fidelity and error controls hold, the technique could materially reduce the classical compilation and queuing overhead that currently limits randomized subroutines such as classical shadows on near-term hardware. The reported scale (10 million circuits) constitutes a concrete experimental strength. No free parameters or fitted models are introduced; results are presented as direct hardware executions.

major comments (2)

[Experimental results (random Pauli and hydrogen-chain sections)] The central performance claims (14,000-fold speedup and valid classical-shadow estimators) rest on the assumption that the dynamic-circuit sampling reproduces the target distribution to within statistical error. No section reports a direct fidelity or Kolmogorov-Smirnov test comparing the empirical distribution of chosen Paulis (or random unitaries) against the ideal uniform distribution, nor quantifies bias from mid-circuit readout errors or feedback latency. This verification is load-bearing for both the speedup interpretation and the unbiasedness guarantee.
[Hydrogen-chain results] For the 28- and 40-qubit hydrogen-chain shadow estimates, the manuscript provides no error budget, calibration data, or controls addressing how reset infidelity and classical-feedback latency affect the 10-million-circuit ensemble. Without these, it is impossible to confirm that the reported expectation values retain the statistical guarantees of classical shadow.

minor comments (2)

[Abstract] The abstract states a '14,000-fold acceleration of executing time' without defining the timing protocol (quantum runtime only, or including classical post-processing and queue time).
A circuit diagram or pseudocode illustrating the dynamic-circuit construction for the random-Pauli case would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on the need for explicit verification of sampling distributions and error controls. We address each major comment below.

read point-by-point responses

Referee: [Experimental results (random Pauli and hydrogen-chain sections)] The central performance claims (14,000-fold speedup and valid classical-shadow estimators) rest on the assumption that the dynamic-circuit sampling reproduces the target distribution to within statistical error. No section reports a direct fidelity or Kolmogorov-Smirnov test comparing the empirical distribution of chosen Paulis (or random unitaries) against the ideal uniform distribution, nor quantifies bias from mid-circuit readout errors or feedback latency. This verification is load-bearing for both the speedup interpretation and the unbiasedness guarantee.

Authors: We agree that direct verification of the sampled distribution is necessary to substantiate the claims. The original manuscript did not include a Kolmogorov-Smirnov test, fidelity metric, or explicit quantification of readout/feedback biases. In the revised manuscript we will add an appendix with the empirical distribution of measured Paulis, the KS test statistic and p-value against the uniform target, and an analysis of readout error effects drawn from the device's published calibration data. This will directly address the load-bearing assumption for both the speedup and estimator validity. revision: yes
Referee: [Hydrogen-chain results] For the 28- and 40-qubit hydrogen-chain shadow estimates, the manuscript provides no error budget, calibration data, or controls addressing how reset infidelity and classical-feedback latency affect the 10-million-circuit ensemble. Without these, it is impossible to confirm that the reported expectation values retain the statistical guarantees of classical shadow.

Authors: We acknowledge the absence of a detailed error budget in the original text. In revision we will incorporate available IBM calibration data on reset infidelity and provide a discussion of classical-feedback latency effects on the ensemble. Aggregate controls and summary statistics will be added to support retention of the classical-shadow guarantees; a full per-circuit error trace for 10 M circuits is not feasible at this scale but aggregate metrics will be supplied. revision: partial

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on standard assumptions about dynamic circuit fidelity on superconducting hardware; no free parameters, invented entities, or ad-hoc axioms are introduced in the abstract.

axioms (1)

domain assumption Dynamic circuits with intermediate measurement and classical feedback can be executed reliably enough on the target hardware to sample the intended distribution.
Central to the claimed time reduction and statistical correctness.

pith-pipeline@v0.9.0 · 5723 in / 1258 out tokens · 72415 ms · 2026-05-22T22:51:59.627306+00:00 · methodology

discussion (0)

Reference graph

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