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arxiv: 2509.16002 · v2 · submitted 2025-09-19 · 🪐 quant-ph · cs.LG

Scalable Quantum Reinforcement Learning on NISQ Devices with Dynamic-Circuit Qubit Reuse and Grover Optimization

Thet Htar Su , Shaswot Shresthamali , Masaaki Kondo This is my paper

Pith reviewed 2026-05-18 15:25 UTC · model grok-4.3

classification 🪐 quant-ph cs.LG
keywords quantum reinforcement learningNISQ devicesdynamic circuitsqubit reuseGrover optimizationQMDPmid-circuit measurementtrajectory fidelity
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The pith

Dynamic circuits with mid-circuit resets reduce qubit needs for multi-step quantum reinforcement learning from O(T) to O(1) while preserving trajectory fidelity.

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

The paper introduces a quantum reinforcement learning framework that encodes environment dynamics entirely in quantum Hilbert space for coherent superposition over state-action sequences. It proposes a dynamic execution model that uses mid-circuit measurement and reset to recycle a fixed set of seven physical qubits across an arbitrary number of interaction steps. This replaces the static unrolled circuit that would otherwise require seven qubits per time step. The method maintains functional equivalence at the level of generated trajectories and applies Grover amplitude amplification to favor high-return sequences. Simulations and hardware runs on an IBM processor confirm the approach works on current noisy devices.

Core claim

The central claim is that the dynamic execution model for multi-step QMDPs employs mid-circuit measurement and reset to recycle a fixed physical quantum register across sequential interactions, generating identical state-action sequences to a static unrolled QMDP while reducing the physical qubit requirement from 7xT to a constant 7 independent of the interaction horizon T, thereby transforming qubit complexity from O(T) to O(1) while maintaining trajectory fidelity.

What carries the argument

The dynamic execution model with mid-circuit measurement and reset that recycles a fixed seven-qubit register across sequential interactions in the QMDP.

Load-bearing premise

Mid-circuit measurements and resets can be performed with low enough error that the generated state-action sequences remain functionally equivalent to a static unrolled circuit without cumulative decoherence altering the sampled trajectories.

What would settle it

Execute both the dynamic and static unrolled circuits for successively larger interaction horizons T on the same NISQ device and check whether the distribution of sampled trajectory returns begins to diverge beyond the level expected from hardware noise alone.

Figures

Figures reproduced from arXiv: 2509.16002 by Masaaki Kondo, Shaswot Shresthamali, Thet Htar Su.

Figure 1
Figure 1. Figure 1: FIG. 1. Graphical representation of a classical MDP with four states [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Quantum circuit of the MDP encoding states, actions, transitions, and rewards into qubits. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. QMDP circuit utilizing dynamic circuit capability for three time steps of agent–environment interaction. Each interaction applies the [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Visualization of state visitation patterns across three time steps for quantum trajectories generated by a dynamic QMDP circuit, [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Quantum trajectory distribution from the qubit-reuse QMDP circuit executed over three time steps on the 133-qubit IBM Heron [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Sampling distribution of quantum trajectories from Grover’s search. The horizontal axis denotes the unique trajectory identifiers, and [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Static QMDP circuit implementation of agent–environment interactions across three time steps (t = 0, 1, 2). Each colored block [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

A scalable and resource-efficient quantum reinforcement learning framework is presented that eliminates the linear qubit-scaling barrier in multi-step quantum Markov decision processes (QMDPs). The proposed framework integrates a QMDP formulation, dynamic-circuit execution, and Grover-based amplitude amplification into a unified quantum-native architecture. Environment dynamics are encoded entirely within quantum Hilbert space, enabling coherent superposition over state-action sequences and a direct quantum agent-environment interface without intermediate quantum-to-classical conversion. The central contribution is a dynamic execution model for multi-step QMDPs that employs mid-circuit measurement and reset to recycle a fixed physical quantum register across sequential interactions. This approach preserves trajectory fidelity relative to a static unrolled QMDP, generating identical state-action sequences while reducing the physical qubit requirement from 7xT to a constant 7, independent of the interaction horizon T. Thus, the qubit complexity of multi-step QMDPs is transformed from O(T) to O(1) while maintaining functional equivalence at the level of trajectory generation. Trajectory returns are evaluated via quantum arithmetic, and high-return trajectories are marked and amplified using amplitude amplification to increase their sampling probability. Simulations confirm preservation of trajectory fidelity with a 66% qubit reduction compared to a static design. Experimental execution on an IBM Heron-class processor demonstrates feasibility on noisy intermediate-scale quantum hardware, establishing a scalable and resource-efficient foundation for large-scale quantum-native reinforcement learning.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript presents a quantum reinforcement learning framework for multi-step QMDPs that combines a quantum-native formulation with dynamic-circuit execution using mid-circuit measurement and reset to reuse a fixed 7-qubit register across T steps, reducing qubit count from 7T to 7 (O(T) to O(1)). It incorporates Grover amplitude amplification to boost sampling of high-return trajectories and claims that the dynamic model produces identical state-action sequences and preserves trajectory fidelity relative to a static unrolled circuit, supported by simulations showing 66% qubit reduction and experimental runs on an IBM Heron processor.

Significance. If the fidelity-preservation claim holds under realistic NISQ noise, the work would remove a major resource barrier for scaling quantum RL to longer horizons, enabling practical quantum-native agents on current hardware. The architectural synthesis of dynamic circuits, QMDP encoding, and Grover optimization is a concrete step toward resource-efficient quantum algorithms.

major comments (2)
  1. [Abstract] Abstract: The central claim that the dynamic execution model 'preserves trajectory fidelity relative to a static unrolled QMDP' and generates 'identical state-action sequences' is presented without any quantitative fidelity metrics, error bounds, or direct distributional comparisons (e.g., total variation distance or KL divergence between trajectory returns). This absence prevents verification that mid-circuit measurement/reset errors do not cumulatively alter sampled trajectories differently from the parallel noise channels in the 7T-qubit static circuit.
  2. [Results] Results/Experimental section: The simulation confirmation of fidelity preservation and the IBM Heron execution are described only qualitatively ('demonstrates feasibility'). No numerical values for per-step reset/measurement error rates, accumulated fidelity after T steps, success probabilities, or baseline comparisons against the static unrolled circuit are supplied, leaving the O(1) scaling claim without load-bearing empirical support.
minor comments (1)
  1. [Abstract] Abstract: The reported 66% qubit reduction is specific to a particular T (presumably T=3); stating the exact horizon used in the simulations would clarify how the general O(1) claim maps to the concrete result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments highlight opportunities to strengthen the quantitative presentation of our fidelity-preservation results. We address each point below and will revise the manuscript to incorporate the requested metrics and comparisons.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the dynamic execution model 'preserves trajectory fidelity relative to a static unrolled QMDP' and generates 'identical state-action sequences' is presented without any quantitative fidelity metrics, error bounds, or direct distributional comparisons (e.g., total variation distance or KL divergence between trajectory returns). This absence prevents verification that mid-circuit measurement/reset errors do not cumulatively alter sampled trajectories differently from the parallel noise channels in the 7T-qubit static circuit.

    Authors: We agree that explicit quantitative metrics improve verifiability. By construction, the dynamic-circuit model with mid-circuit measurement and reset replicates the exact unitary evolution and measurement outcomes of the static unrolled circuit on a per-step basis; therefore the generated state-action sequences and trajectory returns are identical in the absence of hardware noise. In the revised manuscript we will add to the abstract and a new results subsection the total variation distance (which equals zero under ideal simulation) together with analytic error bounds on the cumulative deviation arising from realistic per-step measurement/reset error rates. These bounds will be compared directly against the parallel noise channels present in the 7T-qubit static circuit. revision: yes

  2. Referee: [Results] Results/Experimental section: The simulation confirmation of fidelity preservation and the IBM Heron execution are described only qualitatively ('demonstrates feasibility'). No numerical values for per-step reset/measurement error rates, accumulated fidelity after T steps, success probabilities, or baseline comparisons against the static unrolled circuit are supplied, leaving the O(1) scaling claim without load-bearing empirical support.

    Authors: The referee is correct that the current text is primarily qualitative. We will expand the Results section with concrete numerical data: per-step reset and measurement error rates extracted from the IBM Heron calibration data, accumulated fidelity after T = 5 and T = 10 steps for both dynamic and static circuits, success probabilities of the Grover-amplified high-return trajectories, and side-by-side distributional comparisons (including total variation distance and KL divergence) between the two implementations. Additional figures will display fidelity-decay curves and qubit-count scaling, thereby supplying the load-bearing empirical support for the O(1) claim. revision: yes

Circularity Check

0 steps flagged

No circularity: qubit scaling is an architectural construction, not a reduction to fitted inputs or self-citations.

full rationale

The paper introduces a dynamic-circuit execution model that recycles a fixed register via mid-circuit measurement and reset, claiming this transforms qubit complexity from O(T) to O(1) while preserving trajectory fidelity by construction of the circuit design. No equations, fitted parameters, or self-citations are presented that reduce the central claim back to its own inputs; the equivalence to the static unrolled QMDP is asserted as a property of the proposed architecture rather than derived from prior results or data fits. The framework remains self-contained against external benchmarks as a novel hardware-efficient implementation for QMDPs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract does not enumerate explicit free parameters or axioms; the approach implicitly assumes that environment dynamics admit a coherent quantum encoding and that mid-circuit operations preserve sufficient coherence for trajectory equivalence.

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