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REVIEW 4 major objections 6 minor 31 references

Approximate Quantum State Preparation Through Proximal Policy Optimization

T0 review · 4 major / 6 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read A proximal-policy-optimization agent, building circuits one gate at a time with separate angle tuning, claims to reach 10^-14 approximation error and rediscover known optimal gate counts for 2- and 3-qubit states.

desk verdict A plausible 2-3 qubit result that overclaims in the abstract and never shows the RL policy is doing more than a random search would, but the paper is honest about its limits and deserves a serious referee for the subfield. read the letter →

arxiv 2607.21121 v1 pith:4UOOT7PH submitted 2026-07-23 quant-ph cs.ETcs.LG

Marco Mordacci , Michele Amoretti This is my paper · ORCID
classification quant-phcs.ETcs.LG
keywords quantumstatepreparationproximalpolicyoptimizationreinforcementlearningarchitecturesearchparameterizedcircuitscircuitsynthesisfidelitygatecount
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that a reinforcement-learning agent using proximal policy optimization (PPO) can automatically construct quantum circuits for approximate state preparation, discovering near-optimal gate sequences without human design. The agent appends one gate at a time to a circuit, and after each append a short numerical optimization tunes the continuous rotation angles. For two- and three-qubit states—both standard entangled states and random states—the agent reaches trace distances of 10^-14 and recovers known minimal gate counts (7 gates for an arbitrary two-qubit state, 17 for three qubits). For four-qubit W and Dicke states it produces compact 10–16-gate circuits, while four-qubit random and five-qubit states remain only partially solved. If the approach scales, it would automate a core bottleneck in quantum computation: translating a target quantum state into a concrete circuit.

What carries the argument

The central mechanism is the split between discrete structure search and continuous parameter fitting. The PPO agent picks the next gate from a discrete action space of single-qubit rotations (Rx, Ry, Rz) and CNOT gates, and a separate inner loop re-optimizes all rotation angles after each gate is appended. This division lets the agent reason about circuit topology while ignoring exact parameter values, guided by a logarithmic reward that keeps small fidelity improvements visible as the error approaches 10^-14. The agent's observation is the current quantum state, the number of gates used, and the difference between the target and current state.

What would settle it

Run a control experiment in which random gate sequences from the same action space are each followed by the identical short angle-training routine, and count how often they achieve the reported gate counts and fidelities. If the random baseline matches the PPO agent on 2- and 3-qubit states, the claim that the policy's search drives the result collapses.

Watch

Extended reading notes

Core claim

On its own terms, the paper shows that a PPO actor-critic agent, guided by a logarithmic fidelity-based reward and a gate-count penalty, can discover circuits that approximate target states to a trace distance of 10^-14. The evidence is the gate counts found for standard and random states: the agent rediscovers the 2-gate Bell circuit, the 3-gate GHZ circuit, and the 7-gate optimal decomposition for arbitrary two-qubit states; for three-qubit random states it typically produces 17–20 gates, which match the known 17-gate optimum once redundant rotations are merged. For four-qubit W and Dicke states, it finds circuits of 11–16 and 10–12 gates respectively, but for four-qubit random states the

Load-bearing premise

That the short per-gate training of the rotation angles reliably converges to near-optimal parameters, so the fidelity signal the agent receives reflects the quality of the gate sequence rather than noise from the optimizer.

Editorial extensions

If this is right

  • For arbitrary two- and three-qubit states, the framework rediscovers known minimal gate counts (7 and 17 gates), so a learned policy can match hand-derived decompositions without prior structural hints.
  • Reaching 10^-14 trace distance in simulation means the generated circuits are effectively exact for high-precision use cases such as quantum chemistry state preparation.
  • The same reward and architecture produce compact 10–16-gate circuits for four-qubit W and Dicke states, indicating that structured (non-random) states of moderate size are within reach of the method.
  • The logarithmic reward, which amplifies incremental improvements near unit fidelity, offers a concrete recipe for training agents in other high-precision quantum control tasks.
  • The reported gate counts are pre-simplification; merging redundant rotations can further reduce them, so the practical circuits are even more compact than the raw agent output.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not compare against a random search over gate sequences with the same per-gate angle optimization; if that baseline performed equally well, the RL policy's role would be largely exploration rather than learning. Testing this is a natural next step.
  • The inner angle optimization is doing substantial work: the agent's apparent decisions may partly reflect whether the optimizer can fit a given topology. A Monte-Carlo baseline could separate structural discovery from parameter fitting.
  • The success-buffer mechanism used for four-qubit structured states—replaying the ten best circuits found—resembles episodic memory in classical RL; a more systematic replay scheme might stabilize the currently unsolved four-qubit random and five-qubit cases.
  • The 10^-14 errors are achieved under a statevector simulator; on noisy real hardware the same circuits would not reach that precision, so the practical claim is about discovering circuit structure, not about the accuracy of physical state preparation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes a quantum architecture search framework for approximate quantum state preparation using proximal policy optimization. An agent iteratively appends gates from {Rx,Ry,Rz,CNOT} to a quantum circuit; after each append, the environment performs a short gradient-based training of the rotation angles (Adam, lr=0.05, early stopping), computes the fidelity/distance, and returns a log-fidelity reward with a gate penalty. The agent is evaluated on 2- to 5-qubit states (Bell, GHZ, W, Dicke, random), with claims of 1e-14 approximation errors and gate counts matching known lower bounds (7 gates for 2-qubit random, 17 for 3-qubit random). The paper reports representative learning curves, generated circuits, and a summary table of gate counts.

Significance. If the empirical results hold, the framework is a useful contribution to quantum architecture search for state preparation: it recovers known optimal gate counts for 2- and 3-qubit random states, works for several structured states, and uses a standard RL algorithm with clearly specified hyperparameters. The experiments are grounded in independent lower bounds [22,31,11], and the target states are external. The main value would be demonstrating that PPO-style discrete gate selection combined with fast angle fitting can discover competitive circuits. However, the current manuscript does not yet establish the marginal contribution of the PPO policy, and the headline accuracy claim is broader than the reported data. With additional baseline/ablation experiments and accuracy reporting, the result would be of clear interest to the QAS/QSP community.

major comments (4)
  1. [Abstract and §3, Table 1] The abstract's claim that the framework achieves approximation errors of 1e-14 is not supported for all reported cases. For 4-qubit random states the text states that the agent 'is still not able to consistently find the state precisely but is starting to learn', and for 5-qubit states 'the model is not fully trained'. Table 1 has no error column, so the accuracy of the R4 and R5 results cannot be verified. The claim should be restricted to the cases actually demonstrated (2- and 3-qubit states, and 4-qubit W/Dicke where applicable), or the missing error data should be provided.
  2. [§2.3 and §3] The paper does not establish that the PPO policy, rather than the per-step angle training, is responsible for the reported fidelities. Every candidate circuit is post-processed by an internal Adam optimization of rotation angles (lr=0.05, early stopping), and the observation/reward are computed only after this training. The Bell-state result is reached 'from the start' (Fig. 1 and §3), demonstrating that the inner optimizer alone can saturate the 1e-14 threshold for at least some circuits. To support the central claim, the authors should compare against a random-search baseline that generates the same number of random gate sequences and applies the same angle training, and report success rates over multiple seeds. Without this, the 7- and 17-gate results may be attributable to the angle optimizer rather than to PPO's structural search.
  3. [§3 (3-qubit random), Table 1] The 'Optimized #gates' column and the statement that 'even sub-optimal solutions can be simplified to the optimal one' mean that the advertised 17-gate result is not always the raw circuit produced by the agent, but often a post hoc compressed version. The paper does not describe the simplification procedure (automatic vs manual, based on which rules), nor how often the raw circuit is exactly optimal. The gate-count claims for R3 (and the 7-gate claim for R2, where Fig. 2b includes a dashed redundant Ry) therefore conflate the agent's output with post-processing. Please report the distribution of raw counts, the simplification procedure, and the success rate for exact optimal raw circuits.
  4. [§3, Figs. 1-7 and Table 1] All reported trajectories are single runs, and the only multi-run information is '1 out of 10 runs' for one 3-qubit configuration. Since PPO is stochastic and the internal angle optimizer has early stopping, the 'consistently identified' claims (e.g., 'starts to be consistently identified after around 4000 episodes' for R2) need error bars or success-rate statistics over seeds. This is necessary to judge whether the observed optimal gate counts are reliable or occasional.
minor comments (6)
  1. [§2.3, Eq. (4)] D_t is called 'distance' but not formally defined; figure captions say 'trace distance' while the text says 'fidelity error' (Eq. 3). Please define D_t and state whether the 1e-14 threshold applies to trace distance or infidelity.
  2. [§2.3] The action space 'gate-wire combinations' is not explicit about whether CNOT is allowed in both orientations and whether repeated identical gates are allowed; clarify to make the search space reproducible.
  3. [§3] The 'Dicke 2' state is not defined; include its explicit state vector or a reference.
  4. [§3] The 'success buffer' used for 4-qubit W/Dicke is described only briefly; clarify how sampling from the buffer updates the PPO agent (behavior cloning, reward shaping, or something else).
  5. [§1] The introduction says 'proximal policy approximation'; this should be 'proximal policy optimization'.
  6. [Table 1] The 'Optimized #gates' for R2 is listed as '-' despite Figure 2b showing a simplification (removing the dashed Ry); clarify why no optimized value is reported for R2.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: empirical state-preparation results are measured against external targets and independent gate-count bounds.

full rationale

The paper's contribution is an empirical RL pipeline, not a mathematical derivation whose conclusion reduces to its inputs. The PPO agent sequentially appends gates, an internal Adam optimizer tunes rotation angles, and the reported fidelities are computed in the PennyLane simulator against external target states (Bell, GHZ, W, Dicke, random). The gate-count minima (7 for 2-qubit random, 17 for 3-qubit random) are actively compared with independent lower-bound references [22,31,11], so these results are externally anchored rather than fitted-then-predicted. The few self-citations ([3,5,20]) appear only in the introductory related-work discussion and are not load-bearing for the central claim. The absence of a random-search baseline is a legitimate validation concern about the marginal contribution of PPO, but it does not make any stated result circular: the claim is about the full framework, and no parameter is fitted to a subset of data and then reported as an independent prediction. No step in the paper's own equations or argument reduces to its inputs by construction.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The framework's headline numbers depend on hand-chosen hyperparameters (lambda, p, threshold, gate caps, buffer tuning). The only external benchmarks are gate-count lower bounds borrowed from references without verifying gate-set equivalence. No new physical entities are introduced.

free parameters (7)
  • reward scaling coefficient lambda = 10 (and 1 in variant)
    Chosen by hand; controls the magnitude of log-fidelity reward increments in Eq. (4). Changes behavior in the 3-qubit random state experiment (Fig. 5).
  • gate penalty p = 10 (and 5 x #gates in variant)
    Chosen by hand to discourage deep circuits; the text reports that overly restrictive penalty prevents the agent from finding solutions in 1 of 10 runs.
  • fidelity threshold for final reward = 10^-14
    User-set tolerance that defines 'approximation error' in the abstract and the reward of 50.
  • internal circuit learning rate = 0.05
    Adam learning rate for the short training of rotation angles each time a gate is appended; load-bearing for the reported 10^-14 fidelities.
  • PPO agent learning rate = 10^-4
    Adam learning rate for actor-critic networks.
  • maximum number of gates per circuit = 20 (2q), 30 (3q), 40/70 (4q), up to 190 (5q)
    Episode horizon caps chosen per qubit count and state type; directly bounds the reported #gates values.
  • success buffer size and sample cadence = 10 best circuits; sampled every 5 x 128 steps
    Ad hoc mechanism added for 4-qubit stability; changes training dynamics.
assumptions (5)
  • standard math PPO clipped surrogate objective is a valid policy-gradient update for reinforcement learning
    Eq. (1)-(2) invoke the standard PPO objective from Schulman et al. [26]; accepted background.
  • domain assumption The gate set {Rx, Ry, Rz, CNOT} with continuous angles is universal for quantum circuits
    The action space in Section 2.3 assumes these gates can prepare any target state with enough gates; standard but unproved in the paper.
  • domain assumption Fidelity error 1-F is a valid distance metric for state approximation
    Used in Eq. (3) and the reward; the paper also calls it 'trace distance' in figure captions without defining the relationship.
  • domain assumption Known gate-count lower bounds (7 for 2-qubit, 17 for 3-qubit random states) apply to the authors' gate set
    Cited from [22,31,11] in Section 3; the authors do not verify that the gate sets and decomposition conventions in those references match their action space.
  • domain assumption PennyLane simulator faithfully computes state evolution and fidelity
    All experiments are simulations; results are not tested on noisy hardware, so the fidelity numbers are ideal-simulator values.

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Cite this review

Pith. "Pith review of Approximate Quantum State Preparation Through Proximal Policy Optimization." pith.science (2026). https://pith.science/paper/4UOOT7PH

@misc{pith2026260721121,
  author       = {Pith},
  title        = {Pith review of: Approximate Quantum State Preparation Through Proximal Policy Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4UOOT7PH}},
  note         = {Machine review of arXiv:2607.21121}
}
abstract

In this work, a quantum architecture search framework for approximate quantum state preparation (QSP) is proposed. QSP is a challenging task, since the search space grows exponentially with the number of qubits, making the identification of the optimal circuit non-trivial. To address this problem, deep reinforcement learning is employed through an agent based on proximal policy optimization. The objective of the agent is to identify the best possible approximation of the target state while simultaneously minimizing the number of gates used. At each step, the agent appends a new gate to the circuit and recomputes the fidelity between the approximated state and the target states. Various experiments have been performed from 2 to 5 qubits. Both predefined states, such as Bell, GHZ, W, and Dicke states, and completely random states are considered. The proposed framework is able to achieve approximation errors of $10^{-14}$.

Figures

Figures reproduced from arXiv: 2607.21121 by the authors.

Figure 1
Figure 1. (a) Number of gates and trace distance achieved during training for the Bell state. (b) Circuit learned by [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. a) Number of gates and trace distance achieved during the training for a random 2-qubit state. b) Circuit [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Number of gates and trace distance achieved during the training for a) GHZ and b) W states. Furthermore, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: a) Number of gates and trace distance achieved during the training for a 3-qubit random state. b) Circuit [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Number of gates achieved during the training for a 3-qubit random state with [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Number of gates and trace distance achieved during the training for W and Dicke [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Number of gates and trace distance achieved during the training for a 4-qubit random state. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

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Reference graph

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