Running Quantum Computers in Discovery Mode

Alessio Lerose; Aydin Deger; Benedikt Placke; G. J. Sreejith; S. L. Sondhi

Running Quantum Computers in Discovery Mode

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that a feedback loop - classical optimization of a quantum-measured interest function over circuit parameters - rediscovers discrete time crystals when the interest function rewards state-sequence classifiability, and…

desk verdict A promising framework for automated discovery of quantum many-body dynamics, but the evidence for reliable DTC discovery rests on one adaptive loop with a post-hoc fix. read the letter →

arxiv 2507.01013 v2 pith:RAVUGUAA submitted 2025-07-01 quant-ph cond-mat.str-elhep-th

Aydin Deger , Benedikt Placke , G. J. Sreejith , Alessio Lerose , S. L. Sondhi This is my paper · ORCID

classification quant-phcond-mat.str-elhep-th

keywords discoverymodeinterestfunctiondiscretetimecrystaldual-unitarycircuitsspectralformfactorclassicalshadowsquantummachinelearningmany-bodydynamics

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

This paper proposes a third way to use a quantum computer: instead of running a known algorithm or simulating a known Hamiltonian, let a classical learning agent tune the parameters of a quantum circuit to maximize a user-chosen 'interest function' evaluated from measurements on the device. The claim, tested numerically on simulated devices of up to 10-14 qubits, is that this feedback loop, started from random parameters, rediscovers nontrivial many-body physics. Maximizing the binary classifiability of the sequence of states produced by repeated application of the circuit converges with high probability to a discrete time crystal, a period-doubled non-equilibrium phase of matter; maximizing a spectral interest function built from the traces of powers of the unitary converges to dual-unitary circuits, the fastest-possible quantum scramblers. The proposal therefore turns 'what is interesting?' into a design problem for interest functions, and makes the quantum computer itself propose the phenomena worth studying. Both demonstrations are numerical, and the paper identifies scalable estimators such as the partial spectral form factor as the route to experiments.

What carries the argument

The machinery is the pairing of a quantum-evaluated scalar interest function with a classical optimizer, instantiated twice. For time crystals, the interest function is the binary classifiability of the state sequence: each state $U^t|\psi\rangle$ is represented by classical shadows, embedded through the shadow kernel $K(\psi,\psi')$ with hyperparameters $\tau=4$, $\gamma=0.1$, $N_s=500$, reduced by principal component analysis, and scored by the normalized distance between the last two clusters under variance-minimizing agglomerative clustering; the optimizer is a gradient-free simplex method. For dual unitaries, the interest function is the negative time-integrated spectral form factor, $f(U)=-\sum_{t=1}^{t_{\max}}|z_t(U)|^2$ with $z_t(U)=\mathrm{tr}\,U^t/2^n$, averaged over uniformly random single-qubit gates in a brickwork circuit built from two-qubit gates $\exp[\frac{i}{4}(J_x XX+J_y YY+J_z ZZ)]$. The key structural input is the universal random-matrix formula $|z_t(U)|^2\approx (t/D^2)[1+\binom{n}{2}(t-1)e^{-2t/\tau}+\cdots]$, whose parameter $\tau$ - an inverse domain-wall tension - vanishes exactly at dual unitarity, making the landscape locally concave with all derivatives vanishing at the maximum.

What would settle it

Re-run the DTC discovery protocol as prescribed - random computational-basis initial states, $N_s=500$ shadows, time window $t_1=10$ to $T=32$, gradient-free simplex optimization - and count the fraction of runs that converge to $J\approx\pi/4$, $h\approx\pi/2$ with $\hat{s}\perp\hat{m}$; the claim predicts a high success rate, so a success rate near zero under realistic shot noise, or a loss of the $J\approx\pi/4$ peak when the kernel hyperparameters $\tau$ and $\gamma$ are varied, would falsify it. Appendix B already exposes a fragility: for the maximally polarized initial state with the original time window, 2000 iterations cannot improve the interest function, and success returns only after switching to later time steps.

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Extended reading notes

Core claim

The paper's central assertion is that a quantum computer running in discovery mode - a feedback loop in which a classical optimizer repeatedly adjusts a parameterized unitary to increase an interest function evaluated from quantum measurements - would have led to two nontrivial discoveries had it been run earlier. For the classifiability interest function, defined as the highest-level cluster separation in agglomerative clustering of classical-shadow representations of the state sequence $\{U^t|\psi\rangle\}$, numerical optimization over the kicked-Ising circuit family converges with high probability to the discrete-time-crystal regime: $J\approx\pi/4$, field $h\approx\pi/2$, and Ising axis perpendicular to the field axis, which implies a $Z_2$ symmetry. For the spectral interest function, defined as a sum of even powers of the normalized traces $z_t(U)=\mathrm{tr}\,U^t/2^n$, the paper shows that the disorder-averaged interest landscape is concave and attains its maximum exactly on the parameter submanifolds $J_a=J_b=\pi$ with $a\neq b$, which are the dual-unitarity condition; this maximum value matches that of fully random unitaries. The paper reads these two cases as evidence that natural interest functions exist, that their landscapes are optimizable rather than barren, and that the same machinery can be aimed at genuinely unknown phenomena.

Load-bearing premise

The load-bearing premise is that a score computed from a few hundred randomized measurements at hand-chosen time steps, with fixed hyperparameters, faithfully tracks what makes a circuit physically interesting, so that climbing the score reliably finds physical phenomena rather than statistical artifacts.

Editorial extensions

If this is right

Discovery mode gives a concrete workflow: a physicist specifies only the statistical signature of interest, and the quantum-classical loop supplies the circuit that realizes it.
Maximizing classifiability over up to 10 qubits lands on the discrete-time-crystal phase with high probability, so interest landscapes need not be barren even when the objective is estimated from noisy shadow data.
Finite-depth circuits can attain the spectral statistics of fully random unitaries: the spectral interest function reaches the circular-unitary-ensemble value at dual unitarity despite the finite-depth constraint.
The partial spectral form factor offers a scalable experimental route: estimating it on a subsystem of size $|A|$ costs roughly $10^{|A|}$ randomized measurements, making the dual-unitary discovery protocol plausible on current hardware.
Interest-function design becomes the central scientific bottleneck, since both examples use simple statistical functionals (cluster separation and $|z_t|^2$) as the only guidance.

Reading between the lines

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

Beyond the paper, the same loop could be aimed at phenomena whose order parameters are unknown - Hilbert-space fragmentation, prethermal time crystals, or measurement-induced phases - as long as they leave a learnable clustering or spectral fingerprint in measurement data.
Beyond the paper, the flatness of the spectral landscape at the dual-unitary maximum (all derivatives vanishing) suggests that maximally chaotic finite-depth circuits are stable to perturbations, which would make them easier to hit than fine-tuned phases but harder to locate by gradient methods; the paper does not settle whether this flatness survives at larger system sizes.
Beyond the paper, Appendix B's dependence of the time-crystal result on the time window and initial-state ensemble implies that a practical discovery protocol needs automatic, data-driven rules for choosing $t_1$, $T$, $N_s$, $\tau$, and $\gamma$; without them, an optimizer may be chasing fluctuations of the interest function rather than physics.
Beyond the paper, a direct numerical stress test suggested by its Appendix D would be to run the partial-spectral-form-factor minimization on small classically simulated systems and confirm that it steers into the dual-unitary manifold, since the paper only analyzes that route analytically.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Dear X,

Here is the bottom line: this is a solid proof-of-principle for a new way to use quantum hardware, but the claim that the loop 'reliably discovers' DTCs is supported by exactly one adaptive simulation, and that simulation needed a post-hoc time-window change for a natural initial state. Send it to review, conditional on code/data release and on the robustness issues being addressed.

What is actually new: the explicit framing of 'discovery mode' as an optimization problem over unitary circuits with human-defined interest functions, evaluated from classical shadows on a quantum device. That is a clean conceptual step, and the paper lays out a research program around designing interest functions. The two worked examples are well chosen: maximizing binary classifiability of the evolved state sequence pushes a kicked-Ising family to the period-2 DTC phase, and the disorder-averaged SFF landscape for their brickwork family is concave with the maximum at dual-unitary parameters. The theoretical hook connecting this to the domain-wall-tension prediction (Eqs. 5-6) is nice, and the experimental route via partial SFF is realistic. The citation pattern is sensible, covering the relevant ML-for-physics, MELVIN, autonomous labs, DTC, and dual-unitary literature.

The soft spots are real, and the stress-test note captures them. The DTC example is the only full adaptive loop, and Appendix B states plainly that starting from the maximally polarized state, 2000 iterations over t=1..32 made no progress; switching to t=1..100 fixed it. That is a post-hoc choice. Without error bars on the interest-function estimates and without a hyperparameter scan (tau, gamma, Ns, T), the success histograms in Figs. 2H/I could be confined to a narrow favorable region. The dual-unitary section never runs the loop; it shows landscapes only. Both interest functions encode the target phase properties in their definition, so this is targeted rediscovery rather than open-ended discovery. Still, the optimizer's convergence to a DTC from random parameters is a nontrivial empirical finding; the circularity concern is moderate, not fatal. No code or data is shipped, which for a numerical methods paper is a legitimate but fixable complaint: release code and shadow data, add error bars, and discuss the sensitivity to the post-hoc window choice.

Who gets value: anyone working on automated quantum experiment search, ML-for-physics, or Floquet quantum simulation. I'd bring it to a reading group, and I'd cite it as a reference point for the discovery-mode framing. My verdict: it deserves a serious referee. I would accept a revised version once the robustness questions are addressed.

Referee Report

4 major / 6 minor

Summary. The paper proposes a 'discovery mode' for quantum computers: define an interest function f(U) on a parameterized unitary circuit, evaluate it from classical shadows on the quantum device, and classically optimize the circuit parameters to maximize f. Two concrete interest functions are studied numerically. The first, based on binary classifiability of the state sequence {U^t|ψ>}, is maximized by circuits in the discrete time crystal (DTC) phase of a kicked Ising model; the authors simulate the full adaptive optimization loop for up to n=10 qubits and report high-probability convergence to DTC parameters. The second, based on the spectral form factor (SFF), is claimed to have optima at dual-unitary circuits; the authors compute disorder-averaged landscapes for n≤14 but do not run an adaptive loop. The paper argues that these two examples establish discovery mode as a viable paradigm.

Significance. If the central claims are correct, the paper introduces a genuinely new mode of quantum-computer use and provides a concrete design principle (interest functions) for automated discovery of dynamical phases. The numerical work is mostly careful and the appendices are candid about limitations, including the pSFF measurement proposal in App. D. However, the significance is tempered by three issues: the only full adaptive-loop demonstration (DTC) is shown in App. B to be sensitive to the choice of initial state and time window; no error bars or hyperparameter sensitivity analysis are provided for the interest-function estimates; and the dual-unitary claim is supported only by a disorder-averaged landscape, not by an actual optimization. These issues do not invalidate the idea, but they mean the paper's load-bearing assertion—that the discovery loop reliably finds these phases from random starting parameters—is not yet fully established.

major comments (4)

[Appendix B, Fig. 5D,H,I] The DTC adaptive-loop demonstration is not robust in the way claimed in the main text. For the maximally polarized initial state, the optimizer made no progress for 2000 iterations when f was estimated from time steps 1–32; only after changing the estimation window to 1–100 did optimization succeed. This post-hoc change matters because the interest function is supposed to be a general proxy for 'interesting' dynamics, not a hand-tuned detector requiring a particular late-time window. The main-text claim that 'an attempt at maximizing the binary classifiability ... would lead us to a DTC unitary' (Sec. II) is therefore only demonstrated for random computational-basis initial states and one favorable window; a systematic study over initial state ensembles and time windows, or an explicit qualification of the claim, is needed.
[Appendix A, Methods; Figs. 2H/I and 4] No error bars are given for the interest-function estimates, and the Methods state that the kernel hyperparameters τ=4 and γ=0.1 were not explored. The success histograms in Figs. 2H/I and 4F/G could in principle be confined to a narrow favorable region of protocol space. The authors should at least quantify the statistical fluctuations of f (e.g., across shadow realizations and initial states) and show that the optimizer's success is not destroyed by moderate changes in Ns, Ninit, t1, T, or the kernel parameters. Without this, the claim that the protocol 'reliably' finds DTCs is not supported.
[Sec. III; Fig. 3E; App. C, Fig. 6] The dual-unitary section never runs the adaptive optimization loop. The claim that 'an optimization cycle would successfully steer the parametrized circuit towards a dual-unitary submanifold' (Fig. 3E caption) is an inference from a disorder-averaged, noiseless landscape. Since the SFF is known not to be self-averaging (Ref. 57), single-circuit interest functions may be noisy, and the actual optimization dynamics could differ substantially from the averaged landscape. The authors should either run the loop for small systems or explicitly label this as a conjecture rather than a demonstration.
[Secs. II and III] The interest functions are constructed to favor exactly the properties characteristic of the target phases: binary classifiability for DTC and small spectral form factor for dual unitarity. This is not circular in a logical sense, but it substantially weakens the 'discovery' framing. The paper should more explicitly separate the claim 'this objective, once chosen, steers to a known phase' from the stronger claim 'an unbiased discovery loop would find new phases'. A concrete test would be to apply the protocol to a circuit family where the interesting phase is not known in advance, or to discuss what class of unknown phenomena these interest functions could plausibly discover.

minor comments (6)

[Fig. 2E caption] The caption contains a typo: 'wih ˆs = ˆz' should be 'with ˆs = ˆz'.
[Appendix A, after Eq. (A1)] There is a stray word 'ow' in the sentence 'in an extended space. ow A convenient extended feature space...' which should be removed.
[Eqs. (3)–(4)] The notation α_{1,t}, α_{2,t} and then α_{n,t} is confusing because n is already used for the number of qubits; please use a different index, e.g., α_{k,t}.
[Sec. III, Eq. (6)] The quantity τ is described as an inverse domain-wall tension, but the argument of the exponential in Eq. (6) is −4/τ, which is dimensionally unclear; please define the units or clarify the definition of τ.
[App. C] The choice tmax=20 is introduced without sensitivity analysis; a brief statement on how the landscape depends on tmax would strengthen the spectral-statistics story.
[Sec. II, paragraph after Eq. (1)] The text says 'We have checked that the optimization works for any choice of the three orthogonal directions for measurement' but the Pauli measurement angle is fixed to 0.7 radians in all reported runs; please clarify whether this check is shown somewhere or is anecdotal.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the interest functions are generic objectives whose optimizers are identified by explicit computation, not by construction.

full rationale

The two central claims are that maximizing a classifiability-based interest function steers the circuit family to a DTC (Sec. II) and that minimizing a spectral-form-factor-based interest function has optima at dual-unitary circuits (Sec. III). Neither claim reduces to its own input by definition. The classifiability objective f(U) is defined as the highest-level cluster separation of shadow-represented states {U^t|psi>}; it contains no explicit period-2, Z2, or DTC ingredient. The numerical optimization from random parameters, and the landscape calculation in the kicked Ising family, are genuine computations showing that the maximizer lies in the DTC phase. Similarly, f(U) = -sum_t |z_t(U)|^2 is a generic spectral statistic; dual-unitarity is not inserted into the objective, and the result that the maximum of this landscape in the brickwork family occurs at J_a = J_b = pi is an independent analytical/numerical finding. The paper explicitly acknowledges that the examples are known phenomena and that the human input is the definition of 'interesting', which is the designed research program rather than a covert restatement of the conclusion. Self-citations to prior DTC work by co-authors are contextual references to established phase structure, not load-bearing justifications for the present derivations. Appendix B's report that optimization with a maximally polarized initial state failed until the time window was changed is a robustness limitation, not evidence of circularity; the same appendix also shows successful optimization from random computational-basis states. The Methods statement that kernel hyperparameters were not explored is a sensitivity caveat, not a circular step. No equation is identical to another by construction, no fitted parameter is renamed as a prediction, and no uniqueness theorem is imported from the authors' prior work to force the chosen optimum. The core numerical results stand independently of the definitions used to motivate them.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claims rest on hand-chosen kernel hyperparameters (tau, gamma), protocol sampling parameters (Ns, Ninit, tmax), and several domain assumptions from prior literature. The paper does not introduce new physical entities. The most fragile input is the assumption that the interest functions, defined with knowledge of the targets, remain meaningful proxies for genuinely new physics.

free parameters (5)

tau (kernel hyperparameter) = 4
Chosen by hand in Appendix A; controls the weight of higher tensor powers in the shadow kernel. No sensitivity analysis is provided, and it affects which circuits appear 'classifiable'.
gamma (kernel hyperparameter) = 0.1
Chosen by hand in Appendix A; controls the emphasis on few-site reduced density matrices. The authors note that other choices may improve performance but were not explored.
tmax (SFF summation cutoff) = 20
Used in Sec. III and Appendix C for the spectral interest function; the landscape and maximum may depend on this cutoff.
Ns (shadows per state) = 500
Number of classical shadow samples per state in the DTC protocol; affects the statistical accuracy of the interest function, but no error bars were computed.
Ninit (initial states averaged) = 30-50
Number of computational basis initial states averaged over to estimate the interest function; affects noise but no convergence analysis.

assumptions (4)

domain assumption The parameterized circuit families (Eq. 1 and the brickwork family shown in Fig. 3B) are expressive enough to include the target phases and are representative of 'generic' finite-depth circuits.
The entire search happens within these families; if they were not representative, the discovered maxima would not generalize.
standard math The shadow kernel in Eq. (A2), taken from Ref. [16], faithfully represents the distinguishability of quantum states for the purpose of classifiability.
The interest function is built from this kernel; the paper relies on its validity for small Ns.
standard math The spectral form factor formulas (|z_t|^2 approx t/D^2 for CUE, Eq. (5) for finite-depth circuits, and the dual-unitary behavior) from Refs. [48,49,51,53,58,59] are correct.
These are used to interpret the SFF minima as chaotic and to compute the theoretical maximum.
ad hoc to paper The initial state ensemble (random computational basis states) and time window (t=10..49) are representative; Appendix B shows behavior changes with maximally polarized states.
The optimization outcome depends on these choices; the paper adjusts the window when the initial protocol fails.

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Cite this review

Pith. "Pith review of Running Quantum Computers in Discovery Mode." pith.science (2026). https://pith.science/paper/RAVUGUAA

@misc{pith2026250701013,
  author       = {Pith},
  title        = {Pith review of: Running Quantum Computers in Discovery Mode},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RAVUGUAA}},
  note         = {Machine review of arXiv:2507.01013}
}

read the original abstract

Using a 36-qubit quantum processor, we demonstrate that, by operating in conjunction with a classical machine learning agent, quantum computers can discover instances of interesting quantum many-body dynamics. The central object in this new mode of use of a quantum device is an "interest function" defined for a given circuit (family) instance that can be evaluated on a quantum computer. The circuit is adapted by the learning agent to maximize interest. We illustrate this approach using two examples and show that, within a sufficiently general circuit family, two simple interest functions based on (i) binary classifiability of evolved states and (ii) spectral properties of the unitary circuit, are maximized by discrete time crystals (DTCs) and dual-unitary circuits, respectively. For the classifiability-based interest function, we implement the protocol on a superconducting quantum processor and find that it indeed discovers DTCs with high probability. For the dual-unitaries, our simulations of the dynamics suggest that an interest-function optimization would have set us close to a discovery of such unitaries. Our results using quantum devices and accompanying simulations suggest that learning agents with access to quantum-computing resources can almost autonomously discover new phenomena in many-body quantum dynamics, and establish the design of good interest functions optimizable in hybrid devices as a paradigm for quantum many-body physics.