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arxiv: 2107.09809 · v2 · submitted 2021-07-20 · 🪐 quant-ph

Simulating quantum chaos on a quantum computer

Amit Anand , Sanchit Srivastava , Sayan Gangopadhyay , Shohini Ghose This is my paper

Pith reviewed 2026-05-24 13:25 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum kicked topNISQquantum chaoshybrid quantum-classicalentanglementquantum simulationIBMQ
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The pith

A hybrid classical-quantum circuit lets NISQ computers simulate the quantum kicked top for any number of kicks with fixed gate count.

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

The paper presents a hybrid method that programs a quantum computer to evolve the quantum kicked top, a standard model of quantum chaos, across all regimes of chaoticity. The circuit design ensures the quantum gate count stays constant no matter how many kicks are applied, avoiding the usual buildup of errors over long times. Experiments run on IBMQ hardware detect periodic motion in the two-qubit version and clear signatures of chaos in the time-averaged entanglement, matching theoretical links between entanglement and delocalization. A sympathetic reader would see this as evidence that current noisy hardware can already access dynamical features of quantum chaos previously limited to ideal or classical simulations.

Core claim

We show that currently available NISQ computers can be used for versatile quantum simulations of chaotic systems. We introduce a novel classical-quantum hybrid approach for exploring the dynamics of the chaotic quantum kicked top on a universal quantum computer. The programmability of this approach allows us to experimentally explore the complete range of QKT chaoticity parameter regimes. Furthermore, the number of gates in our simulation does not increase with the number of kicks, thus making it possible to study the QKT evolution for arbitrary number of kicks without fidelity loss. Using a publicly accessible NISQ computer, we observe periodicities in the evolution of the 2-qubit QKT, as a

What carries the argument

The classical-quantum hybrid circuit that decomposes the QKT unitary so the quantum portion remains fixed per kick while classical control handles parameter changes.

If this is right

  • The full range of QKT chaoticity parameters can be explored experimentally on existing hardware.
  • QKT time evolution becomes accessible for arbitrarily large kick numbers without fidelity loss from added gates.
  • Signatures of chaos appear directly in measurable two-qubit entanglement on NISQ devices.
  • The predicted connection between entanglement growth and delocalization in the QKT is confirmed by hardware data.

Where Pith is reading between the lines

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

  • The fixed-gate hybrid technique may extend to other quantum maps or kicked systems without requiring deeper circuits.
  • Long-time chaos studies on NISQ hardware could become routine once the hybrid decomposition is generalized beyond the top.
  • Small-system entanglement measurements might serve as practical diagnostics for chaos before larger error-corrected machines arrive.

Load-bearing premise

The hybrid circuit on noisy hardware produces entanglement and periodicity patterns that match the ideal QKT dynamics rather than being produced by device noise or circuit truncation.

What would settle it

Running the identical hybrid circuit on an ideal classical simulator of the QKT and finding that the observed periodicities or the chaoticity dependence of time-averaged entanglement disappear or change sign relative to the IBMQ data.

Figures

Figures reproduced from arXiv: 2107.09809 by Amit Anand, Sanchit Srivastava, Sayan Gangopadhyay, Shohini Ghose.

Figure 1
Figure 1. Figure 1: Stroboscopic map showing the classical time evolution over 150 kicks for [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Fidelity of the tomographically reconstructed 2-qubit state for different initial states and different [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Fidelity of the tomographically reconstructed 2-qubit state averaged over initial states with ( [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Time-averaged concurrence plotted against [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Contour plot of concurrence over (a) 50 kicks for different values of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Stroboscopic map, (b) average concurrence over 200 kicks on IBMQ simulator and (c) average [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Evolution of OSCS values for two different initial states for 50 kicks on on IBMQ quito. The evolution of initial state leading to higher concurrence ((θ, φ) = (π/2, 0)) is more delocalized, i.e., has lower average OSCS than that corresponding to lower concurrence ((θ, φ) = (2.25, 1)). 5 Summary and discussion In this work, we have proposed a quantum circuit-based approach to simulate and explore quantum c… view at source ↗
read the original abstract

We show that currently available noisy intermediate-scale quantum (NISQ) computers can be used for versatile quantum simulations of chaotic systems. We introduce a novel classical-quantum hybrid approachfor exploring the dynamics of the chaotic quantum kicked top (QKT) on a universal quantum computer. The programmability of this approach allows us to experimentally explore the complete range of QKT chaoticity parameter regimes inaccessible to previous studies. Furthermore, the number of gates in our simulation does not increase with the number of kicks, thus making it possible to study the QKT evolution for arbitrary number of kicks without fidelity loss. Using a publicly accessible NISQ computer (IBMQ), we observe periodicities in the evolution of the 2-qubit QKT, as well as signatures of chaos in the time-averaged 2-qubit entanglement. We also demonstrate a connection between entanglement and delocalization in the 2-qubit QKT, confirming theoretical predictions.

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

1 major / 1 minor

Summary. The manuscript introduces a hybrid classical-quantum approach for simulating the quantum kicked top (QKT) on NISQ hardware. It claims that the method permits exploration of all chaoticity regimes with a gate count independent of kick number, enabling arbitrary-length evolutions without fidelity degradation. On IBMQ, the 2-qubit implementation reportedly exhibits periodicities in the evolution and chaos signatures in the time-averaged entanglement, together with a demonstrated link between entanglement and delocalization that confirms prior theoretical predictions.

Significance. If the constant-gate hybrid circuit is shown to implement the exact QKT unitary on noisy hardware, the work would provide a practical route to long-time quantum-chaos simulations on present-day devices and would strengthen the case for using entanglement measures as diagnostics of chaos in small systems.

major comments (1)
  1. [IBMQ results paragraph] The central claim that the hybrid circuit reproduces the ideal QKT unitary for arbitrary kicks on noisy IBMQ hardware (so that reported periodicities and time-averaged entanglement reflect dynamical chaos rather than device artifacts) is load-bearing yet unsupported by any fidelity benchmark, circuit diagram, or error-mitigation protocol in the IBMQ-results paragraph of the abstract. Without these data it is impossible to exclude truncation or noise as the origin of the observed signatures.
minor comments (1)
  1. [Methods] The abstract states that the gate count is independent of kick number; the methods section should explicitly show the decomposition that achieves this independence for the full range of the chaoticity parameter.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for highlighting the need for clearer support of the central claims in the abstract. We address the major comment below.

read point-by-point responses

  1. Referee: [IBMQ results paragraph] The central claim that the hybrid circuit reproduces the ideal QKT unitary for arbitrary kicks on noisy IBMQ hardware (so that reported periodicities and time-averaged entanglement reflect dynamical chaos rather than device artifacts) is load-bearing yet unsupported by any fidelity benchmark, circuit diagram, or error-mitigation protocol in the IBMQ-results paragraph of the abstract. Without these data it is impossible to exclude truncation or noise as the origin of the observed signatures.

    Authors: We agree that the IBMQ-results paragraph in the abstract is concise and does not itself contain the fidelity benchmarks, circuit diagram, or error-mitigation protocol. These supporting elements appear in the main text, where the hybrid circuit is explicitly constructed and its output is compared to the ideal QKT unitary for increasing kick numbers. To ensure the abstract is self-contained and directly addresses the load-bearing claim, we will revise the IBMQ-results paragraph to include a short reference to the fidelity benchmarks that confirm agreement with the ideal evolution (independent of kick number) and to the error-mitigation steps employed. This change will make explicit that the reported periodicities and time-averaged entanglement are not attributable to truncation or hardware artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity; experimental demonstration on IBMQ hardware is self-contained

full rationale

The paper introduces a hybrid classical-quantum circuit for the quantum kicked top whose gate count is independent of kick number, then reports direct experimental observations of periodicities and time-averaged entanglement on public IBMQ hardware. No derivation step reduces to a fitted parameter renamed as a prediction, a self-definitional loop, or a load-bearing self-citation whose content is itself unverified. The central mapping from hardware output to QKT dynamics rests on circuit construction and measurement rather than on any quantity defined in terms of the reported signatures. The work is therefore an experimental verification whose claims do not collapse by construction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard quantum-circuit model for the kicked-top unitary and the assumption that NISQ noise does not qualitatively alter the reported entanglement-delocalization link; no new entities or fitted parameters are introduced in the abstract.

axioms (1)
  • standard math The quantum kicked top can be implemented via a fixed set of single- and two-qubit gates whose action matches the classical map in the appropriate limit.
    Invoked when the hybrid circuit is said to explore the complete chaoticity parameter range.

pith-pipeline@v0.9.0 · 5690 in / 1195 out tokens · 25220 ms · 2026-05-24T13:25:55.686877+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quantum recurrences in the kicked top

    quant-ph 2023-07 unverdicted novelty 6.0

    An infinite family of stroboscopic unitary evolutions in the quantum kicked top act as the identity after finite kicks, representing a state-independent periodicity that violates the correspondence principle in all di...

Reference graph

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