pith. sign in

arxiv: 2605.20078 · v1 · pith:BVPFELWRnew · submitted 2026-05-19 · 🪐 quant-ph

On Performance and Limitations of NISQ Hardware for Simulations of Quantum Wave Packet Dynamics

Tamila Kuanysheva , Jonathan Andrade-Plascencia , Jayakrushna Sahoo , Brian Kendrick , Dmitri Babikov This is my paper

Pith reviewed 2026-05-20 04:59 UTC · model grok-4.3

classification 🪐 quant-ph
keywords wave packet dynamicsquantum simulationNISQ hardwaresplit-operator methodquantum Fourier transformgrid encodingPauli-Z operators
0
0 comments X

The pith

A grid-based split-operator method reduces Hamiltonian scaling from O(4^n) to O(2^n) for quantum wave packet simulations and enables hardware benchmarks up to five qubits.

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

The paper shows that mapping a continuous wave function to a finite qubit grid and evolving it with alternating kinetic and potential steps allows practical quantum simulations. The kinetic part uses the quantum Fourier transform while the potential is handled by a set of commuting Pauli-Z gates. This change cuts the number of required operators from exponential growth with base four down to base two. When run on actual devices, the method reproduces the expected dynamics for two and three qubits across platforms, yet larger registers expose differences in how well IBM and IonQ hardware preserve the motion. Readers care because the work supplies a concrete, scalable route for testing how near-term machines can handle continuous quantum motion rather than abstract spin models.

Core claim

By encoding the wave function on a discrete spatial grid mapped to qubit registers and implementing time evolution via the split-operator technique, the kinetic energy operator is applied through the quantum Fourier transform while the potential energy operator is realized as a sum of commuting Pauli-Z terms; this representation lowers the operator count from the full Pauli decomposition scaling of O(4^n) to O(2^n) for n qubits, and direct execution on IBM Quantum and IonQ processors reproduces the classical benchmark dynamics for two- and three-qubit cases while showing progressive departures at four and five qubits.

What carries the argument

Split-operator decomposition on a grid-encoded wave function, with quantum Fourier transform realizing the kinetic operator and diagonal Pauli-Z gates realizing the potential operator.

If this is right

  • Arbitrary discretized potentials can be included by simple adjustment of the Z-gate coefficients without altering circuit structure.
  • Qualitative wave-packet motion is achievable on present NISQ hardware for two- and three-qubit registers.
  • At four and five qubits, hardware noise produces measurable departures whose severity varies by platform.
  • The O(2^n) scaling makes simulations with more spatial points or longer times more tractable than full decompositions.

Where Pith is reading between the lines

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

  • The same grid-plus-split-operator pattern could be tested on two-dimensional wave packets to check whether the scaling advantage persists in higher dimensions.
  • The observed platform gap suggests that error-corrected trapped-ion devices may reach useful dynamics simulations sooner than superconducting ones.
  • The encoding may transfer directly to related problems such as quantum scattering or vibrational dynamics where spatial grids are natural.

Load-bearing premise

Discretization from the finite grid and Trotter splitting errors remain smaller than hardware noise so that platform comparisons still reflect true device performance.

What would settle it

Execute the identical grid size and time-step sequence on a classical exact simulator and measure whether the five-qubit hardware deviation from that benchmark exceeds the difference already seen between IBM and IonQ runs.

Figures

Figures reproduced from arXiv: 2605.20078 by Brian Kendrick, Dmitri Babikov, Jayakrushna Sahoo, Jonathan Andrade-Plascencia, Tamila Kuanysheva.

Figure 1
Figure 1. Figure 1: Circuit depth as a function of the number of qubits (2–7) for a single time step of the time-evolution operator. Red curve corresponds to a full Pauli decomposition of the Hamiltonian, while blue curve represents the approach used in this work, where only the potential energy operator is expanded in Pauli-Z strings and the kinetic energy operator is implemented via the Quantum Fourier Transform (QFT). Circ… view at source ↗
Figure 2
Figure 2. Figure 2: The green curve corresponds to the benchmark obtained using a classical emulator of a quantum computer. For the two-qubit case (Figure 2a), all hardware platforms reproduce the qualitative broadening behavior, with varying levels of accuracy. The IBM Torino backend (blue curve) incorporates Heron r1 processor and captures the overall trend but exhibits a systematic offset from the benchmark. The newer IBM … view at source ↗
Figure 3
Figure 3. Figure 3: Quantum tunneling through a rectangular barrier. Panels (a)-(d) correspond to simulations with 2 to 5 qubits, respectively. Symbols correspond to eight individual time-steps. Green curves represent results obtained from a classical emulator of a quantum computer. Blue, purple, and pink curves correspond to results obtained on IBM quantum processors: IBM Torino (Heron architecture), IBM Boston (updated Hero… view at source ↗
Figure 4
Figure 4. Figure 4: Time evolution of a wave packet in a harmonic oscillator potential. Panels (a)-(d) correspond to simulations with 2 to 5 qubits, respectively. Symbols correspond to eight individual time-steps. Green curves represent results obtained from a classical emulator of a quantum computer. Blue, purple, and pink curves correspond to results obtained on IBM quantum processors: IBM Torino (Heron architecture), IBM B… view at source ↗
read the original abstract

Digital quantum simulation offers a promising route for studying quantum dynamics, but efficient operator representations and circuit depth remain key challenges for near-term hardware. We investigate one-dimensional wave packet dynamics using a grid-based encoding of the wave function onto qubit registers. Time evolution is implemented via split-operator approach, with kinetic energy operator applied using Quantum Fourier Transform (QFT) with polynomial scaling and potential energy operator expressed through commuting Pauli-Z gates, improving accuracy and enabling incorporation of arbitrary discretized potentials. While the full Pauli decomposition of Hamiltonian scales exponentially as O(4^n ), the present approach reduces the operator scaling to O(2^n) for n qubits. We benchmark this approach on classical simulators and quantum hardware (IBM Quantum and IonQ) for two- to five-qubit implementations. For two- and three-qubit cases, all platforms qualitatively reproduce the benchmarked dynamics; at larger qubit counts, the IBM results deviate more strongly, whereas IonQ remains closer to the benchmark.

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 grid-based encoding for one-dimensional quantum wave packet dynamics on NISQ devices, implementing time evolution via the split-operator method: kinetic energy through the Quantum Fourier Transform and potential energy as a sum of commuting Pauli-Z operators on a 2^n-point grid. It claims this reduces Hamiltonian operator scaling from O(4^n) to O(2^n) and reports benchmarking on classical simulators plus IBM Quantum and IonQ hardware for n=2 to 5 qubits, with qualitative agreement to classical benchmarks at small n and increasing platform-dependent deviations at larger n.

Significance. If discretization and Trotter errors are controlled and subdominant, the work supplies a concrete, hardware-executable decomposition for structured Hamiltonians that improves on naive Pauli decomposition and yields comparative NISQ performance data across platforms. The approach is internally consistent for the chosen encoding and could be extended to other diagonal potentials.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (split-operator implementation): the O(2^n) operator scaling is stated for the potential and QFT-based kinetic terms, yet the manuscript provides no explicit gate-count or depth analysis that folds in the number of Trotter steps and the polynomial cost of the QFT; without this, it is unclear whether the claimed scaling advantage survives the full simulation.
  2. [Results for n=4 and n=5] Results for n=4 and n=5 (16- and 32-point grids): the interpretation that observed IBM vs. IonQ deviations reflect hardware limitations assumes the discretized model faithfully reproduces the target continuous dynamics. No convergence tests against finer classical grids or explicit bounds on spatial discretization and accumulated Trotter error are reported, which is load-bearing for attributing differences solely to NISQ noise rather than model error.
minor comments (1)
  1. [Figure captions] Figure captions and axis labels should explicitly state the time step dt, total evolution time, and grid spacing used in each panel to allow direct reproduction of the plotted dynamics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment below and have revised the manuscript to strengthen the presentation of scaling and error analysis.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (split-operator implementation): the O(2^n) operator scaling is stated for the potential and QFT-based kinetic terms, yet the manuscript provides no explicit gate-count or depth analysis that folds in the number of Trotter steps and the polynomial cost of the QFT; without this, it is unclear whether the claimed scaling advantage survives the full simulation.

    Authors: The reported O(2^n) scaling specifically refers to the number of terms in the Hamiltonian decomposition: the potential energy, being diagonal in the computational basis, decomposes into O(2^n) commuting Pauli-Z operators, while the kinetic energy is implemented via the QFT whose gate complexity is polynomial in n. This is an improvement over the generic O(4^n) Pauli decomposition of an arbitrary Hamiltonian. We agree that a complete resource estimate must also account for the number of Trotter steps and total circuit depth. In the revised manuscript we have added to Section 3 an explicit discussion of the total gate count, including the O(n^2) cost of each QFT and the dependence of Trotter steps on desired accuracy and evolution time, thereby clarifying the regime in which the approach retains a practical advantage on NISQ hardware. revision: yes

  2. Referee: [Results for n=4 and n=5] Results for n=4 and n=5 (16- and 32-point grids): the interpretation that observed IBM vs. IonQ deviations reflect hardware limitations assumes the discretized model faithfully reproduces the target continuous dynamics. No convergence tests against finer classical grids or explicit bounds on spatial discretization and accumulated Trotter error are reported, which is load-bearing for attributing differences solely to NISQ noise rather than model error.

    Authors: We concur that separating model error from hardware noise is essential for the interpretation of the n=4 and n=5 results. In the revised manuscript we have included additional classical benchmarks on 64- and 128-point grids that demonstrate convergence of the wave-packet dynamics for the parameters and evolution times used in the hardware experiments. We have also added explicit bounds on the spatial discretization error and on the accumulated Trotter error derived from the split-operator commutator estimates. These supplementary analyses indicate that, for the reported simulation durations, discretization and Trotter errors remain subdominant relative to the platform-dependent deviations observed, thereby supporting the attribution of the IBM–IonQ differences primarily to hardware characteristics. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation or claims

full rationale

The paper presents a grid-based encoding of wave-packet dynamics with split-operator time evolution, using QFT for the kinetic term and commuting Pauli-Z gates for the diagonal potential. The stated reduction from O(4^n) to O(2^n) operator scaling follows directly from this structured representation on a 2^n-point grid and is not obtained by fitting parameters or redefining quantities in terms of the target result. Hardware executions on IBM and IonQ are compared against independent classical benchmarks, with no load-bearing steps that reduce by construction to self-citations, ansatzes imported from prior author work, or renamed empirical patterns. The derivation chain remains self-contained against external simulation references.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum computing primitives and the validity of the split-operator Trotterization for the chosen time steps; no new entities or heavily fitted parameters are introduced.

axioms (1)
  • domain assumption Standard qubit encoding of discretized position space and validity of split-operator Trotterization for short time steps
    Invoked to justify the grid representation and time-evolution decomposition in the abstract.

pith-pipeline@v0.9.0 · 5712 in / 1349 out tokens · 40943 ms · 2026-05-20T04:59:10.832594+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages · 1 internal anchor

  1. [1]

    J.; Tacchino, F.; Tavernelli, I

    (1) Miessen, A.; Ollitrault, P. J.; Tacchino, F.; Tavernelli, I. Quantum Algorithms for Quantum Dynamics. Nat Comput Sci 2022, 3 (1), 25–37. (2) Tacchino, F.; Chiesa, A.; Carretta, S.; Gerace, D. Quantum Computers as Universal Quantum Simulators: State-of-the-Art and Perspectives. Adv Quantum Technol. 2020, 3, 1900052. (3) Cortes, C. L.; Gray, S. K. Quant...

    work page 2022

  2. [2]

    R.; Lu, Y .; Hao, L.; Zhang, F

    (18) Feng, G. R.; Lu, Y .; Hao, L.; Zhang, F. H.; Long, G. L. Experimental Simulation of Quantum Tunneling in Small Systems. Sci Rep 2013, 3,

    work page 2013

  3. [3]

    J.; Mazzola, G.; Tavernelli, I

    (19) Ollitrault, P . J.; Mazzola, G.; Tavernelli, I. Nonadiabatic Molecular Quantum Dynamics with Quantum Computers. Phys Rev Lett 2020, 125 (26), 260511. (20) Greene, S. M.; Batista, V . S. Tensor -Train Split -Operator Fourier Transform (TT -SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics. J Chem Theory Comput 2017, 13 (9), 4034–4042. (21) ...

    work page 2020

  4. [4]

    H.; Sajjan, M.; Oh, S.; Kais, S

    (29) Sureshbabu, S. H.; Sajjan, M.; Oh, S.; Kais, S. Implementation of Quantum Machine Learning for Electronic Structure Calculations of Periodic Systems on Quantum Computing Devices. J Chem Inf Model 2021, 61, 2667-2674. (30) Xia, R.; Kais, S. Qubit Coupled Cluster Singles and Doubles Variational Quantum Eigensolver Ansatz for Electronic Structure Calcul...

    work page 2021

  5. [5]

    (32) O’Malley, P . J. J.; Babbush, R.; Kivlichan, I. D.; Romero, J.; McClean, J. R.; Barends, R.; Kelly, J.; Roushan, P .; Tranter, A.; Ding, N. et al . Scalable Quantum Simulation of Molecular Energies. Phys Rev X 2016, 6 (3), 031007. (33) Aarabi, M.; Sarka, J.; Pandey, A.; Nieman, R.; Aquino, A. J. A.; Eckert, J.; Poirier, B. Quantum Dynamical Investiga...

    work page 2016

  6. [6]

    Full -Dimensional Schrödinger Wavefunction Calculations Using Tensors and Quantum Computers: The Cartesian Component -Separated Approach

    (34) Poirier, B.; Jerke, J. Full -Dimensional Schrödinger Wavefunction Calculations Using Tensors and Quantum Computers: The Cartesian Component -Separated Approach. Phys Chem Chem Phys 2022, 24 (7), 4437–4454. (35) Gulania, S.; Gray, S. K.; Alexeev, Y .; Peng, B.; Govind, N. Hybrid Algorithm for the Time -Dependent Hartree -Fock Method Using the Yang -Ba...

    work page 2022

  7. [7]

    Variational Quantum Simulation of Chemical Dynamics with Quantum Computers

    (37) Lee, C.-K.; Hsief, C.-Y .; Zhang, S.; Shi, L. Variational Quantum Simulation of Chemical Dynamics with Quantum Computers. J Chem Theory Comput 2022, 18, 2105−2113. (38) Kandala, A.; Mezzacapo, A.; Temme, K.; Takita, M.; Brink, M.; Chow, J. M.; Gambetta, J. M. Hardware -Efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets....

    work page 2022

  8. [8]

    Quantum computing with Qiskit

    (44) Andrade-Plascencia, J.; Kuanysheva, T.; Bostan, D.; Kendrick, B. K.; Babikov, D. Mixed Quantum/Classical Theory Approach to Rotationally Inelastic Molecular Collisions Implemented on a Quantum Computer. J Chem Theory Comput 2025, 21 (13), 6305–6314. (45) van den Berg, E.; Temme, K. Circuit Optimization of Hamiltonian Simulation by Simultaneous Diagon...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  9. [9]

    Quantum Computing in the NISQ Era and Beyond

    (47) Preskill, J. Quantum Computing in the NISQ Era and Beyond. Quantum 2018, 2,

    work page 2018

  10. [10]

    The Bitter Truth about Gate -Based Quantum Algorithms in the NISQ Era

    (48) Leymann, F.; Barzen , J. The Bitter Truth about Gate -Based Quantum Algorithms in the NISQ Era. Quantum Sci Technol 2020, 5 (4), 044007. (49) Dasgupta, S.; Humble, T. Impact of Unreliable Devices on Stability of Quantum Computations. ACM Trans. Quantum Comput. 2024, 5 (4),

    work page 2020

  11. [11]

    Understanding and Compensating for Noise on IBM Quantum Computers

    (50) Johnstun, S.; Van Huele, J.-F. Understanding and Compensating for Noise on IBM Quantum Computers. Am J Phys 2021, 89 (10), 935–942. (51) Tannor, D. J. Introduction to Quantum Mechanics: A Time - Dependent Perspective; University Science Books: Sausalito,

    work page 2021

  12. [12]

    H.; Cerjan, C .; Feit, M

    (52) Leforestier, C.; Bisselinc, R. H.; Cerjan, C .; Feit, M . D.; Friesner, R .; Guldberg, A .; Hammerich, A .; Jolicard, G .; Karrlein W.; Meyer, H.-D.; Lipkin, N.; Roncero, O.; Kosloff, R. A Comparison of Different Propagation Schemes for the Time Dependent Schrodinger Equation. J Comput Phys 1991, 94, 59-

    work page 1991

  13. [13]

    A.; Morris, J

    (53) Fleck, J. A.; Morris, J. R.; Feit, M. D. Time-Dependent Propagation of High Energy Laser Beams through the Atmosphere. Appl Phys 1976, 10, 129-160. (54) Zalka, C. Simulating Quantum Systems on a Quantum Computer. Proc R Soc A 1998, 454, 313−322. (55) Ronnie, K. The Fourier Method. In Numerical Grid Methods and Their Application to Schrödinger’ s Equa...

    work page 1976

  14. [14]

    Accuracy of Gates in a Quantum Computer based on Vibrational Eigenstates

    (57) Babikov, D. Accuracy of Gates in a Quantum Computer based on Vibrational Eigenstates. J Chem Phys 2004, 121, 7577-7585. (58) Benhelm, J.; Kirchmair, G.; Roos, C. F.; Blatt, R. Towards Fault-Tolerant Quantum Computing with Trapped Ions. Nat Phys 2008, 4 (6), 463–466. (59) Wright, K.; Beck, K. M.; Debnath, S.; Amini, J. M.; Nam, Y .; Grzesiak, N.; Chen...

    work page 2004

  15. [15]

    -S.; Nielsen, E.; Ebert, M.; Inlek, V .; Wright, K.; Chaplin, V .; Maksymov, A.; Páez, E.; Poudel, A.; Maunz, P

    (60) Chen, J. -S.; Nielsen, E.; Ebert, M.; Inlek, V .; Wright, K.; Chaplin, V .; Maksymov, A.; Páez, E.; Poudel, A.; Maunz, P. et al. Benchmarking a Trapped -Ion Quantum Computer with 30 Qubits. Quantum 2024, 8,

    work page 2024