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

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.

• The paper introduces an operator decomposition method that reduces circuit depth, enabling efficient simulation of quantum wave packet dynamics on NISQ hardware.
• It employs the split-operator method combining QFT for kinetic energy with a tailored Pauli-Z technique for potential energy, reducing scaling from O(4^n) to O(2^n).
• Benchmarking on IBM superconducting and IonQ trapped-ion devices reveals that IonQ maintains higher fidelity with increasing qubit counts despite noise challenges.

Performance and Limitations of NISQ Quantum Hardware in Simulating Quantum Wave Packet Dynamics

Introduction

The simulation of quantum wave packet dynamics is essential for probing molecular phenomena such as vibrations, quantum tunneling, and nonadiabatic transitions. Classical numerical approaches face exponential scaling with system size, making real-time propagation of complex quantum systems intractable. Quantum computers, operating within an exponentially large Hilbert space, offer natural prospects for overcoming these challenges, particularly through digital quantum simulation. However, practical implementation is constrained by the circuit depth and noise in noisy intermediate-scale quantum (NISQ) hardware.

This study presents an efficient scheme for simulating one-dimensional quantum wave packet dynamics, accentuating operator decompositions to minimize both circuit complexity and hardware error. The performance of this approach is benchmarked across classical emulators and NISQ platforms—specifically IBM superconducting devices and the IonQ Forte trapped-ion architecture—demonstrating the qualitative and quantitative fidelity attainable with current quantum hardware.

Algorithmic Framework

The simulation maps the discretized wave function onto $n$ qubits, representing $M = 2^n$ spatial grid points. The split-operator method is applied for time evolution, where:

• Kinetic energy operator: Implemented via the Quantum Fourier Transform (QFT) with polynomial circuit complexity $\mathcal{O}(n^2)$, transforming the wave function to momentum space where the kinetic operator is diagonal.
• Potential energy operator: Encoded by a sum of commuting Pauli-Z strings. Unlike a full Pauli decomposition (which scales as $\mathcal{O}(4^n)$), this approach exploits the diagonal structure in the position basis, reducing the scaling to $\mathcal{O}(2^n)$. The potential landscape, arbitrary and non-analytic, is incorporated directly into the quantum circuit.

This architectural choice enables a substantial reduction in circuit depth, a critical factor in mitigating noise-induced fidelity loss on NISQ devices.

Hardware Benchmarking and Numerical Results

The simulation targets three representative quantum dynamics scenarios:

• Free wave packet propagation
• Quantum tunneling through a barrier
• Vibrational dynamics in a harmonic oscillator

Implementations vary from two to five qubits, capturing grid resolutions from $M = 4$ to $M = 32$.

Free Particle Propagation

All platforms capture qualitative broadening of the wave packet. For two-qubit runs, IBM devices (Boston, Miami, Torino) yield near-quantitative agreement with benchmarks; IBM Boston (Heron r3) exhibits the highest fidelity. As qubit number increases, IBM superconducting hardware shows marked fidelity decline, most notably at five qubits, where the wave packet collapses to a uniform state after several time steps. In contrast, IonQ Forte maintains close agreement up to five qubits, reflecting superior gate fidelity and connectivity inherent to trapped-ion architectures.

Barrier Tunneling

Tunneling probabilities (final $p \approx 7-10\%$) grow monotonically and are captured across all hardware for low qubit counts. IonQ Forte again demonstrates higher accuracy at four and five qubits, with IBM devices diverging from benchmark results due to accumulated gate errors and circuit depth limitations.

Harmonic Oscillator Dynamics

Oscillatory motion of the wave packet in a parabolic potential is observed, with expectation values following classical emulation. For two and three qubits, IBM Boston, Miami, and IonQ Forte all track the benchmark. Fidelity loss in IBM superconducting devices becomes substantial by four qubits; at five qubits, none reliably tracks the wave packet dynamics. IonQ Forte maintains reasonable agreement through four qubits, outperforming the IBM platforms.

Hardware-Specific Observations

• IBM Superconducting Devices: Performance is heavily architecture-dependent. Newer systems (Boston and Miami) outperform Torino, but all display rapid fidelity loss with increased circuit depth and qubit number. The underlying gate errors and noise dominate as circuit size grows.
• IonQ Forte (Trapped-Ion): Demonstrates robust performance due to high-fidelity two-qubit gates and all-to-all qubit connectivity. Maintains agreement with benchmarks, particularly in free-particle and tunneling scenarios, up to five qubits.

Implications and Future Directions

This work underscores the critical importance of operator decomposition methods for NISQ quantum simulations, showing that careful exploitation of the Hamiltonian structure (diagonal potential, QFT-based kinetic energy) substantially enhances feasibility and accuracy. The marked sensitivity of quantum dynamics simulations to circuit depth and device noise suggests that scalable, high-fidelity quantum simulations will require both algorithmic and hardware advances.

Practically, trapped-ion systems currently offer superior performance for time-dependent quantum dynamics owing to their connectivity and gate fidelities, though circuit depth and noise remain limiting factors across platforms. Theoretical implications extend to scalable simulation strategies, including hybrid decomposition methods, error mitigation, and variational time-evolution techniques that further minimize circuit overhead.

The results also suggest that operator-specific circuit optimizations and hardware-aware algorithm design will be fundamental for practical quantum simulation of chemical dynamics on future quantum platforms. With increased qubit counts and improved noise characteristics, quantum simulation could facilitate numerically intractable studies in molecular physics and chemistry, paving the way for automated quantum computation of reaction rates, molecular spectra, and energy transfer processes.

Conclusion

The presented operator decomposition method, combining QFT-based kinetic energy implementation with Pauli-Z expansion for potential energy, achieves substantial circuit depth reduction for wave packet dynamics on NISQ hardware. Benchmarking across IBM superconducting and IonQ trapped-ion devices reveals that qualitative agreement with classical emulation is possible for small systems, with IonQ Forte outperforming IBM platforms at higher qubit counts. However, rapid fidelity degradation due to circuit depth and noise persists, highlighting essential algorithmic and hardware requirements for scalable, accurate quantum simulations. This study informs future quantum software and hardware co-design for chemical physics applications, with immediate practical implications for exploiting trapped-ion platforms and optimizing quantum circuit structures.