quantum-computing

Quantum Simulation of Nuclear Dynamics in First Quantization

Luca Spagnoli, Chiara Lissoni, and Alessandro Roggero

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In this work we provide the first complete characterization of the resource requirements for studying nuclear dynamics with the full Leading Order (LO) pionless EFT Hamiltonian in first quantization employing simulation strategies using both product formulas as well as Quantum Signal Processing. In particular, we show that time evolution of such an Hamiltonian can be performed with polynomial resources in the number of particles, and logarithmic resources in the number of single-particle basis states. We find that interesting simulations for low energy nuclear scattering could be achievable with tens of millions of T gates and few hundred logical qubits suggesting that the study of simple nuclear reactions could be amenable for early fault tolerant quantum platforms.

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AbstractThe study of real time dynamics of nuclear systems is of great importance to provide theoretical predictions of cross sections relevant for both terrestrial experiments as well as applications in astrophysics. First principles simulations of these dynamical processes is however hindered by an exponential cost in classical resources and the possibility of performing scalable simulations using quantum computers is currently an active field of research. In this work we provide the first complete characterization of the resource requirements for studying nuclear dynamics with the full Leading Order (LO) pionless EFT Hamiltonian in first quantization employing simulation strategies using both product formulas as well as Quantum Signal Processing. In particular, we show that time evolution of such an Hamiltonian can be performed with polynomial resources in the number of particles, and logarithmic resources in the number of single-particle basis states. This result provides an exponential improvement compared with previous work on the same Hamiltonian model in second quantization. We find that interesting simulations for low energy nuclear scattering could be achievable with tens of millions of T gates and few hundred logical qubits suggesting that the study of simple nuclear reactions could be amenable for early fault tolerant quantum platforms.Featured image: Estimated number of T gates for nuclear reactions in a small $8^3$ spatial box as a function of the number of nucleons. The blue line correspond to the best Trotter results in second quantization (Watson et al. 2023) while the red and black lines correspond to our first quantization scheme with either Trotter at second order (red curve) or Generalized Quantum Signal Processing (black curve).Popular summarySimulating nuclear reactions is a major challenge for classical computers, making them a promising target for quantum simulation. In this work, we show that representing individual nucleons directly on a quantum computer, rather than encoding the entire space in which they can move, can greatly reduce the resources required to simulate their real-time dynamics, especially as the spatial size of the problem increases. Our estimates suggest that simple low-energy nuclear scattering processes could eventually be studied using a few hundred logical qubits and tens of millions of fault-tolerant operations, placing them within the possible range of early applications of fault-tolerant quantum computers.► BibTeX data@article{Spagnoli2026quantumsimulationof, doi = {10.22331/q-2026-09-02-2200}, url = {https://doi.org/10.22331/q-2026-09-02-2200}, title = {Quantum {S}imulation of {N}uclear {D}ynamics in {F}irst {Q}uantization}, author = {Spagnoli, Luca and Lissoni, Chiara and Roggero, Alessandro}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2200}, month = sep, year = {2026} }► References [1] Daniel S. Abrams and Seth Lloyd. Simulation of many-body fermi systems on a universal quantum computer. Phys. Rev. Lett., 79: 2586–2589, 9 1997. 10.1103/PhysRevLett.79.2586. 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URL https://arxiv.org/abs/2506.03094. arXiv:2506.03094Cited byCould not fetch Crossref cited-by data during last attempt 2026-09-02 09:33:09: Could not fetch cited-by data for 10.22331/q-2026-09-02-2200 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-09-02 09:33:10: Cannot retrieve data from ADS due to rate limitations.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractThe study of real time dynamics of nuclear systems is of great importance to provide theoretical predictions of cross sections relevant for both terrestrial experiments as well as applications in astrophysics. First principles simulations of these dynamical processes is however hindered by an exponential cost in classical resources and the possibility of performing scalable simulations using quantum computers is currently an active field of research. In this work we provide the first complete characterization of the resource requirements for studying nuclear dynamics with the full Leading Order (LO) pionless EFT Hamiltonian in first quantization employing simulation strategies using both product formulas as well as Quantum Signal Processing. In particular, we show that time evolution of such an Hamiltonian can be performed with polynomial resources in the number of particles, and logarithmic resources in the number of single-particle basis states. This result provides an exponential improvement compared with previous work on the same Hamiltonian model in second quantization. We find that interesting simulations for low energy nuclear scattering could be achievable with tens of millions of T gates and few hundred logical qubits suggesting that the study of simple nuclear reactions could be amenable for early fault tolerant quantum platforms.Featured image: Estimated number of T gates for nuclear reactions in a small $8^3$ spatial box as a function of the number of nucleons. The blue line correspond to the best Trotter results in second quantization (Watson et al. 2023) while the red and black lines correspond to our first quantization scheme with either Trotter at second order (red curve) or Generalized Quantum Signal Processing (black curve).Popular summarySimulating nuclear reactions is a major challenge for classical computers, making them a promising target for quantum simulation. In this work, we show that representing individual nucleons directly on a quantum computer, rather than encoding the entire space in which they can move, can greatly reduce the resources required to simulate their real-time dynamics, especially as the spatial size of the problem increases. Our estimates suggest that simple low-energy nuclear scattering processes could eventually be studied using a few hundred logical qubits and tens of millions of fault-tolerant operations, placing them within the possible range of early applications of fault-tolerant quantum computers.► BibTeX data@article{Spagnoli2026quantumsimulationof, doi = {10.22331/q-2026-09-02-2200}, url = {https://doi.org/10.22331/q-2026-09-02-2200}, title = {Quantum {S}imulation of {N}uclear {D}ynamics in {F}irst {Q}uantization}, author = {Spagnoli, Luca and Lissoni, Chiara and Roggero, Alessandro}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2200}, month = sep, year = {2026} }► References [1] Daniel S. Abrams and Seth Lloyd. Simulation of many-body fermi systems on a universal quantum computer. Phys. Rev. Lett., 79: 2586–2589, 9 1997. 10.1103/PhysRevLett.79.2586. 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Quantum Simulation of Nuclear Dynamics in First Quantization

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