[Paper Review] Quantum Algorithms for Simulating Nuclear Effective Field Theories

James D. Watson, Jacob Bringewatt+4 more|arXiv (Cornell University)|Dec 8, 2023

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper develops and analyzes quantum algorithms for simulating low-energy nuclear effective field theories (EFTs) using quantum computers, focusing on pionless, one-pion-exchange, and dynamical-pion EFTs. By leveraging fermion and boson qubit encodings, symmetry exploitation, and improved Trotter error bounds, the authors achieve orders-of-magnitude reductions in qubit and gate costs—particularly for pionless EFT—demonstrating that quantum simulation of nuclear systems is increasingly feasible with near-term devices.

ABSTRACT

Quantum computers offer the potential to simulate nuclear processes that are classically intractable. With the goal of understanding the necessary quantum resources to realize this potential, we employ state-of-the-art Hamiltonian-simulation methods, and conduct a thorough algorithmic analysis, to estimate the qubit and gate costs to simulate low-energy effective field theories (EFTs) of nuclear physics. Within the framework of nuclear lattice EFT, we obtain simulation costs for the leading-order pionless and pionful EFTs. For the latter, we consider both static pions represented by a one-pion-exchange potential between the nucleons, and dynamical pions represented by relativistic bosonic fields coupled to non-relativistic nucleons. Within these models, we examine the resource costs for the tasks of time evolution and energy estimation for physically relevant scales. We account for model errors associated with truncating either long-range interactions in the one-pion-exchange EFT or the pionic Hilbert space in the dynamical-pion EFT, and for algorithmic errors associated with product-formula approximations and quantum phase estimation. We find that the pionless EFT is the least costly to simulate, followed by the one-pion-exchange theory, then the dynamical-pion theory. We demonstrate how symmetries of the low-energy nuclear Hamiltonians can be utilized to obtain tighter error bounds. By retaining the locality of nucleonic interactions when mapped to qubits, we achieve reduced circuit depth and substantial parallelization. In the process, we develop new methods to bound the algorithmic error for classes of fermionic number-preserving Hamiltonians, and obtain tighter Trotter error bounds by explicitly computing nested commutators of Hamiltonian terms. Compared to previous estimates for the pionless EFT, our results represent an improvement by several orders of magnitude.

Motivation & Objective

• To estimate the quantum resource costs—qubits, gates, circuit depth—for simulating low-energy nuclear effective field theories (EFTs) on quantum computers.
• To analyze and minimize algorithmic errors in product-formula-based time evolution and quantum phase estimation for nuclear Hamiltonians.
• To develop tighter Trotter error bounds for fermionic and fermion-boson Hamiltonians that preserve particle number, improving simulation accuracy.
• To demonstrate how physical symmetries and locality in nuclear interactions can be exploited to reduce circuit depth and enable parallelization.
• To compare simulation costs across three EFT models: pionless, one-pion-exchange, and dynamical-pion EFTs, identifying the most resource-efficient to simulate.

Proposed method

• Employing the Verstraete-Cirac encoding to map non-relativistic nucleons to qubits while preserving locality and particle number.
• Using Jordan-Wigner and Bravyi-Kitaev-like mappings for bosonic pion fields, with truncation to finite Fock space to reduce qubit count.
• Applying product-formula algorithms (Trotterization) for time evolution, with explicit computation of nested commutators to bound Trotter error.
• Deriving analytical bounds on simulation error for number-preserving Hamiltonians using semi-norms and commutator expansions.
• Implementing quantum phase estimation (QPE) for energy spectroscopy, with error analysis for both algorithmic and model truncation effects.
• Integrating physics insights—such as rotational invariance and locality—into circuit design to minimize depth and maximize parallelization.

Experimental results

Research questions

• RQ1 What are the qubit and gate resource costs for simulating pionless, one-pion-exchange, and dynamical-pion effective field theories on a quantum computer?
• RQ2 How can symmetries in low-energy nuclear Hamiltonians be leveraged to tighten error bounds and reduce circuit depth?
• RQ3 What is the impact of truncating long-range interactions (in OPE-EFT) or the pion Fock space (in dynamical-pion EFT) on simulation accuracy?
• RQ4 Can tighter analytical bounds on Trotter error be derived for fermionic and fermion-boson Hamiltonians that conserve particle number?
• RQ5 How do improvements in algorithmic design and encoding strategies reduce resource costs compared to prior estimates for pionless EFT?

Key findings

• The pionless EFT is the least costly to simulate, with resource estimates improved by several orders of magnitude over previous work.
• The one-pion-exchange EFT requires higher resource costs than pionless EFT due to long-range interactions, but remains feasible with optimized encoding.
• The dynamical-pion EFT incurs the highest cost due to the inclusion of relativistic pion fields and their coupling to nucleons, but is still within reach for fault-tolerant quantum devices.
• By explicitly computing nested commutators, the authors achieve tighter Trotter error bounds than previous methods, particularly for pionless EFT with p=2.
• The use of locality-preserving encodings reduces circuit depth and enables substantial parallelization, significantly improving resource efficiency.
• The paper provides explicit error bounds for all three EFT models, accounting for both algorithmic (Trotterization) and model (truncation) errors, with bounds scaling favorably with system size and interaction strength.