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arXiv:2507.14690 · Physical Review C

Toward scalable quantum computations of atomic nuclei

Chenyi Gu, M. Heinz, Oriel Kiss, T. Papenbrock

Published Jan 22, 2026• 3 citations
arXivHTMLPDF

Abstract

We solve the nuclear two-body and three-body bound states via quantum simulations of pionless effective field theory on a lattice in position space. While the employed lattice remains small, the usage of local Hamiltonians including two- and three-body forces ensures that the number of Pauli terms scales linearly with increasing numbers of lattice sites. We use an adaptive ansatz grown from unitary coupled cluster theory to parametrize the ground states of the deuteron and $^3$He, compute their corresponding energies, and analyze the scaling of the required computational resources. Our quantum simulations reproduce exact benchmarks for $^2$H and $^3$He within 100 keV, requiring at most 30 layers in the ansatz and thus resulting in modest circuit depths. Additionally, we find the number of shots required to reach a given precision scales linearly in the lattice size and more mildly in the system size. Based on the agreement with exact benchmarks and mild scaling, we conclude that this can be an efficient, scalable approach for quantum computations of nuclear ground states, particularly to prepare initial states for quantum phase estimation or other filtering algorithms.

DOI
10.1103/gqdy-dvps

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We solve the nuclear two-body and three-body bound states via quantum simulations of pionless effective field theory on a lattice in position space. While the employed lattice remains small, the usage of local Hamiltonians including two- and three-body forces ensures that the number of Pauli terms scales linearly with increasing numbers of lattice sites. We use an adaptive ansatz grown from unitary coupled cluster theory to parametrize the ground states of the deuteron and 3^33He, compute their corresponding energies, and analyze the scaling of the required computational resources. Our quantum simulations reproduce exact benchmarks for 2^22H and 3^33He within 100 keV, requiring at most 30 layers in the ansatz and thus resulting in modest circuit depths. Additionally, we find the number of shots required to reach a given precision scales linearly in the lattice size and more mildly in the system size. Based on the agreement with exact benchmarks and mild scaling, we conclude that this can be an efficient, scalable approach for quantum computations of nuclear ground states, particularly to prepare initial states for quantum phase estimation or other filtering algorithms.
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.
We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansatze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion, and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of ${E}_{4}=\ensuremath{-}2.220\ifmmode\pm\else\textpm\fi{}0.179$ MeV may be compared with the exact deuteron ground-state energy $\ensuremath{-}2.224$ MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.
The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum circuit design strategy to find nuclear ground states by exploiting an adaptive variational quantum eigensolver algorithm. Our circuit implementation is in excellent agreement with classical shell-model simulations for a dozen of light and medium-mass nuclei, including neon and calcium isotopes. We quantify the circuit depth, width and number of gates to encode realistic shell-model wavefunctions. Our strategy also addresses explicitly energy measurements and the required number of circuits to perform them. Our simulated circuits approach the benchmark results exponentially with a polynomial scaling in quantum resources for each nucleus. This work paves the way for quantum computing shell-model studies across the nuclear chart and our quantum resource quantification may be used in configuration-interaction calculations of other fermionic systems.
We explore the preparation of specific nuclear states on gate-based quantum hardware using variational algorithms. Large-scale classical diagonalizations of the nuclear shell model have reached sizes of 109−−1010{10}^{9}--{10}^{10}109−−1010 basis states but are still severely limited by computational resources. Quantum computing can, in principle, solve such systems exactly with exponentially fewer resources than classical computing. Exact solutions for large systems require many qubits and large gate depth, but variational approaches can effectively limit the required gate depth. We use the unitary coupled cluster approach to construct approximations of the ground-state vectors, later to be used in dynamics calculations. The testing ground is the phenomenological shell model space, which allows us to mimic the complexity of the internucleon interactions. We find that often one needs to minimize over a large number of parameters, using a large number of entanglements that makes the application on existing hardware challenging. Prospects for rapid improvements with more capable hardware are, however, very encouraging.
We present a framework for benchmarking quantum algorithms for nuclear many-body systems based on realistic nuclear Hamiltonians such as chiral effective field theory. To this end, we introduce a workflow that maps nuclear interactions in second quantization formalism to qubit Hamiltonians. This enables the systematic construction of benchmark instances spanning no-core and valence-space formulations with two-body (NN) and selected three-body (3N) interactions. Then, we proceed to provide resource estimates for three representative eigenvalue algorithms: Quantum Phase Estimation, Quantum Krylov methods, and Observable Dynamic Mode Decomposition. We compare their resource requirements in terms of T-gate counts and system size, and examine the impact of model-space choices and many-body interactions. The primitives included in our analysis are Trotterization, Qubitization, and Quantum Singular Value Transformation. Our results quantify scaling trends across algorithms and problem classes, and provide a basis for consistent comparisons of quantum approaches to nuclear many-body problems. The implementation is provided by the NuQuLib software stack.
We report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.