Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1904.04338 · Physical Review A

Toward convergence of effective-field-theory simulations on digital quantum computers

Omar Shehab, K. A. Landsman, Yunseong Nam, Daiwei Zhu, Norbert M. Linke, Matthew Keesan, Raphael C. Pooser, Christopher R. Monroe

Published Dec 16, 2019• 38 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.100.062319

Related papers

Toward scalable quantum computations of atomic nuclei

Chenyi Gu, M. Heinz, Oriel Kiss +1 more

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.

arXiv:2507.14690•Physical Review C•Jan 22, 2026•3 citations

Cloud Quantum Computing of an Atomic Nucleus

Eugene Dumitrescu, Alex McCaskey, G. Hagen +6 more

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.

arXiv:1801.03897•Physical Review Letters•May 23, 2018•393 citations

Full Quantum Computing on Binding Energy of Light Nuclei

PENG Baining1,  CUI Ying1,  YAN Yuliang1,  GAO Zaochun1,  WEI Shijie2 ,  ZHANG Yingxun1, 3, 4

Accurate calculations of nuclear binding energies in theory is a long-standing problem in nuclear physics, as it provides critical insights the effective interactions and structures of atomic nuclei. Currently, there are severe limitations in theory due to the exponential growth of the Hilbert space with increasing nucleon number, i.e., curse of the dimension. There are some effort to mitigate this problem by using the state-of-art methods, such as the machine learning and quantum computing. Recent advances in quantum computing have opened new avenues for addressing these challenges, enabling the direct simulation of nuclear many-body systems on quantum hardware. In this work, a detailed study on the calculation of nuclear binding energies using the full quantum eigensolver (FQE) algorithm, implemented on a real quantum processor, i.e. Quafu, was presented. Two nuclear systems (2H and 6He) were investigated. The deuteron, as the simplest bound nucleus with just one proton and one neutron, serves as an ideal benchmark for testing quantum algorithms, FQE. 6He, a light, two-valence neutron nucleus, was used for estimating the ability of the Quafu quantum cloud platform and its “Baihua” quantum chip. Our results demonstrate that for the deuteron, the FQE algorithm on the “Baihua” quantum processor achieves a higher level of accuracy compared to previously reported results obtained using the variational quantum eigensolver (VQE) on the IBM_QX5 and IBM_19Q platforms, as discussed in Dumitrescu’s article. For 6He, the FQE-calculated binding energy shows accuracy comparable to recent VQE-based calculations reported in Yoshida’s article. These findings highlight the feasibility of performing precise nuclear structure calculations on near-term quantum devices and underscore the potential of the FQE approach for future applications in nuclear physics. Overall, this study extends the scope of quantum computing in nuclear physics by demonstrating that the FQE algorithm can serve as a practical and accurate tool for computing binding energies on real quantum hardware. The results provide a benchmark for future developments in quantum simulations of nuclei and suggest promising directions for scaling these methods to larger nuclear systems, ultimately contributing to a deeper understanding of nuclear structure and dynamics.

•May 1, 2026•0 citations

Ground-state energy estimation of the water molecule on a trapped-ion quantum computer

Yunseong Nam, Jwo-Sy Chen, Neal C. Pisenti +24 more

Abstract Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here we describe an extensible co-design framework for solving chemistry problems on a trapped-ion quantum computer and apply it to estimating the ground-state energy of the water molecule using the variational quantum eigensolver (VQE) method. The controllability of the trapped-ion quantum computer enables robust energy estimates using the prepared VQE ansatz states. The systematic and statistical errors are comparable to the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics, without resorting to any error mitigation techniques based on Richardson extrapolation.

arXiv:1902.10171•npj Quantum Information•Apr 3, 2020•344 citations

High-precision Quantum Phase Estimation on a Trapped-ion Quantum Computer

Tranter, Andrew, Gowland, Duncan, Yamamoto, Kentaro +2 more

Emergent quantum computing technologies are widely expected to provide novel approaches in the simulation of quantum chemistry. Despite rapid improvements in the scale and fidelity of quantum computers, high resource requirements make the execution of quantum chemistry experiments challenging. Typical experiments are limited in the number of qubits used, incur a substantial shot cost, or require complex architecture-specific optimization and error mitigation techniques. In this paper, we propose a conceptually simple benchmarking approach involving the use of multi-ancilla quantum phase estimation. Our approach is restricted to very small chemical systems, and does not scale favorably beyond molecular systems that can be described with $2$ qubits; however, this restriction allows us to generate circuits that scale quadratically in gate count with the number of qubits in the readout register. This enables the execution of quantum chemistry circuits that act on many qubits, while producing meaningful results with limited shot counts. We use this technique (with $200$ shots per experiment) to calculate the ground state energy of molecular hydrogen to $50$ bits of precision ($8.9 \times 10^{-16}$ hartree) on a $56$-qubit trapped-ion quantum computer, negating Trotter error. Including Trotter error, we obtain between $32$ and $36$ bits of precision ($1.5 * 10^{-10}$ and $6.0 * 10^{-11}$ hartree respectively), vastly exceeding chemical accuracy ($1.6 * 10^{-3}$ hartree) against Full Configuration Interaction. We consider application of the approach to deeper circuits, and discuss potential as a benchmark task for near-term quantum devices.

arXiv:2506.17207•Jun 20, 2025•0 citations

Error-Mitigation Enabled Multicomponent Quantum Simulations Beyond the Born-Oppenheimer Approximation

Delmar G. A. Cabral, Brandon Allen, Fabijan Pavošević +6 more

We introduce a multicomponent unitary coupled cluster framework for quantum simulations of molecular systems that incorporate both electronic and nuclear quantum effects beyond the Born-Oppenheimer approximation. Using the nuclear-electronic orbital formalism, we construct mcUCC ansätze for positronium hydride and molecular hydrogen with a quantum proton, and analyze hardware requirements for different excitation truncations. To further reduce resource costs effectively, we employ the local unitary cluster Jastrow ansatz and implement it experimentally on IBM Q's Heron superconducting hardware. With the Physics-Inspired Extrapolation error mitigation protocol, the computed ground-state energies remain within chemical accuracy, consistent with the stated uncertainty level. These results provide the first demonstration of error-mitigated multicomponent correlated simulations on quantum hardware and outline a path toward scalable algorithms unifying electronic and nuclear degrees of freedom.

quant-pharXiv:2511.11941•Journal of Chemical Theory and Computation•Nov 18, 2025•2 citations
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 E4=\ensuremath−2.220\ifmmode±\else\textpm\fi0.179{E}_{4}=\ensuremath{-}2.220\ifmmode\pm\else\textpm\fi{}0.179E4​=\ensuremath−2.220\ifmmode±\else\textpm\fi0.179 MeV may be compared with the exact deuteron ground-state energy \ensuremath−2.224\ensuremath{-}2.224\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.
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.
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.
Accurate calculations of nuclear binding energies in theory is a long-standing problem in nuclear physics, as it provides critical insights the effective interactions and structures of atomic nuclei. Currently, there are severe limitations in theory due to the exponential growth of the Hilbert space with increasing nucleon number, i.e., curse of the dimension. There are some effort to mitigate this problem by using the state-of-art methods, such as the machine learning and quantum computing. Recent advances in quantum computing have opened new avenues for addressing these challenges, enabling the direct simulation of nuclear many-body systems on quantum hardware. In this work, a detailed study on the calculation of nuclear binding energies using the full quantum eigensolver (FQE) algorithm, implemented on a real quantum processor, i.e. Quafu, was presented. Two nuclear systems (2H and 6He) were investigated. The deuteron, as the simplest bound nucleus with just one proton and one neutron, serves as an ideal benchmark for testing quantum algorithms, FQE. 6He, a light, two-valence neutron nucleus, was used for estimating the ability of the Quafu quantum cloud platform and its “Baihua” quantum chip. Our results demonstrate that for the deuteron, the FQE algorithm on the “Baihua” quantum processor achieves a higher level of accuracy compared to previously reported results obtained using the variational quantum eigensolver (VQE) on the IBM_QX5 and IBM_19Q platforms, as discussed in Dumitrescu’s article. For 6He, the FQE-calculated binding energy shows accuracy comparable to recent VQE-based calculations reported in Yoshida’s article. These findings highlight the feasibility of performing precise nuclear structure calculations on near-term quantum devices and underscore the potential of the FQE approach for future applications in nuclear physics. Overall, this study extends the scope of quantum computing in nuclear physics by demonstrating that the FQE algorithm can serve as a practical and accurate tool for computing binding energies on real quantum hardware. The results provide a benchmark for future developments in quantum simulations of nuclei and suggest promising directions for scaling these methods to larger nuclear systems, ultimately contributing to a deeper understanding of nuclear structure and dynamics.
Abstract Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here we describe an extensible co-design framework for solving chemistry problems on a trapped-ion quantum computer and apply it to estimating the ground-state energy of the water molecule using the variational quantum eigensolver (VQE) method. The controllability of the trapped-ion quantum computer enables robust energy estimates using the prepared VQE ansatz states. The systematic and statistical errors are comparable to the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics, without resorting to any error mitigation techniques based on Richardson extrapolation.
Emergent quantum computing technologies are widely expected to provide novel approaches in the simulation of quantum chemistry. Despite rapid improvements in the scale and fidelity of quantum computers, high resource requirements make the execution of quantum chemistry experiments challenging. Typical experiments are limited in the number of qubits used, incur a substantial shot cost, or require complex architecture-specific optimization and error mitigation techniques. In this paper, we propose a conceptually simple benchmarking approach involving the use of multi-ancilla quantum phase estimation. Our approach is restricted to very small chemical systems, and does not scale favorably beyond molecular systems that can be described with 222 qubits; however, this restriction allows us to generate circuits that scale quadratically in gate count with the number of qubits in the readout register. This enables the execution of quantum chemistry circuits that act on many qubits, while producing meaningful results with limited shot counts. We use this technique (with 200200200 shots per experiment) to calculate the ground state energy of molecular hydrogen to 505050 bits of precision (8.9×10−168.9 \times 10^{-16}8.9×10−16 hartree) on a 565656-qubit trapped-ion quantum computer, negating Trotter error. Including Trotter error, we obtain between 323232 and 363636 bits of precision (1.5∗10−101.5 * 10^{-10}1.5∗10−10 and 6.0∗10−116.0 * 10^{-11}6.0∗10−11 hartree respectively), vastly exceeding chemical accuracy (1.6∗10−31.6 * 10^{-3}1.6∗10−3 hartree) against Full Configuration Interaction. We consider application of the approach to deeper circuits, and discuss potential as a benchmark task for near-term quantum devices.
We introduce a multicomponent unitary coupled cluster framework for quantum simulations of molecular systems that incorporate both electronic and nuclear quantum effects beyond the Born-Oppenheimer approximation. Using the nuclear-electronic orbital formalism, we construct mcUCC ansätze for positronium hydride and molecular hydrogen with a quantum proton, and analyze hardware requirements for different excitation truncations. To further reduce resource costs effectively, we employ the local unitary cluster Jastrow ansatz and implement it experimentally on IBM Q's Heron superconducting hardware. With the Physics-Inspired Extrapolation error mitigation protocol, the computed ground-state energies remain within chemical accuracy, consistent with the stated uncertainty level. These results provide the first demonstration of error-mitigated multicomponent correlated simulations on quantum hardware and outline a path toward scalable algorithms unifying electronic and nuclear degrees of freedom.