Quantum simulation of actinide chemistry: towards scalable algorithms on trapped ion quantum computers

TL;DR

This work demonstrates the use of quantum computing to model actinide chemistry, benchmarking two approaches—QPE with Hamiltonian simulation and QCM4 subspace methods—against classical references on Pu-containing systems. By employing variational compilation and Pauli-term filtering, the authors push QPE experiments on trapped-ion hardware to 19 qubits, achieving energies within chemical accuracy for select Pu models, and show QCM4 can yield near-exact energies with shallower circuits, albeit with larger measurement overhead. The study includes molecular fragments Pu$_2$O$_3$, PuH$_2$, PuH$_3$, and an O$_2$ dissociation on PuH$_2$ surfaces, illustrating both the current capabilities and the scaling challenges of quantum algorithms for actinide chemistry. Overall, the results validate quantum computational chemistry as a viable pathway for exploring complex electronic structures in actinide systems, while highlighting the need for further advances in measurement efficiency, error mitigation, and scalable state preparation.

Abstract

Due to the wide range of technical applications of actinide elements, a thorough understanding of their electronic structure could complement technological improvements in many different areas. Quantum computing could greatly aid in this understanding, as it can potentially provide exponential speedups over classical approaches, thereby offering insights into the complex electronic structure of actinide compounds. As a first foray into quantum computational chemistry of actinides, this paper compares the method of quantum computed moments (QCM) as a noisy intermediate-scale quantum algorithm with a single-ancilla version of quantum phase estimation (QPE), a quantum algorithm expected to run on fault-tolerant quantum computers. We employ these algorithms to study the reaction energetics of plutonium oxides and hydrides. In order to enable quantum hardware experiments, we use several techniques to reduce resource requirements: screening individual Hamiltonian Pauli terms to reduce the measurement requirements of QCM and variational compilation to reduce the depth of QPE circuits. Finally, we derive electronic structure descriptions from a series of representative chemical models and compute the energetics from quantum experiments on Quantinuum's H-series ion trap devices using up to 19 qubits. We find our experiments to be in excellent agreement with results from classical electronic structure calculations and state vector simulations.

Figures (8)

• Figure 1: Circuits diagrams for QPE/QCELS and QCM4. (a1) Hadamard test that measures the complex overlap between the initial and time-evolved states, $\bra{\psi}e^{-itH}\ket{\psi}$. For the real part we set $V=I$, whereas for the imaginary part we use $V=S^{\dagger}$. The green dashed line labeled $\ket{\Psi(t)}$ marks the exact state after the controlled time evolution. (a2) Circuit schematic in which the deep controlled time evolution is replaced by a variationally compiled ansatz that prepares an approximation $\ket{\Psi}\approx\vert{\tilde{\Psi}(\theta)\rangle}$. (a3) First layer of the recompiled state-preparation circuit for the $2+1$-qubit case. Single qubit gates: Hadamard in yellow and rotation gates around the X-axis (R$_x$) and Z-axis (R$_z$) of the Bloch sphere in red and light green, respectively. 2-qubit gates: ZZPhase gate between ancilla qubit (q$_0$) and the qubits in the state register (q$_1$ or q$_2$). (b): Quantum circuit for the calculation of the expected value of Pauli string $i$ contributing to the Hamiltonian moment $n$ on a 4-qubit model. The qubit register is initialized to zero. Then, a state preparation circuit is applied to prepare the QCM4 input state. After preparing the input state, a Pauli string $\hat{P}_i^n$ of $\hat{H}^n$ is measured in the computational basis. This procedure is repeated for all Pauli strings (or for all sets of commuting Pauli strings, when commuting sets are used) contributing to Hamiltonian moments up to $n=4$.
• Figure 2: Plutonium, hydrogen and oxygen are represented by light blue, yellow and red spheres, respectively. (a): Structural arrangements (bond lengths in Å, angles and dihedrals in degrees relaxed at the DFT level) of plutonium dihydride (PuH$_2$), trihydride (PuH$_3$) and plutonium sesquioxide (Pu$_2$O$_3$) isolated fragments. (b): Structural arrangements of: S1, S2) O$_2$ and atomic oxygen on PuH$_2$ (110) fluorite-like face-centred cubic (FCC) surface, respectively, in periodic boundary conditions (PBS). D1, D2) periodic supercell depicted with the difference in total electron density (DFT) as $\Delta \rho = \rho(PuH_2 + O_2/ 2O) - \rho(PuH_2) - \rho(O_2 / 2O))$ where $\rho$ is the total density. Red and blue volumetric data with isovalue 10$^{-4}$ [$e$/bohr$^{3}$] represent gain and loss in $\rho$, respectively. C1, C2) 5 plutonium atoms clusters (19 atoms in total, also called 5Pu or Pu$_5$H$_{12}$ model) obtained by cutting a smaller fragment (area delimited by red boxes) from the periodic surface. C1 model also referred to as Pu$_5$H$_{12}$+O$_2$ or O$_2$@PuH$_2$ and C2 as Pu$_5$H$_{12}$+2O or 2O@PuH$_2$ in the main text.
• Figure 3: (a): CASCI energies of Pu$_2$O$_3$ as a function of active space size. At (2e,2o), roughly 16 mHa of correlation energy (relative to Hartree-Fock) is obtained. Large plateaus in energy are seen with increasing active space size, indicating the importance of excitations to higher virtual orbitals; (b1): Real and imaginary part of the complex overlaps $\langle\psi\vert\psi(t)\rangle$ calculated with state vector (blue curve) and measured with the hardware H1-1 with 100 SPC (red curve). The total number of qubits is 3. Values of the standard deviations over the hardware measured overlaps due to shots sampling are shown in Tabs. S1 and S2 in the SI; (b2): Phase estimation with QCELS using the overlaps from state vector (blue curve) and from measurements with the hardware H1-1 with 100 shots per circuit (red curve). The total number of qubits is 3. The x axis is the phase while the y axis represents the QCELS objective function (Eq. S6 in the SI); (c): QCM4 method applied to the active space (2e,6o), for Pu$_2$O$_3$, obtained from moments measured on the H1-1 device using 500 SPC. The measurement results are resampled using a bootstrapping technique to emulate a distribution over statistically independent device runs (100 resamples). Orange shaded region indicates the standard deviation of the resampled results.
• Figure 4: Pu2O3 (singlet) active spaces, number of qubits, number of 2-qubit gates depths, CASCI energies, energies for the state vector, emulator and hardware runs (calculations with 100 SPC when not specified), and energy differences between the emulator(emu)/hardware(har) and state vector ($\Delta$Eemu and $\Delta$Ehar) in the QPE framework.
• Figure 5: QCM4 energies, with bootstrapped values obtained from the H1-1 emulator (H1-1E). "State vector" refers to the ideal, classically evaluated value. The green dotted line corresponds to measurements of the Hamiltonian moments filtered by Pauli strings (in this case only strings of $Z$ rotations remain after filtering). Bootstrapping corresponds to 500 resamples. Blue circles correspond to QCM4 energies averaged over the bootstrapped ensemble, while orange error bars represent the standard deviations. Top: PuH$_2$; bottom: PuH$_3$.