Kentaro Yamamoto

Dynamical structure factors (DSF) measured with neutron-scattering experiments provide key insights into the structure of materials. Their computation requires both the preparation of an equilibrium state and the implementation of Hamiltonian dynamics. We demonstrate the feasibility of computing DSF on the Quantinuum Reimei trapped-ion quantum computer, comparing the DSF of 1D Heisenberg model on $20$ sites, and that of the copper sulfate crystal. To that end, we introduce a pumping approach for computing the DSF $S(q,ω)$ on quantum computers that enables targeting specific arbitrary values of frequencies $ω$. This method time-evolves the initial state using a time-dependent Hamiltonian perturbed by a source term oscillating at the target frequency $ω$. When targeting only a few frequency values, this approach provides a significant reduction in shot overhead compared to previous methods.

We introduce population-transfer dynamics as a practical validation observable for active-space-derived reduced Hamiltonians in multistate reaction-center chemistry. Using a cytochrome P450-inspired Fe-complex model, we construct a reaction-coordinate-dependent effective Hamiltonian from state-averaged complete active-space self-consistent field (SA-CASSCF) calculations, map it to a quantum-circuit representation suitable for current hardware, and propagate dynamics from the reactant-side ground state. The reduced Hamiltonian reproduces the SA-CASSCF reference with an RMS deviation of 0.030 eV and a maximum absolute deviation of 0.143 eV. As a dynamics-based diagnostic, the product-manifold population p_P(t) identifies a pronounced near-degeneracy region around x = 0.3, where state mixing is strongest. Classical exact time evolution yields a product population of 0.488 at x = 0.3 after 10 fs, compared with 7.26 x 10^-2 at x = 0.2 and 5.90 x 10^-3 at x = 0.0. To enable execution on current trapped-ion hardware, we examine the trade-off between dynamical fidelity and circuit resources through coupling pruning and first-order Trotterization. A coupling cutoff of 0.02 eV reduces the non-zero coupling set from 32 to 7 while preserving the dominant transfer pathways, and M = 30 provides the best practical operating point. Finally, we demonstrate the workflow on Quantinuum's trapped-ion quantum computer Reimei. The hardware reproduces the key reaction-coordinate trend identified by the classical model, including the maximum at x = 0.3, where the measured product population is 0.42 on hardware and 0.43 on the matched emulator. This work establishes a dynamics-based framework for assessing active-space-derived reduced Hamiltonians and demonstrates chemically interpretable multistate electronic dynamics on current trapped-ion hardware.

We develop a workflow within the ONIOM framework and demonstrate it on the hybrid computing system consisting of the supercomputer Fugaku and the Quantinuum Reimei trapped-ion quantum computer. This hybrid platform extends the layered approach for biomolecular chemical reactions to accurately treat the active site, such as a protein, and the large and often weakly correlated molecular environment. Our result marks a significant milestone in enabling scalable and accurate simulation of complex biomolecular reactions

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.

In this paper, we present a quantum computational method to calculate the many-body Green's function matrix in a spin orbital basis. We apply our approach to finite-sized fermionic Hubbard models and related impurity models within Dynamical Mean Field Theory, and demonstrate the calculation of Green's functions on Quantinuum's H1-1 trapped-ion quantum computer. Our approach involves a cumulant expansion of the Lanczos method, using Hamiltonian moments as measurable expectation values. This bypasses the need for a large overhead in the number of measurements due to repeated applications of the variational quantum eigensolver (VQE), and instead measures the expectation value of the moments with one set of measurement circuits. From the measured moments, the tridiagonalised Hamiltonian matrix can be computed, which in turn yields the Green's function via continued fractions. While we use a variational algorithm to prepare the ground state in this work, we note that the modularity of our implementation allows for other (non-variational) approaches to be used for the ground state.

Quantum phase estimation (QPE) serves as a building block of many different quantum algorithms and finds important applications in computational chemistry problems. Despite the rapid development of quantum hardware, experimental demonstration of QPE for chemistry problems remains challenging due to its large circuit depth and the lack of quantum resources to protect the hardware from noise with fully fault-tolerant protocols. In the present work, we take a step towards fault-tolerant quantum computing by demonstrating a QPE algorithm on a Quantinuum trapped-ion computer. We employ a Bayesian approach to QPE and introduce a routine for optimal parameter selection, which we combine with a $[[ n+2,n,2 ]]$ quantum error detection code carefully tailored to the hardware capabilities. As a simple quantum chemistry example, we take a hydrogen molecule represented by a two-qubit Hamiltonian and estimate its ground state energy using our QPE protocol. In the experiment, we use the quantum circuits containing as many as 920 physical two-qubit gates to estimate the ground state energy within $6\times 10^{-3}$ hartree of the exact value.