The quantum-selected configuration interaction identifies important determinantal basis functions through real-time evolution of a reference wavefunction and diagonalizing the Hamiltonian matrix in the resulting selected subspace. However, implementing the full electronic Hamiltonian on noisy quantum devices leads to rapidly increasing circuit complexity, limiting its scalability. To address this issue, we identify the dominant fermionic excitation operators and perform reference-state fidelity loss analysis to construct a compact Hamiltonian, reducing computational overhead while retaining high precision. Applied to Group IIIA monofluorides (BF, AlF, GaF, InF, and TlF), the proposed framework achieves a near-quadratic improvement in Hamiltonian-term scaling, enabling resource-efficient simulations. We employ this framework to compute the relativistic ground-state energies and permanent electric dipole moments (PDMs) of the systems under consideration. After validating the framework via simulations, we demonstrate hardware execution for AlF and TlF on the IBM Marrakesh processor using active spaces of up to 20 qubits. For a 20-qubit TlF system, the reduced Hamiltonian yields a reduction of higher than $ 98\%$ in both circuit depth and two-qubit gate counts, with the resulting PDMs from quantum hardware matching complete active space configuration interaction values within $99.99\%$. These results demonstrate the scalability of this approach on noisy intermediate-scale quantum devices.
Quantum-selected configuration interaction (QSCI) methods use a quantum computer to identify dominant electronic configurations in the molecular ground state, while a classical computer diagonalizes the Hamiltonian within the reduced subspace spanned by those configurations. Sample-based quantum diagonalization (SQD), a leading QSCI approach, uses iterative classical post-processing to correct noisy quantum measurement to ensure that the corresponding configurations remain physically sensible. In this work, we show that SQD performance can be strongly influenced by uncontrolled growth of the classical diagonalization subspace. When classical resources are not explicitly constrained, classical uniform random sampling can reproduce SQD benchmarks as noise increases the diversity of sampled configurations. We show any fair benchmarking protocol of SQD must explicitly control diagonalization size over unique samples. We then address the problem of efficiently discovering physically relevant, energy-lowering configurations by introducing a measurement protocol based on non-orthogonal configuration interaction (NOCI). By distributing measurements across orbital bases optimized with respect to the molecular Hamiltonian, we obtain improved sample efficiency relative to measurements performed solely in the Hartree--Fock basis. Importantly, these improvements persist even under fixed classical resource budgets, demonstrating that the resulting configurations are of higher quality rather than being more numerous. Under our proposed benchmarking procedure, we establish measurement-basis engineering as a promising route to improving quantum sampling methods for electronic structure.
Connor van Rossum, Jeffery Cohn, Sally Shrapnel et al.· 1 citation
This work presents a hybrid DFT-Quantum Embedding (QDFT) framework integrating classical HPC-based DFT with a quantum electronic-structure solver, demonstrating quantum embedding's potential to improve selected electronic-structure properties while retaining classical HPC's scalability.
N. Manglani, S. Maity, Shashank Sharma et al.· 0 citations
A protocol for approximating the measurement distributions of quantum states, extending beyond standard observable estimation is introduced, and tightened gate complexity bounds for practically relevant systems, including those with k-local interactions, long-tailed matrix ensembles, and conserved quantities are provided.
A. Mazumder, James D. Watson, Samson Wang· 0 citations
Quantum computing provides a promising framework for the simulation of quantum field theories, where the computational cost depends both on the quantum algorithm employed and on the representation of the Hamiltonian. We investigate a formulation of the $\phi^4$ model based on the harmonic-oscillator basis in coordinate space. We derive the lattice $\phi^4$ Hamiltonian in this representation and analyze the structure of the resulting one-body matrix and interaction tensor. We show that both exhibit an effective band-diagonal structure, allowing controlled truncations of the Hamiltonian while preserving the low-energy spectrum. We validate this formulation by comparing low-energy observables obtained from numerical diagonalization with those computed in the standard harmonic-oscillator momentum-space representation. Finally, we estimate the resources required to encode the Hamiltonian on a quantum computer using both binary and unary boson-to-qubit mappings. By exploiting effective locality, the coordinate-space representation reduces the resources required for quantum simulation over a broad range of parameters.
Gaétan Bardy, M. Saubanère, A. Tanasa· 0 citations
Engineering interactions that stabilize non-Abelian fractional quantum Hall phases is a central challenge in strongly correlated topological matter and quantum simulation. We introduce a differentiable framework for inverse Hamiltonian design, in which Haldane pseudopotentials are optimized by gradient-based exact diagonalization to stabilize target fractional quantum Hall phases. In spherical geometry, the Haldane pseudopotentials are treated as variational parameters and optimized in a JAX-based exact-diagonalization framework. By directly maximizing the overlap between the many-body ground state and the Moore-Read state, we obtain a robust pseudopotential profile that has Pfaffian overlaps exceeding $99\%$ for systems up to $N_e=12$, substantially improving over conventional Coulomb interactions. Analyses of the neutral excitation spectrum and orbital entanglement spectrum further confirm that the optimized interaction stabilizes the Pfaffian topological phase. Our results demonstrate that essential features of the three-body Pfaffian parent Hamiltonian can be effectively encoded in a suitably designed two-body interaction. Furthermore, they identify a nearly universal exponentially decaying pseudopotential profile that stabilizes the Pfaffian phase and establishes a general framework toward engineering non-Abelian topological order in quantum simulation.
We present a quantum-classical algorithm for electronic structure calculations that dramatically reduces the quantum measurement cost of variational quantum eigensolver (VQE) approaches. While conventional VQE methods require measurements scaling as O(M^4) with system size M, the proposed occupation-number VQE (ON-VQE) reduces this cost to O(M/2) by avoiding reduced density matrix (RDM) measurements and relying exclusively on ONs. The method exploits only the diagonal elements of the one-particle RDM in the natural orbital representation, where occupations are obtained directly from computational-basis measurement outcomes. By restricting the variational ansatz to double excitations within orbital subspaces associated with electron pairs, the required measurements can be grouped into a small number of qubit-wise commuting observables, yielding an efficient and scalable measurement strategy. The approach is validated through simulations and executions on quantum hardware for the cubic H$_8$ cluster, demonstrating the feasibility of extracting accurate ONs from quantum measurements and evaluating electronic energies within the natural orbital functional (NOF) framework. Across representative molecular systems, the extracted ONs enable accurate energy evaluation with state-of-the-art NOFs while maintaining a dramatically reduced measurement cost. These results establish a scalable route toward quantum simulation of strongly correlated electronic systems, demonstrating that accurate electronic energies can be obtained from quantum measurements of ONs alone.
Edison X Salazar, Juan Felipe Huan Lew-Yee, and Mario Piris· 0 citations
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