Sample-based quantum diagonalization can reduce the classical cost of many-body calculations by restricting diagonalization to configurations identified through quantum sampling, but its efficiency depends on how compactly the target state is represented in the sampled basis. We investigate this dependence for sample-based Krylov quantum diagonalization of the half-filled Fermi-Hubbard ladder using physically motivated one-body orbital rotations. Across position, momentum, bonding/antibonding, and leg-mode representations, the most compressible basis varies systematically with interaction strength and hopping anisotropy, with momentum sampling favored in the weakly interacting regime and geometry- or interaction-adapted representations becoming advantageous as the dominant energy scale changes. Near intermediate interaction and isotropic hopping, however, even the most favorable representation remains poorly compressible. Statevector SKQD calculations further show that basis choice strongly affects sampling efficiency. Hardware calculations on systems containing up to 120 qubits retain qualitative signatures of this basis dependence while revealing increasing particle-number leakage and reconstruction sensitivity with system size. These results show that scalable sample-based diagonalization requires co-design of the sampled representation, quantum circuit, and classical reconstruction procedure.
Sample-based quantum diagonalization can reduce the classical cost of many-body calculations by restricting diagonalization to configurations identified through quantum sampling, but its efficiency depends on how compactly the target state is represented in the sampled basis. We investigate this dependence for sample-based Krylov quantum diagonalization of the half-filled Fermi-Hubbard ladder using physically motivated one-body orbital rotations. Across position, momentum, bonding/antibonding, and leg-mode representations, the most compressible basis varies systematically with interaction strength and hopping anisotropy, with momentum sampling favored in the weakly interacting regime and geometry- or interaction-adapted representations becoming advantageous as the dominant energy scale changes. Near intermediate interaction and isotropic hopping, however, even the most favorable representation remains poorly compressible. Statevector SKQD calculations further show that basis choice strongly affects sampling efficiency. Hardware calculations on systems containing up to 120 qubits retain qualitative signatures of this basis dependence while revealing increasing particle-number leakage and reconstruction sensitivity with system size. These results show that scalable sample-based diagonalization requires co-design of the sampled representation, quantum circuit, and classical reconstruction procedure.
We present a symmetry-adapted extension of sample-based quantum diagonalization (SQD) that rigorously embeds space-group symmetry into the many-body subspace sampled by quantum hardware. The method is benchmarked on the two-leg ladder Hubbard model using both molecular orbital and momentum bases. Energy convergence is shown to be improved in the momentum basis compared to the molecular orbital basis for both the spin-quintet ground state and the spin-singlet excited state. We clarify the relationship between the compactness of the many-body wave function and the sparsity of the representation matrices of symmetry operations. Furthermore, the enhancement of the superconducting correlation function due to the Coulomb interaction is demonstrated. Our method highlights the importance of symmetry structure in random-sampling quantum simulation of correlated systems
Sample-based Krylov quantum diagonalization (SKQD) is a paradigmatic example of a quantum-centric supercomputing workflow that combines the convergence structure of Krylov quantum diagonalization with classical sampling-based post-processing. It provides convergence guarantees assuming that the important computational-basis configurations can be sampled from a set of Krylov states with sufficient probability. We analyze this assumption under depolarizing noise, deriving shot-count resource estimates that expose an exponential depth penalty, and perform experiments on current noisy hardware with the one-dimensional single-impurity Anderson model on a 20-site (40-qubit) instance. Device noise breaks the practical convergence predicted by the noiseless SKQD analysis, but approximate compilation techniques can compress the Krylov time-evolution circuits before execution. The compressed circuits accumulate less hardware noise, recover the expected energy convergence, and reduce both the quantum shot budget and the classical subspace dimension, remaining beneficial even when classical configuration recovery is applied.
We evaluate the Sample-based Krylov Quantum Diagonalization (SKQD) algorithm on one- and two-dimensional Heisenberg models, including strongly correlated regimes in which the ground state is dense. Using problem-informed initial states and magnetization-sector sweeps, SKQD accurately reproduces ground-state energies and field-dependent magnetization across a range of anisotropies. Benchmarks against DMRG and exact diagonalization show consistent qualitative agreement, with accuracy improving systematically in more anisotropic regimes. We further demonstrate SKQD on quantum hardware by implementing 18- and 30-qubit Heisenberg chains, obtaining magnetization curves that match theoretical expectations. Simulations on small 2D square-lattice systems further demonstrate that the method applies effectively beyond 1D geometries.
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.
We introduce a Basis Adaptive (BA) algorithm for hybrid quantum-classical simulation of correlated quantum many-body systems. Starting from a small set of physically motivated bitstrings, the algorithm iteratively applies a single-step first-order Trotterized circuit on a quantum processor, filters the sampled configurations by enforcing U(1) spin conservation and lattice reflection symmetry, and classically diagonalizes the Hamiltonian in the resulting reduced Hilbert space. This design avoids the variational optimization overhead of VQE, the deep coherent circuits required by QPE, and the symmetry-violating subspaces that arise in SKQD. The ground-state energy error is bounded analytically by 8∥H∥(1−αDT)1/2, where αDT is the probability weight captured by the DT sampled basis states. This bound connects algorithm performance directly to ground-state sparsity and explains the observed accuracy hierarchy across different phases. Benchmarked on the spin-1/2 Heisenberg XXZ chain (up to N=62 qubits on the IBM Heron processor), the algorithm achieves a 3.5% energy error in the gapped Neel phase (Δ=2.0) and below 0.5% at the ferromagnetic boundary (Δ=−1.0). The accuracy degrades to 28.7% in the strongly quasi-long-range-ordered regime (Δ=0.5). Spin-spin correlation functions are reproduced across all regimes, confirming that symmetry-filtered real-time sampling provides a practical and noise-resilient pathway to ground-state properties on near-term quantum hardware.
Sample-based quantum diagonalization (SQD) offers a powerful route to accurate quantum chemistry on noisy intermediate-scale quantum (NISQ) devices by combining quantum sampling with classical diagonalization. Here we introduce HSQD, a novel half-qubit SQD approach that halves the qubit requirement for simulating a chemical system and drastically reduces overall circuit depth and gate counts, suppressing hardware noise. When modeling the dissociation of the nitrogen molecule with a (10e, 26o) active space, HSQD matches the accuracy of SQD on IBM quantum hardware using only half the number of qubits and 40% fewer measurements. We further enhance HSQD with a heat-bath configuration interaction (HCI) inspired selection of the samples, forming HCI-HSQD. This yields sub-millihartree accuracy across the N2 potential energy surface and produces subspaces up to 39% smaller than those from classical HCI, showing a significant improvement in the compactness of the ground-state representation. Finally, we demonstrate the scalability of HCI-HSQD using iron-sulfur clusters, reaching active spaces of up to (54e, 36o) while using only half as many qubits as the original SQD. For these systems, HCI-HSQD reduces SQD energy errors by up to 76% for [2Fe-2S] and 26% for [4Fe-4S], while also reducing subspace sizes, halving measurement requirements, and eliminating expensive post-processing. Together, these results establish half-qubit SQD as a noise-resilient and resource-efficient pathway toward practical quantum advantage in strongly correlated chemistry.