David Arthur Mazziotti

A benzenetetrathiolate-bridged dinuclear platinum(diimine)(dithiolene) complex exhibits unprecedented deep near-infrared luminescence (1172 nm) upon two-electron oxidation.

We introduce a data-driven framework for approximating the convex set of N-representable two-electron reduced density matrices (2-RDMs). Traditional approaches characterize this set through linear matrix inequalities that define its supporting hyperplanes. Here, we instead learn a vertex-based approximation to its boundary from molecular data and use this information to improve the set defined by low-order positivity constraints, without explicitly constructing higher order conditions. The resulting semidefinite machine learning approach, combining an input convex neural network with semidefinite programming, drives a direct variational calculation of the 2-RDM with enhanced accuracy at a computational cost comparable to two-positivity calculations. Applications to the potential energy curves of C22–, N2, O22+, CO, NO+, and CN– demonstrate these systematic improvements as well as close agreement with complete active space configuration interaction results. Overall, semidefinite machine learning interweaves data-driven boundary information with semidefinite positivity constraints to yield more accurate energies and 2-RDMs without explicit higher order positivity conditions.

Quantum phenomena such as entanglement provide powerful resources for enhancing classical sensing. Here, we theoretically show that collective entanglement of spin qubits, arising from a condensation of particle-hole pairs, can strongly amplify transitions between ground and excited spin states, potentially improving signal contrast in optically detected magnetic resonance. This collective state exhibits an O ( N ) enhancement of the transition amplitude with respect to an applied microwave field, where N is the number of entangled spin qubits. We computationally realize this amplification using an ensemble of N triplet spins with magnetic dipole interactions, where the largest transition amplitudes occur at geometries for which the condensation of particle-hole pairs is strongest. This effect, robust to noise, originates from the concentration of entanglement into a single collective mode, reflected in a large eigenvalue of the particle-hole reduced density matrix—an entanglement witness of condensation analogous to off-diagonal long-range order, though realized here in a finite system. These results offer a design principle for quantum sensors that exploit condensation-inspired entanglement to boost sensitivity in spin-based platforms.

Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and computational demands limit scalability, motivating efficient alternatives such as classical shadows, which enable accurate prediction of many observables from randomized measurements. In this work, we introduce a bi-objective semidefinite programming approach for constrained shadow tomography, designed to reconstruct the two-particle reduced density matrix (2-RDM) from noisy or incomplete shadow data. By integrating N-representability constraints and nuclear-norm regularization into the optimization, the method builds an N-representable 2-RDM that balances fidelity to the shadow measurements with energy minimization. This unified framework mitigates noise and sampling errors while enforcing physical consistency in the reconstructed states. Numerical and hardware results demonstrate that the approach significantly improves accuracy, noise resilience, and scalability, providing a robust foundation for physically consistent fermionic state reconstruction in realistic quantum simulations.

Representability determines when a two-particle reduced density matrix (2-RDM) corresponds to a physical quantum state, enabling many-particle quantum calculations with 2-RDMs rather than the wave function. In this Letter, we present a solution of the representability problem for quantum systems without particle-number conservation. The physically allowed set of 2-RDMs can be characterized from a geometrically "orthogonal" set, the polar cone. We derive explicit linear equations for the two-body operators in the polar cone-the intersection of the p-positive cone with the two-body operator space-to obtain a systematic hierarchy of representability conditions that do not depend on higher RDMs or the wave function. Moreover, by augmenting these conditions with the particle-number variance, we obtain a unified framework for treating both particle-number-conserving and nonconserving systems. We illustrate with a spin system and molecular H_{4}.

Hybrid quantum-classical algorithms have begun to leverage quantum devices to efficiently represent many-electron wave functions, enabling early demonstrations of molecular simulations on real hardware. A key prerequisite for scalable quantum chemistry, however, is size consistency: the energy of non-interacting subsystems must scale linearly with system size. While many algorithms are theoretically size-consistent, noise on quantum devices may couple nominally independent subsystems and degrade this fundamental property. Here, we systematically evaluate size consistency on quantum hardware by simulating systems composed of increasing numbers of non-interacting H₂ molecules using optimally shallow unitary circuits. We find that molecular energies remain size-consistent within chemical accuracy for an estimated 118 and 71 H₂ subsystems for one- and two-qubit unitary designs, respectively, demonstrating that current quantum devices preserve size consistency over chemically relevant system sizes and supporting the feasibility of scalable, noise-resilient simulation of strongly correlated molecules and materials.