arXiv subjects

Federico Zahariev

Publications and source records attributed to Federico Zahariev.

10 recordsLinked to original sources

arXiv2026

Fragmentation of Virtual Orbitals for Quantum Computing: Reducing Qubit Requirements through Many-Body Expansion

We introduce quantum virtual-orbital fragmentation (Q-FVO), a systematic method for reducing the largest active space in correlated quantum-chemistry calculations. The complete occupied space is retained, the localized virtual space is partitioned into chemically motivated fragments, and the correlation energy is recovered through an inclusion-exclusion many-body expansion. Across six molecular benchmarks, the largest one-body Q-FVO calculations reduce the qubit requirement by 46 to 66 percent, while two-body calculations reduce it by approximately 31 to 42 percent relative to the corresponding unfragmented spaces. Two-body expansions recover most of the correlation energy, with errors of 0.9 to 7.5 kcal/mol; three-body expansions are below 1 kcal/mol for all CCSD tests and remain below 2 kcal/mol at CCSD(T). Illustrative statevector UCCSD calculations also reduce implementation-reported circuit depth while retaining accuracy below 1 kcal/mol. Q-FVO can be nested inside Q-EFMO real-space fragmentation and, in turn, the resulting cluster can be embedded in a Q-EFP environment. The hierarchy therefore reduces quantum-resource growth along three complementary dimensions: environment, molecular fragments, and virtual-orbital space.

quant-ph↗

arXiv2026

Quantum-Classical Effective Fragment Potential Embedding for Condensed-Phase Quantum Chemistry

Quantum simulation of chemistry in realistic environments is constrained by the orbital cost of explicit solvent, ions, and other surroundings. We present the quantum-classical effective fragment potential (Q-EFP) method, in which a chemically active region is treated with a quantum algorithm and the environment is represented by the effective fragment potential (EFP) in GAMESS. Coulomb and polarization potentials enter the active-region one-electron Hamiltonian, while EFP-EFP and short-range environment contributions are assembled classically. Statevector UCCSD/STO-3G benchmarks for LiH in a mixed water/methanol environment, H2O in a five-water environment, and BeH2 in an ammonium/nitrate environment differ from matched classical CCSD/EFP calculations by 0.03, 0.38, and 0.01 kcal/mol, respectively. The active calculations require 4 to 8 qubits, compared with estimated full-system counts of approximately 84 to 246 qubits, corresponding to register reductions of about 10-fold to 35-fold. These proof-of-concept results validate the embedded Hamiltonian and Q-GAMESS workflow while separating environmental size from quantum-register size. Q-EFP is complementary to real-space Q-EFMO fragmentation and virtual-orbital Q-FVO reduction, enabling a layered route to larger solvated systems.

quant-ph↗

arXiv2026

Quantum-Classical Fragmentation with the Effective Fragment Molecular Orbital Method

We present the quantum effective fragment molecular orbital (Q-EFMO) method, a hybrid framework that evaluates selected molecular-fragment correlation energies with the variational quantum eigensolver and assembles them through the size-consistent EFMO energy expression. A Hartree-Fock EFMO calculation supplies monomer references, many-body polarization, and distant-pair EFP interactions; independent VQE/UCCSD calculations provide correlation increments for monomers and selected near-field dimers. Consequently, the maximum quantum register is determined by the largest active fragment or fragment pair rather than by total system size. For a three-layer LiH benchmark in STO-3G, a full 2.5 to 3.5 Angstrom separation scan shows that two orbital-reduction schemes approach the full CCSD reference monotonically. The more aggressive scheme remains below 1 kcal/mol for separations of 2.6 Angstrom and greater and reaches 0.10 kcal/mol at 3.5 Angstrom, using 6 qubits for monomers and 12 for the largest dimers, compared with 14 qubits for the frozen-core dimer baseline. An implementation-specific cost proxy decreases from 1000 to 40, a factor of 25. These noise-free results establish the equations, software path, and resource scaling; broader chemical validation, larger bases, and hardware tests remain necessary.

quant-ph↗

arXiv2026

Certified Optimal Measurement Reduction over Quantum Context Landscapes

Quantum-measurement reduction contains two distinct global-optimization layers: a continuous problem of splitting an observable and allocating shots within a fixed measurement dictionary, and a nonconvex outer problem of designing the dictionary and calibrating its data-driven uncertainty model. We solve the inner layer globally and certifiably as a second-order cone program (SOCP), and use RANGE, a robust adaptive nature-inspired global optimizer, for the combinatorial and statistical outer layer. For any declared set of contexts, per-shot costs, score functions, and covariance model, the SOCP returns the minimum leading shot cost among unbiased linear stratified estimators. The conic dual supplies an independently checkable lower-bound witness; after feasibility repair, an external verifier recomputes $L \le Φ\le U$ from stored data without trusting the optimizer. Pilot measurements yield simultaneous finite-sample covariance brackets, and the dual becomes a pricing oracle for omitted contexts. Discrete RANGE searches covering sub-dictionaries, Pareto compression fronts, and candidate contexts; continuous RANGE performs an explicitly empirical, coverage-constrained calibration of covariance-radius models, while rigorous certificates retain the proved finite-sample radius. RANGE compresses molecular context dictionaries by 4.3-6.1x at 0.2-2.1% certified-frontier excess. Standard strategies are exactly optimal for H2 yet leave factors of 2.1-7.7 in shots within their own settings by H2O. Adding fully commuting contexts lowers the certified optimum by up to 56%; on 29-35-qubit production f-element Hamiltonians under a declared Hartree-Fock-proxy covariance model, the capped-dictionary enlargement saves 31-70% of the shots, and transformations reducing block-encoding cost need not reduce sampling cost.

quant-ph↗

arXiv2026

Beyond Orbital Rotations: Correlation-Rank Limits and Clifford-Accessible Measurement, from Algebra and Global Optimization

Algebra and RANGE global optimization play complementary, explicitly separated roles in identifying measurement structure beyond orbital rotations. In the fixed (1,1)-particle sector of two spatial orbitals per spin, algebra proves that one particle-number-preserving orbital-rotation context contributes a rank-one two-body correlation block $T$: an observable needs at least $\mathrm{rank}\,T$ such contexts, and its best $K$-context correlation-block approximation is exactly the Eckart-Young singular-value tail, attained by the truncated SVD. A continuous RANGE search over the physical rotation angles independently corroborates this exact trade-off. A Bell-diagonal, Heisenberg-type witness has correlation rank three: it needs at least three orbital-rotation contexts, while one explicit physical Clifford circuit measures its commuting Pauli representatives. For spin-conserving Jordan-Wigner molecular Hamiltonians we also prove the parity ceiling $r_X \le 2(N-1)$ for any Pauli subset, tight even within commuting subsets; $X$-rank is a routing diagnostic, and the strict separation is carried by the correlation-rank theorem. The discrete mode of RANGE locates high-$X$-rank commuting families across molecular and production f-element Hamiltonians, finding ceiling-saturating witnesses for CH4 and NdO; values are best found unless a proved ceiling is attained. Applying the companion certificate framework, enlarging product settings by fully commuting, Clifford-accessible settings reduces the certified leading shot cost by 31-70% on four 29-35-qubit f-element Hamiltonians, a QWC-versus-QWC+FC result rather than a Gaussian-versus-Clifford pricing. Controlled-Pauli insertions in Hadamard tests are Clifford; these zero-$T$ statements concern measurement circuitry only, while shot counts and state preparation retain their full costs.

quant-ph↗

arXiv2025

A Verified Compiler for Quantum Simulation

Hamiltonian simulation is a central application of quantum computing, with significant potential in modeling physical systems and solving complex optimization problems. Existing compilers for such simulations typically focus on low-level representations based on Pauli operators, limiting programmability and offering no formal guarantees of correctness across the compilation pipeline. We introduce QBlue, a high-level, formally verified framework for compiling Hamiltonian simulations. QBlue is based on the formalism of second quantization, which provides a natural and expressive way to describe quantum particle systems using creation and annihilation operators. To ensure safety and correctness, QBlue includes a type system that tracks particle types and enforces Hermitian structure. The framework supports compilation to both digital and analog quantum circuits and captures multiple layers of semantics, from static constraints to dynamic evolution. All components of QBlue, including its language design, type system, and compilation correctness, are fully mechanized in the Rocq proof framework, making it the first end-to-end verified compiler for second-quantized Hamiltonian simulation.

cs.PL↗

arXiv2025

Quantum Simulation Programming via Typing

Quantum simulations are designed to model quantum systems, and many compilation frameworks have been developed for executing such simulations on quantum computers. Most compilers leverage the capabilities of digital and analog quantum computers by representing quantum particle systems with Pauli strings or digital quantum circuits, making it challenging for users in physics, chemistry, and biology to program simulations effectively. QBLUE is proposed as the first programming language for describing the behaviors of quantum systems in terms of second quantization Hamiltonians. Within QBLUE, a novel type system is proposed to clearly define states across different quantum systems and treat quantum computers as quantum particle systems of specific types. The type system is compatible with the compilation of quantum simulations expressed in QBLUE for digital and analog quantum computers. With QBLUE, users can specify the desired quantum particle system and model the system on quantum computers.

quant-ph↗

arXiv2018

Nodal Variational Principle for Excited States

It is proven that the exact excited-state wave function and energy may be obtained by minimizing the energy expectation value of trial wave functions that are constrained only to have the correct nodes of the state of interest. This excited-state nodal minimum principle has the advantage that it requires neither minimization with the constraint of wave-function orthogonality to all lower eigenstates nor the antisymmetry of the trial wave functions. It is also found that the minimization over the entire space can be partitioned into several interconnected minimizations within the individual nodal regions, and the exact excited-state energy may be obtained by a minimization in just one or several of these nodal regions. For the proofs of the theorem, it is observed that the many-electron eigenfunction (excited state as well as ground state), restricted to a nodal region, is equivalent to a ground-state wave function of one electron in a higher-dimensional space; and, alternatively, an explicit excited-state energy variational expression is utilized by generalizing the Jacobi method of multiplicative variation. In corollaries, error functions are constructed for cases for which the nodes are not necessarily exact. The exact nodes minimize the energy error functions with respect to nodal variations. Simple numerical illustrations of the error functions are presented.

quant-ph↗

arXiv2016

Ground-State Energy as a Simple Sum of Orbital Energies in Kohn-Sham Theory: A Shift in Perspective through a Shift in Potential

It is observed that the exact interacting ground-state electronic energy of interest may be obtained directly, in principle, as a simple sum of orbital energies when a universal density-dependent term is added to $w\left(\left[ ρ\right];\mathbf{r} \right)$, the familiar Hartree plus exchange-correlation component in the Kohn-Sham effective potential. The resultant shifted potential, $\bar{w}\left(\left[ ρ\right];\mathbf{r} \right)$, actually changes less on average than $w\left(\left[ ρ\right];\mathbf{r} \right)$ when the density changes, including the fact that $\bar{w}\left(\left[ ρ\right];\mathbf{r} \right)$ does not undergo a discontinuity when the number of electrons increases through an integer. Thus the approximation of $\bar{w}\left(\left[ ρ\right];\mathbf{r} \right)$ represents an alternative direct approach for the approximation of the ground-state energy and density.

physics.chem-ph↗

arXiv2016

On Augmented Kohn-Sham Potential for Energy as a Simple Sum of Orbital Energies

It has recently been observed [Phys. Rev. Lett. 113, 113002 (2014)] that the ground-state energy may be obtained directly as a simple sum of augmented Kohn-Sham orbital energies, where it was ascertained that the corresponding one-body shifted Kohn-Sham effective potential has appealing features. With this in mind, eigenvalue and virial constraints are deduced for approximating this potential.

physics.chem-ph↗