arXiv subjects

Martina Nibbi

Publications and source records attributed to Martina Nibbi.

6 recordsLinked to original sources

arXiv2026

A Quantum Algorithm with Polylogarithmic Depth per Trotter Step for the Extended Hubbard Model

The extended Hubbard model on a two-dimensional lattice captures key physical phenomena, but its simulation remains challenging because long-range interactions give rise to a large number of interaction terms. Here we present Q2FMM, an efficient quantum algorithm for simulating this model within the Trotter product formula. Inspired by the fast multipole method, Q2FMM replaces site-site interactions with interactions between hierarchical coarse-grained boxes across multiple length scales. In addition, the multipole expansions of boxes are reused for their parent boxes, further enhancing the efficiency. To enable this hierarchical reuse coherently, we design a reversible quantum circuit that removes garbage information through uncomputing. The resulting circuit depth for a single Trotter step scales polylogarithmically with system size.

quant-ph↗

arXiv2026

Practical block encodings of matrix polynomials that can also be trivially controlled

Quantum circuits naturally implement unitary operations on input quantum states. However, non-unitary operations can also be implemented through block encodings, where additional ancilla qubits are introduced and later measured. While block encoding has a number of well-established theoretical applications, its practical implementation has been prohibitively expensive for current quantum hardware. In this paper, we present practical and explicit block encoding circuits implementing matrix polynomial transformations of a target matrix. With standard approaches, block-encoding a degree-$d$ matrix polynomial requires a circuit depth scaling as $d$ times the depth for block-encoding the original matrix alone. By leveraging the recently introduced Fast One-Qubit Controlled Select LCU (FOQCS-LCU) framework, we show that the additional circuit-depth overhead required for encoding matrix polynomials can be reduced to scale linearly in $d$ with no dependence on system size or the cost of block encoding the original matrix. Moreover, we demonstrate that the FOQCS-LCU circuits and their associated matrix polynomial transformations can be controlled with negligible overhead, enabling efficient applications such as Hadamard tests. Finally, we provide explicit circuits for representative spin models, together with detailed non-asymptotic gate counts and circuit depths.

quant-ph↗

arXiv2025

Extending Quantum Computing through Subspace, Embedding and Classical Molecular Dynamics Techniques

The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the workload to classical hardware where tractable, we may broaden the applicability of quantum computation in the near term. In this perspective, we review techniques that facilitate the study of subdomains of chemical systems with quantum computers and present a proof-of-concept demonstration of quantum-selected configuration interaction deployed within a multiscale/multiphysics simulation workflow leveraging classical molecular dynamics, projection-based embedding and qubit subspace tools. This allows the technology to be utilised for simulating systems of real scientific and industrial interest, which not only brings true quantum utility closer to realisation but is also relevant as we look forward to the fault-tolerant regime.

quant-ph↗

arXiv2025

Efficient LCU block encodings through Dicke states preparation

With the Quantum Singular Value Transformation (QSVT) emerging as a unifying framework for diverse quantum speedups, the efficient construction of block encodings -- their fundamental input model -- has become increasingly crucial. However, devising explicit block encoding circuits remains a significant challenge. A widely adopted strategy is the Linear Combination of Unitaries (LCU) method. While general, its practical utility is often limited by substantial gate overhead. To address this, we introduce the Fast One-Qubit-Controlled Select LCU (FOQCS-LCU), a compact LCU formulation that requires only a linear number of ancilla qubits and is explicitly decomposed into one- and two-qubit gates. By exploiting the underlying Hamiltonian structure, we design a parametrized family of efficient Dicke state preparation routines, enabling systematic realization of the state preparation oracle at substantially reduced gate cost. The check matrix formalism further yields a constant-depth SELECT oracle, implemented as two fully parallelizable layers of singly controlled Pauli gates. We construct explicit block encoding circuits for representative spin models such as the Heisenberg and spin glass Hamiltonians and provide detailed, non-asymptotic gate counts. Our numerical benchmarks confirm the efficiency of the FOQCS-LCU approach, illustrating over an order-of-magnitude reduction in CNOT count compared to conventional LCU. This framework opens a pathway toward practical, low-depth block encodings for a broad class of structured matrices beyond those considered here.

quant-ph↗

arXiv2025

Wavefunction optimization at the complete basis set limit with Multiwavelets and DMRG

The density matrix renormalization group (DMRG) is a powerful numerical technique to solve strongly correlated quantum systems: it deals well with systems which are not dominated by a single configuration (unlike Coupled Cluster) and it converges rapidly to the Full Configuration Interaction (FCI) limit (unlike truncated Configuration Interaction (CI) expansions). In this work, we develop an algorithm integrating DMRG within the multiwavelet-based multiresolution analysis (MRA). Unlike fixed basis sets, multiwavelets offer an adaptive and hierarchical representation of functions, approaching the complete basis set limit to a specified precision. As a result, this combined technique leverages the multireference capability of DMRG and the complete basis set limit of MRA and multiwavelets. More specifically, we adopt a pre-existing Lagrangian optimization algorithm for orbitals represented in the MRA domain and improve its computational efficiency by replacing the original CI calculations with DMRG. Additionally, we substitute the reduced density matrices computation with the direct extraction of energy gradients from the DMRG tensors. We apply our method to small systems such H2, He, HeH2, BeH2 and N2. The results demonstrate that our approach reduces the final energy while keeping the number of orbitals low compared to FCI calculations on an atomic orbital basis set.

physics.chem-ph↗

arXiv2024

Block encoding of matrix product operators

Quantum signal processing combined with quantum eigenvalue transformation has recently emerged as a unifying framework for several quantum algorithms. In its standard form, it consists of two separate routines: block encoding, which encodes a Hamiltonian in a larger unitary, and signal processing, which achieves an almost arbitrary polynomial transformation of such a Hamiltonian using rotation gates. The bottleneck of the entire operation is typically constituted by block encoding and, in recent years, several problem-specific techniques have been introduced to overcome this problem. Within this framework, we present a procedure to block-encode a Hamiltonian based on its matrix product operator (MPO) representation. More specifically, we encode every MPO tensor in a larger unitary of dimension $D+2$, where $D = \lceil\log(χ)\rceil$ is the number of subsequently contracted qubits that scales logarithmically with the virtual bond dimension $χ$. Given any system of size $L$, our method requires $L+D$ ancillary qubits in total, while the number of one- and two-qubit gates decomposing the block encoding circuit scales as $\mathcal{O}(L\cdotχ^2)$.

quant-ph↗