arXiv subjects

Brian García Sarmina

Publications and source records attributed to Brian García Sarmina.

6 recordsLinked to original sources

arXiv2026

Q-PIPE: A Practical Quantum Phase Encoding Method

Efficient loading of classical data into quantum states remains a central bottleneck of quantum computing. We propose Quantum-Gray Phase Injection for Pixel Encoding (Q-PIPE), which writes continuous data into the eigenphases of a diagonal oracle by phase kickback and converts them coherently into computational-basis states by quantum phase estimation. Sums and differences between data sets are obtained by sequential oracle application, without quantum arithmetic circuits. We apply Q-PIPE to quantum image processing, using edge detection by directional finite differences as a proof of concept. Synthesized with uniformly controlled rotations, the oracle requires O(qN) controlled-NOT gates without ancillas for N pixels and q estimation qubits. This is the same scaling as optimized preparation of the novel enhanced quantum representation, whose output form Q-PIPE reproduces. A half-spectrum normalization removes phase aliasing, and a probability threshold derived from the phase-estimation kernel and scaled with image size controls spectral leakage. In ideal simulation, edge detection is exact for inputs commensurate with the estimation register and has low mean absolute error for continuous data. Under device noise models, multi-controlled-phase synthesis drives the output close to the maximally mixed state. The uniformly controlled synthesis instead reduces the compiled depth by a factor of 53--59 and preserves the edge structure (Pearson correlation r = 0.99 with the classical gradient). The limiting resource on current hardware is therefore the compiled oracle depth, not the encoding principle.

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arXiv2026

RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers

We introduce RFOX (Rotated-Field Oscillatory eXchange), a parameter-free quantum algorithm for combinatorial optimization that combines an almost constant non-stoquastic $XX$ catalyst with a weak harmonic $ZX$ counter-diabatic term. Using the Floquet-Magnus expansion, we derive an effective Hamiltonian whose leading-order $\mathcal{O}(δ/ω)$ corrections yield local $Y$ fields, field-modulated 2-body terms, and poly-local 3-body topological interactions driven by graph connectivity. This structure ensures a nearly flat instantaneous spectral gap, preventing the unpredictable gap collapses typical of conventional $X$ (stoquastic), $XX$, and $X+sXX$ (non-stoquastic) driver schedules. Extensive noiseless simulations and physical hardware experiments on IBM Quantum processors (up to 20 qubits) validate our spectral predictions. RFOX consistently attains near-optimal or exact ground states in the random-field Ising model using up to an order of magnitude fewer Trotter slices, with an advantage that grows alongside problem disorder. These results suggest that fixed-gap, non-stoquastic drivers augmented with analytically derived counter-diabatic terms offer a scalable, tuning-free route for quantum optimization.

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arXiv2026

Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information

Quantum Fisher Information (QFI) can be used to quantify how sensitive a quantum state reacts to changes in its variational parameters, making it a natural diagnostic for algorithms such as the Quantum Approximate Optimization Algorithm (QAOA). We perform a systematic QFI analysis of QAOA for Max-Cut on cyclic and complete graphs with $N = 4 - 10$ qubits. Two mixer families are studied, RX-only and hybrid RX-RY, with depths $p = 2, 4, 6$ and $p = 3, 6, 9$, respectively, and with up to three entanglement stages implemented through cyclic- or complete-entangling patterns. Complete graphs consistently yield larger QFI eigenvalues than cyclic graphs; none of the settings reaches the Heisenberg limit ($4N^2$), but several exceed the linear bound ($4N$). Introducing entanglement primarily redistributes QFI from diagonal to off-diagonal entries: non-entangled circuits maximize per-parameter (diagonal) sensitivity, whereas entangling layers increase the covariance fraction and thus cross-parameter correlations, with diminishing returns beyond the first stage. Leveraging these observations, we propose, as a proof of concept, a QFI-Informed Mutation (QIm) heuristic that sets mutation probabilities and step sizes from the normalized diagonal QFI. On 7- and 10-qubit instances, QIm attains higher mean energies and lower variance than equal-probability and random-restart baselines over 100 runs, underscoring QFI as a lightweight, problem-aware preconditioner for QAOA and other variational quantum algorithms.

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arXiv2025

Parameter optimization comparison in QAOA using Stochastic Hill Climbing with Random Re-starts and Local Search with entangled and non-entangled mixing operators

This study investigates the efficacy of Stochastic Hill Climbing with Random Restarts (SHC-RR) compared to Local Search (LS) strategies within the Quantum Approximate Optimization Algorithm (QAOA) framework across various problem models. Employing uniform parameter settings, including the number of restarts and SHC steps, we analyze LS with two distinct perturbation operations: multiplication and summation. Our comparative analysis encompasses multiple versions of max-cut and random Ising model (RI) problems, utilizing QAOA models with depths ranging from $1L$ to $3L$. These models incorporate diverse mixing operator configurations, which integrate $RX$ and $RY$ gates, and explore the effects of an entanglement stage within the mixing operator. Our results consistently show that SHC-RR outperforms LS approaches, showcasing superior efficacy despite its ostensibly simpler optimization mechanism. Furthermore, we observe that the inclusion of entanglement stages within mixing operators significantly impacts model performance, either enhancing or diminishing results depending on the specific problem context.

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arXiv2023

PCA and t-SNE analysis in the study of QAOA entangled and non-entangled mixing operators

In this paper, we employ PCA and t-SNE analysis to gain deeper insights into the behavior of entangled and non-entangled mixing operators within the Quantum Approximate Optimization Algorithm (QAOA) at varying depths. Our study utilizes a dataset of parameters generated for max-cut problems using the Stochastic Hill Climbing with Random Restarts optimization method in QAOA. Specifically, we examine the $RZ$, $RX$, and $RY$ parameters within QAOA models at depths of $1L$, $2L$, and $3L$, both with and without an entanglement stage inside the mixing operator. The results reveal distinct behaviors when we process the final parameters of each set of experiments with PCA and t-SNE, where in particular, entangled QAOA models with $2L$ and $3L$ present an increase in the amount of information that can be preserved in the mapping. Furthermore, certain entangled QAOA graphs exhibit clustering effects in both PCA and t-SNE. Overall, the mapping results clearly demonstrate a discernible difference between entangled and non-entangled models, quantified numerically through explained variance in PCA and Kullback-Leibler divergence (after optimization) in t-SNE, where some of these differences are also visually evident in the mapping data produced by both methods.

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arXiv2022

Comparison between the Iterative Local Search and Exhaustive Search methods applied to QAOA in Max-Cut and Ising Spin Model problems

A comparison is made between Exhaustive Search (ES) and Iterative Local Search (ILS). Such comparison was made using the Quantum Approximation Optimization Algorithm (QAOA). QAOA has been extensively researched due to its this potential to be implemented in actual quantum hardware, and its promising future in optimization problems and quantum machine learning. ES and ILS approaches were simulated to determine the pros and cons of these techniques for QAOA in local (classic computer) and real simulations (IBM quantum computer). These classic approaches were used in QAOA to approximate the optimal expected value in Max-Cut and Ising Spin Model (ISM) problems, both of these flavors have three simulated configurations called: linear, cyclic and complete (or full).

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