arXiv subjects

Rafael Gómez-Lurbe

Publications and source records attributed to Rafael Gómez-Lurbe.

6 recordsLinked to original sources

arXiv2026

Sparse-QITE: Discovering Compact Generators for Quantum Imaginary-Time Evolution via Regularization Methods

Quantum imaginary-time evolution (QITE) provides a systematic route to ground-state preparation, but its cost grows rapidly with the locality $D$ of the unitary approximation, for which the local Pauli basis scales as $4^D$. We introduce Sparse-QITE, a regularized formulation that promotes compact generators, reducing the number of quantum operations and yielding circuits with fewer gates and lower depth. We derive rigorous bounds on the sparsification error and benchmark the method in one-dimensional transverse-field Ising and antiferromagnetic Heisenberg models. Sparse-QITE exhibits a controllable sparsity--accuracy trade-off while retaining strong compression even in the high-accuracy regime. In scalability experiments with respect to $D$, the active support grows much more slowly than in standard QITE and, in several regimes, approximately saturates over the domain sizes studied. After circuit construction and transpilation, some of the largest-domain cases require only about $1\%$ of the standard-QITE gate count while maintaining high accuracy. We further introduce adaptive and active-discovery variants: the former selects the regularization strength dynamically during the evolution, while the latter reduces the number of Pauli expectation values that need to be evaluated and, consequently, the measurement requirements. These results establish sparsity-promoting regularization as a route toward more resource-efficient QITE. More broadly, these results suggest that sparsity-promoting regularization may also benefit variational quantum algorithms.

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arXiv2026

Pauli Propagation for Imaginary-Time Evolution

We extend the Pauli Propagation framework to imaginary-time evolution and introduce imaginary-time Pauli Propagation (ITPP), an operator-based algorithm for approximating thermal and ground-state properties directly in the Pauli basis. We derive explicit imaginary-time propagation rules for Pauli strings and analyze the main approximation errors arising from Trotterization and Pauli-space truncation, including bounds that account for the non-unitary nature of the evolution. Benchmarking ITPP on the one-dimensional transverse field Ising model, we find that the method performs best in the high-temperature regime, where thermal states admit a compressed Pauli-basis approximation, while the required number of Pauli terms grows rapidly as the system approaches the ground-state limit. We further compare with tensor network simulations and study finite-temperature scalability through the number of retained Pauli terms required to reach a fixed target accuracy. These results establish ITPP as a complementary framework for imaginary-time simulation and suggest that combining imaginary-time and real-time Pauli Propagation could provide a pathway toward simulating more general non-unitary and open quantum system dynamics within a unified Pauli-based framework.

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arXiv2026

Emergence of a Macroscopic Cat State and Multi-Channel Entanglement in a Frustrated Cluster Spin Chain

We study a one-dimensional frustrated spin chain, which combines cluster-Ising and anisotropic next-nearest neighbor Ising models. We first offer a historical perspective that justifies the studied model. Then we study in detail the two quantum phases and prove that they are separated by a first order quantum phase transition. On one side, the ground state corresponds to a ferromagnetic phase, shows the presence of macroscopic cat states, and a small gap that closes in the thermodynamic limit. On the other phase, competing interactions avoid the establishment of a topological phase, though it conserves large incommensurate quantum correlations. We prove it is fundamentally distinct from a simple paramagnet, and we name it an incommensurate phase. This is a gapped phase, which gap does not close in the thermodynamic limit. While in the ferromagnetic phase there are two dominant Schmidt coefficients, in the incommensurate phase there are four. This corresponds to four distinct bipartite entanglement channels contributing substantially to the ground state. Finally, we discuss the utility of the macroscopic cat states for quantum metrology applications and the experimental feasibility of the system.

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arXiv2026

Adaptive time Compressed QITE (ACQ) and its geometrical interpretation

Imaginary time evolution (ITE) is a well-established method for ground-state preparation, a fundamental problem in many fields such as materials science, chemistry, and optimization. Quantum ITE (QITE) approximates this evolution on quantum hardware but suffers from high circuit depth and numerous measurements. In this work we introduce adaptive-time compressed QITE (ACQ), a novel algorithm that reduces resource-cost by combining adaptive time steps with circuit compression. This approach leverages geometric insights by characterizing its relationship to geodesic trajectories with a measure that distinguishes trajectories in CPN. Recalling that ITE is a gradient flow on the complex projective plane $\mathbb{CP}^N$, such trajectory measures allow one to measure the deviation from geodesicity of said flow. For Hamiltonians with only two distinct eigenvalues (spectral cardiality), ITE and QITE exactly trace geodesics, this fact motivates an adaptive strategy for systems whose corresponding spectral cardinality is greater than 2, where QITE unitaries are reused until an energy increase signals departure from the ITE path. This is implemented via a line search for energy minimization. Circuit compression is achieved by approximating the sequence of QITE unitaries with a single element of a one-parameter group. Numerical simulations on the transverse field Ising model and the Heisenberg model demonstrate that ACQ achieves comparable fidelity to standard QITE while significantly reducing the number of QITE optimizations and maintaining fixed circuit depth during propagation. Gate-count estimates and an analysis of the fidelity scaling with truncation parameters are provided. A gate count and performance comparison with the state of the art method double bracket QITE is also performed.

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arXiv2025

Variational noise mitigation in quantum circuits: the case of Quantum Fourier Transform

We propose using variational quantum algorithms (VQAs) to simulate established quantum algorithms under realistic noise conditions, aiming to surpass the fidelity of theoretical circuits in noisy environments. Focusing on the Quantum Fourier Transform (QFT), we perform numerical simulations for two qubits under both coherent and incoherent noise. To enhance generalization, we further introduce the use of Mutually Unbiased Bases (MUBs) during the optimization. Our results show that the variational circuit can reproduce the QFT with higher fidelity in scenarios dominated by coherent noise. This demonstrates the potential of the approach as an effective error-mitigation strategy for small- to medium-scale quantum systems, particularly in settings where coherent noise strongly impacts performance. Beyond mitigating noise and improving fidelity, the method can be adapted to the noise profile of a specific device, providing a versatile and practical route to enhance the reliability of quantum algorithms in near-term quantum hardware.

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arXiv2025

Efficient protocol to estimate the Quantum Fisher Information Matrix for Commuting-Block Circuits

The Quantum Fisher Information Matrix (QFIM) is a fundamental quantity in various subfields of quantum physics. It plays a crucial role in the study of parameterized quantum states, as it quantifies their sensitivity to variations in its parameters. Recently, the QFIM has been successfully employed to enhance the optimization of variational quantum algorithms. However, its practical applicability is often hindered by the high resource requirements for its estimation. In this work, we introduce a novel protocol for computing the off-block-diagonal elements of the QFIM between different layers in a particular class of variational quantum circuits, known as commuting-block circuits. Our approach significantly reduces the quantum resources required, specifically lowering the number of distinct quantum state preparations from $O(m^2)$ to $O(L^2)$, where $m$ is the total number of parameters and $L$ is the number of layers in the circuit. Consequently, our protocol also minimizes the number of classical measurements and post-processing operations needed to estimate the QFIM, leading to a substantial improvement in computational efficiency.

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