arXiv subjects

Guillermo González-García

Publications and source records attributed to Guillermo González-García.

4 recordsLinked to original sources

arXiv2026

On the stability to noise of fermion-to-qubit mappings

Quantum simulations before fault tolerance suffer from the intrinsic noise present in quantum computers. In this regime, extracting meaningful results greatly benefits from stability against that noise. This stability, defined as an error in observables that is independent of the system's size, is expected in local systems under local noise. In fermionic systems, the encoding of the fermionic degrees of freedom into qubits can introduce non-locality, making stability more delicate. Here, we investigate the stability to noise of fermion-to-qubit mappings. We consider noisy quantum circuits in $D$ dimensions modeled by alternating layers of local unitaries and general, single-qubit Pauli noise. We show that, when using local fermionic encodings, expectation values of quadratic fermionic observables are stable to noise in states with spatially decaying correlations: a power-law decay with exponent $μ>D$ is sufficient for stability. By contrast, we show that this stability cannot be achieved by non-local encodings such as Jordan-Wigner in $2D$, or quasi-local ones such as the Bravyi-Kitaev transform. Our findings formalize the intuition that decaying correlations of the physical systems under study provide protection against noise for local fermionic encodings, and help inform design principles in near-term quantum simulations.

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arXiv2025

Dynamical complexity of non-Gaussian many-body systems with dissipation

We characterize the dynamical state of many-body bosonic and fermionic many-body models with inter-site Gaussian couplings, on-site non-Gaussian interactions and local dissipation comprising incoherent particle loss, particle gain, and dephasing. We first establish that, for fermionic systems, if the dephasing noise is larger than the non-Gaussian interactions, irrespective of the Gaussian coupling strength, the system state is a convex combination of Gaussian states at all times. Furthermore, for bosonic systems, we show that if the particle loss and particle gain rates are larger than the Gaussian inter-site couplings, the system remains in a separable state at all times. Building on this characterization, we establish that at noise rates above a threshold, there exists a classical algorithm that can efficiently sample from the system state of both the fermionic and bosonic models. Finally, we show that, unlike fermionic systems, bosonic systems can evolve into states that are not convex-Gaussian even when the dissipation is much higher than the on-site non-Gaussianity. Similarly, unlike bosonic systems, fermionic systems can generate entanglement even with noise rates much larger than the inter-site couplings.

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arXiv2025

Pauli path simulations of noisy quantum circuits beyond average case

For random quantum circuits on $n$ qubits of depth $Θ(\log n)$ with depolarizing noise, the task of sampling from the output state can be efficiently performed classically using a Pauli path method [Aharonov et al. Proceedings of the 55th Annual ACM Symposium on Theory of Computing. 2023] . This paper aims to study the performance of this method beyond random circuits. We first consider the classical simulation of local observables in circuits composed of Clifford and T gates $\unicode{x2013}$ going beyond the average case analysis, we derive sufficient conditions for simulatability in terms of the noise rate and the fraction of gates that are T gates, and show that if noise is introduced at a faster rate than T gates, the simulation becomes classically easy. As an application of this result, we study 2D QAOA circuits that attempt to find low-energy states of classical Ising models on general graphs. There, our results shows that for hard instances of the problem, which correspond to Ising model's graph being geometrically non-local, a QAOA algorithm mapped to a geometrically local circuit architecture using SWAP gates does not have any asymptotic advantage over classical algorithms if depolarized at a constant rate. Finally, we illustrate instances where the Pauli path method fails to give the correct result, and also initiate a study of the trade-off between fragility to noise and classical complexity of simulating a given quantum circuit.

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arXiv2022

Error propagation in NISQ devices for solving classical optimization problems

We propose a random circuit model to analyze the impact of noise on the performance of variational quantum circuits for classical optimization problems. Our model accounts for the propagation of arbitrary single qubit errors through the circuit. We find that even with a small noise rate, the quality of the obtained classical optima is low on average and a single-qubit error rate of $1 / nD$, where $n$ is the number of qubits and $D$ is the circuit depth, is needed for the possibility of a quantum advantage. We estimate that this translates to an error rate lower than $10^{-6}$ using QAOA for classical optimization problems with 2D circuits.

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