arXiv subjects

Luis Pedro García-Pintos

Publications and source records attributed to Luis Pedro García-Pintos.

At least 19 recordsLinked to original sources

arXiv2026

Temporal information processing on a 4,500-qubit quantum annealer

Quantum machine learning could uncover statistical structure beyond the reach of classical models, but this requires quantum models large and expressive enough to be useful and cheap enough to read out. Most approaches optimize many quantum parameters and are thus limited by expensive training loops. Here we report a quantum machine-learning model implemented on a programmable superconducting quantum annealer that processes temporal data at large scale using up to 4,500 qubits-the largest quantum machine-learning experiment performed to date. Following the quantum reservoir computing paradigm, the untrained native many-body dynamics generated by reverse annealing is directly used to process temporal data. We prove that the interactions produced during annealing are indispensable-a non-interacting reservoir retains no memory of its input. We evaluate our model experimentally on standard memory benchmarks and demonstrate that it can successfully forecast chaotic time series. These results establish quantum annealers as a scalable platform for large-scale quantum machine learning.

quant-ph↗

arXiv2026

Randomized product formulas beyond optimal deterministic scaling

Product formulas, also known as Trotter formulas, are among the most widely used and practical methods for simulating quantum systems on quantum computers. Here we introduce two new classes of randomized product formulas for simulating Hamiltonians with separated energy scales, $H=A+αB$, where $α$ is small. In the standard access model, where one can implement exponentials of $A$ and $B$ separately, our randomized formulas achieve $\mathcal O(α^2)$ error scaling at the cost of only doubling the gate depth of the corresponding deterministic formula. We further prove an $Ω(α)$ lower bound for deterministic product formulas. In a stronger access model, allowing exponentials of $A+αB_\ell$ for $B = \sum_{\ell}B_\ell$, our randomized formula, based on Trotter Heuristic Resource Improved Formulas for Time-dynamics (THRIFT)~[J. L. Bosse et al., Nat. Commun. 16, 2673 (2025)], achieves $\mathcal O(α^3)$ error scaling with only constant-factor expected gate overhead. We also establish an $Ω(α^2)$ lower bound for deterministic product formulas in this access model. Numerical simulations confirm gate-count reductions for simulating physically motivated systems.

quant-ph↗

arXiv2026

Uncovering and Circumventing Noise in Quantum Algorithms via Metastability

The presence of noise is the primary challenge in realizing fault-tolerant quantum computers. In this work, we introduce and experimentally validate a novel strategy to circumvent noise by exploiting the phenomenon of metastability, where a dynamical system exhibits a separation of time scales in its evolution. We demonstrate that if quantum hardware noise exhibits metastability, both digital and analog algorithms can be designed in a noise-aware fashion to achieve intrinsic resilience. We develop a general theoretical framework and introduce an efficiently computable noise vulnerability metric that avoids the need for full classical simulation of the quantum algorithm. We show that the noise vulnerability index bounds errors in noisy implementations, with smaller values indicating greater fidelity between the achieved and target quantum states. We illustrate the use of our framework with applications to variational quantum algorithms and analog adiabatic state preparation. Crucially, we provide experimental evidence supporting the presence of metastable noise in gate-model quantum processors and quantum annealing devices. Thus, we establish that the noise properties in near-term quantum hardware can directly inform practical implementation strategies, enabling the preparation of final noisy states that more closely approximate the ideal ones.

quant-ph↗

arXiv2026

Hamiltonian and double-bracket flow formulations of quantum measurements

We introduce a framework that unifies quantum measurement dynamics, Hamiltonian dynamics, and double-bracket gradient flows. We do so by providing explicit expressions for stochastic Hamiltonians that produce state dynamics identical to those that happen during continuous quantum measurements. When such dynamical processes are integrated over sufficiently long time intervals, they yield the same results and statistics as during wavefunction collapse. That is, wavefunction collapse can be interpreted as coarse-grained (stochastic) Hamiltonian dynamics. Alternatively, wavefunction collapse can be interpreted as double-bracket gradient flows determined by derivatives of (stochastic) potentials defined in terms of observables with direct physical interpretations. The gradient flows minimize the variance of the monitored observable. Our derivations hold for general monitoring described by non-Hermitian jump processes. We show that such reinterpretations of measurement dynamics facilitate the design of feedback processes. In particular, we introduce feedback processes that yield deterministic double-bracket flow equations that prepare ground states of a target Hamiltonian, and state-agnostic feedback processes for state preparation. We apply the latter for entanglement stabilization of a two-qubit system considering a setup with imperfect measurements and feedback delay. We conclude by re-interpreting feedback processes as gradient flows with tilted fixed points.

quant-ph↗

arXiv2026

Precision Limits of Multiparameter Markovian-Noise Metrology

Measuring stochastic signals ("noise metrology") constitutes a central task in quantum sensing and the characterization of open quantum systems. Here we establish ultimate precision bounds for multiparameter estimation of stochastic signals encoded through Markovian Lindblad dynamics, allowing for arbitrary quantum control and noiseless ancillae. Although Markovianity enforces standard-quantum-limit scaling with sensing time $T$, our bounds reveal Heisenberg-type scaling in the number of dissipative channels, $R$: when the stochastic signal exhibits high-rank correlations across the $R$ channels and the probe is entangled, the average variance (per parameter) scales no better than $Ω(1/(TR^2))$. For collective $k$-body dissipation, $R=Θ(N^k)$, signifying super-Heisenberg scaling with the system size $N$. We further show that, when the unknown parameters enter through the dissipative eigenrates, a Rapid Prepare-and-Measure (RPM) protocol that tracks many distinct quantum jumps in parallel attains these limits. In this regime, the estimation problem reduces to a multi-Poisson counting model, providing a conceptually clean route to optimal quantum noise metrology. We illustrate the breadth of the framework with applications to networked noise metrology, collective many-body dissipation, learning Pauli noise, and subdiffraction quantum imaging.

quant-ph↗

arXiv2026

Quantum Uncertainty Relations for Thermodynamic Energy Flows

The Heisenberg uncertainty relation, which links the uncertainties of the position and momentum of a particle, has an important footprint on the quantum behavior of a physical system. Analogous to this principle, we propose that thermodynamic currents associated with work, heat, and internal energy satisfy their own uncertainty relations. To formalize this idea, we represent these currents by well-defined Hermitian operators, constructed so that their expectation values match the corresponding average currents. Because these operators generally do not commute, the resulting quantum currents differ fundamentally from their classical counterparts. Using the Robertson-Schrödinger uncertainty relation, we derive various uncertainty relations that link different thermodynamic flows. We further illustrate this approach by applying it to quantum batteries, where we derive an energy-power uncertainty relationship and show how measurements affect the fluctuations.

quant-ph↗

arXiv2025

Reshaping the Quantum Arrow of Time

While the microscopic laws of physics are often symmetric under time reversal, most natural processes that we observe are not. The emergent asymmetry between typical and time-reversed processes is referred to as the arrow of time. In quantum physics, an arrow of time emerges when a sequence of measurements is performed on a system. We introduce quantum control tools that can yield dynamics more consistent with time flowing backward than forward. The control tools are based on the explicit construction of a Hamiltonian that can replicate the stochastic trajectories of a monitored quantum system. Such Hamiltonian can reverse the effect of monitoring and, via a feedback process, generate trajectories consistent with a reversed arrow of time. It can also be used to simulate the backward-in-time dynamics of an open quantum system. Finally, we design a feedback-driven continuous measurement engine powered by the energy pumped into the system by the monitoring process. We show the engine can operate under experimentally realizable conditions with feedback delay and finite-efficiency measurements.

quant-ph↗

arXiv2025

Thermodynamics of large-scale chemical reaction networks

Chemical and biological networks can describe a wide variety of processes, from gene regulatory networks to biochemical oscillations. Modeled by chemical master equations, these processes are inherently stochastic, as fluctuations dominate deterministic order at mesoscopic scales. These classic many-body processes suffer from the so-called curse of high dimensionality, which makes exact mathematical descriptions exponentially expensive to compute. The exponential cost renders the study of the thermodynamic properties of such systems out of equilibrium intractable and forces approximations of system noise or assumptions of continuous particle numbers. Here, we use tensor networks to numerically explore the thermodynamics of chemical processes by directly solving the ensemble solution of the chemical master equation with efficient (sub-exponential) computational cost. We provide accurate estimates of the entropy production rate, heat flux, chemical work, and nonequilibrium thermodynamic potentials, free from sampling errors or mean-field approximations. We illustrate our results through a dissipative self-assembly model. In this way, we show how tensor networks can inform the design of efficient chemical processes in previously unattainable regimes.

cond-mat.stat-mech↗

arXiv2025

Quantum thermodynamic advantage in work extraction from steerable quantum correlations

Inspired by the primary goal of quantum thermodynamics -- to characterize quantum signatures and leverage their benefits in thermodynamic scenarios -- , we design a work extraction game within a bipartite framework that exhibits a quantum thermodynamic advantage. The steerability of quantum correlations between the two parties is the key resource enabling such an advantage. In designing the game, we exploit the correspondence between steerability and the incompatibility of observables. Our work extraction protocol involves mutually unbiased bases, which exhibit maximum incompatibility and therefore maximum steerability, showcased in maximally entangled quantum states. We derive upper bounds on the extractable work for unsteerable and steerable correlations and devise a protocol that saturates the latter. The ratio between the extractable work in steerable and unsteerable scenarios, which encapsulates the quantum advantage, increases with the dimension of the underlying system (sometimes referred to as an unbounded advantage). This proves a quantum thermodynamic advantage arising from steerable quantum correlations.

quant-ph↗

arXiv2025

Non-classicality at equilibrium and efficient predictions under non-commuting charges

A quantum thermodynamic system can conserve non-commuting observables, but the consequences of this phenomenon on relaxation are still not fully understood. We investigate this problem by leveraging an observable-dependent approach to equilibration and thermalization in isolated quantum systems. We extend such approach to scenarios with non-commuting charges, and show that it can accurately estimate the equilibrium distribution of coarse observables without access to the energy eigenvalues and eigenvectors. Our predictions do not require weak coupling and are not restricted to local observables, thus providing an advantage over the non-Abelian thermal state. Within this approach, weak values and quasiprobability distributions emerge naturally and play a crucial role in characterizing the equilibrium distributions of observables. We show and numerically confirm that, due to charges' non-commutativity, these weak values can be anomalous even at equilibrium, which has been proven to be a proxy for non-classicality. Our work thus uncovers a novel connection between the relaxation of observables under non-commuting charges, weak values, and Kirkwood-Dirac quasiprobability distributions.

quant-ph↗

arXiv2025

Noise-enhanced quantum clocks and global field sensors

I show that incoherent dynamics can lead to metrological advantages in quantum sensing. The results rely on the fact that incoherent dynamics lead to an additive contribution to the quantum Fisher information about time. Such an additive contribution can lead to a decrease in the error of optimal estimation protocols, as implied by the quantum Cramér-Rao bound. I characterize regimes in which the estimation of a time interval or a frequency is enhanced by noise, thus identifying cases where incoherent dynamics serve as a metrological resource. I illustrate with protocols that display improved sensing of time intervals or global fields by qubit and photonic sensor networks.

quant-ph↗

arXiv2025

Lower bounds on the number of rounds of the quantum approximate optimization algorithm required for guaranteed approximation ratios

The quantum approximate optimization algorithm, also known in its generalization as the quantum alternating operator ansatz, (QAOA) is a heuristic hybrid quantum-classical algorithm for finding high-quality approximate solutions to combinatorial optimization problems, such as maximum satisfiability. While the QAOA is well studied, theoretical results as to its runtime or approximation ratio guarantees are still relatively sparse. We provide some of the first lower bounds for the number of rounds (the dominant component of QAOA runtimes) required for the QAOA. For our main result, we (i) leverage a connection between quantum annealing times and the angles of the QAOA to derive a lower bound on the number of rounds of the QAOA with respect to the guaranteed approximation ratio. We apply and calculate this bound with Grover-style mixing unitaries and (ii) show that this type of QAOA requires at least a polynomial number of rounds to guarantee any constant approximation ratios for most problems. We also (iii) show that the bound depends only on the statistical values of the objective functions, and when the problem can be modeled as a $k$-local Hamiltonian, can be easily estimated from the coefficients of the Hamiltonians. For the conventional transverse-field mixer, (iv) our framework gives a trivial lower bound to all bounded-occurrence local cost problems and for all strictly $k$-local cost Hamiltonians matching known results that constant approximation ratio is obtainable with a constant-round QAOA for a few optimization problems from these classes. Using our proof framework, (v) we recover the Grover lower bound for unstructured search and, with small modification, show that our bound applies to any QAOA-style search protocol that starts in the ground state of the mixing unitaries.

quant-ph↗

arXiv2024

Tighter Lower Bounds on Quantum Annealing Times

We derive lower bounds on the time needed for a quantum annealer to prepare the ground state of a target Hamiltonian. These bounds do not depend on the annealing schedule and can take the local structure of the Hamiltonian into account. Consequently, the bounds are computable without knowledge of the annealer's dynamics and, in certain cases, scale with the size of the system. We discuss spin systems where the bounds are polynomially tighter than existing bounds, qualitatively capturing the scaling of the exact annealing times as a function of the number of spins.

quant-ph↗

arXiv2024

Generalized geometric speed limits for quantum observables

Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension $\geq 3$, tighten existing bounds -- in some cases by an arbitrarily large multiplicative constant. The generalized bounds can be used to design "fast" Hamiltonians that enable the rapid driving of the expectation values of observables with potential applications e.g.~to quantum annealing, optimal control, variational quantum algorithms, and quantum sensing. Our theoretical results are supported by illustrative examples and an experimental demonstration using a superconducting qutrit. Possibly of independent interest, along the way to one of our bounds we derive a novel upper bound on the generalized quantum Fisher information with respect to time (including the standard symmetric logarithmic derivative quantum Fisher information) for unitary dynamics in terms of the variance of the associated Hamiltonian and the condition number of the density matrix.

quant-ph↗

arXiv2024

Resilience-Runtime Tradeoff Relations for Quantum Algorithms

A leading approach to algorithm design aims to minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly prevalent in quantum computing, where gates are hard to implement and noise rapidly decreases a quantum computer's potential to outperform classical computers. Here, we find that minimizing the number of operations in a quantum algorithm can be counterproductive, leading to a noise sensitivity that induces errors when running the algorithm in non-ideal conditions. To show this, we develop a framework to characterize the resilience of an algorithm to perturbative noises (including coherent errors, dephasing, and depolarizing noise). Some compilations of an algorithm can be resilient against certain noise sources while being unstable against other noises. We condense these results into a tradeoff relation between an algorithm's number of operations and its noise resilience. We also show how this framework can be leveraged to identify compilations of an algorithm that are better suited to withstand certain noises.

quant-ph↗

arXiv2024

Limits on the Evolutionary Rates of Biological Traits

This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These \emph{rate limits} link the variability in a population to evolutionary rates. In particular, high variances in the fitness of a population and of a quantitative trait allow for fast changes in the trait's average. In contrast, low variability makes a trait less susceptible to random changes due to genetic drift. The results in this article generalize Fisher's fundamental theorem of natural selection to dynamics that allow for mutations and genetic drift, via trade-off relations that constrain the evolutionary rates of arbitrary traits. The rate limits can be used to probe questions in various evolutionary biology and ecology settings. They apply, for instance, to trait dynamics within or across species or to the evolution of bacteria strains. They apply to any quantitative trait, e.g., from species' weights to the lengths of DNA strands.

q-bio.PE↗

arXiv2024

Estimation of Hamiltonian parameters from thermal states

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term's degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than $1/\sqrt{n}$, beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g. a component of a magnetic field) is coupled locally and identically to $n$ qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.

quant-ph↗

arXiv2023

Bounding the Minimum Time of a Quantum Measurement

Measurements take a singular role in quantum theory. While they are often idealized as an instantaneous process, this is in conflict with all other physical processes in nature. In this Letter, we adopt a standpoint where the interaction with an environment is a crucial ingredient for the occurrence of a measurement. Within this framework, we derive lower bounds on the time needed for a measurement to occur. Our bound scales proportionally to the change in entropy of the measured system, and decreases as the number of of possible measurement outcomes or the interaction strength driving the measurement increases. We evaluate our bound in two examples where the environment is modelled by bosonic modes and the measurement apparatus is modelled by spins or bosons.

quant-ph↗