arXiv subjects

Gonzalo Camacho

Publications and source records attributed to Gonzalo Camacho.

11 recordsLinked to original sources

arXiv2026

Observing a $3T$ discrete time crystal on a trapped-ion qudit quantum processor

Time crystals have been observed in various qubit-based quantum platforms. However, the realization of time-crystal behavior beyond period doubling has remained fairly unexplored, in part because established qubit architectures natively encode two-cycle dynamics. Qudits offer a natural route beyond this restriction. Here we propose a one-dimensional, disorder-free $S=1$ Floquet model with short-range interactions that realizes a discrete $3T$ time crystal and implement it on a trapped-ion qudit quantum processor. We observe period tripling dynamics in local observables and spin correlations, confirming the collective subharmonic response of the system in the experiment. The stabilization mechanism is analyzed by deriving the effective Floquet Hamiltonian and performing numerical simulations that demonstrate the existence of a prethermal phase over a wide range of parameters. We compute the phase diagram and verify the presence of multipartite entanglement through the Quantum Fisher Information, showing that this quantity gets enhanced at the crossover between ergodic and localized regimes in non-equilibrium.

quant-ph↗

arXiv2026

Hamiltonian simulation with explicit formulas for Digital-Analog Quantum Computing

Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its digital gate-based counterpart, designing digital-analog circuits that employ optimal quantum resources often requires an exceedingly large classical computational time. In this work we find a suboptimal solution to this exponentially large problem, showing that it can be solved within polynomial computational time. In particular, we provide an exact solution for the problem of expressing arbitrary two-body Hamiltonians as the sum of local unitary transformations of an arbitrary Ising Hamiltonian, with the total number of required terms being at most quadratic in system size. This allows us to design a digital-analog simulation protocol that avoids employing numerical optimization over a large parameter space at the preprocessing stage, minimizing computational resources and allowing for further scaling.

quant-ph↗

arXiv2026

Time Crystals on Quantum Devices

Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external driving or environment. While related phenomena have long been studied in classical nonlinear systems, their realization in entangled quantum matter represents a distinct frontier. The theoretical understanding of discrete time crystals has substantially advanced, yet recent experiments using modern quantum devices and quantum processors reveal regimes beyond established paradigms. These developments call for an extended classification of time-crystalline phases according to both their stabilization mechanisms and their physical character, including discrete and continuous, closed and open, critical, topological, quasiperiodic, and controlled realizations. We review recent implementations of time crystals on quantum platforms and propose such a classification framework, identifying promising directions for the discovery of novel time-crystalline phases of matter.

quant-ph↗

arXiv2025

Critical Scaling of the Quantum Wasserstein Distance

Distinguishing quantum states with minimal sampling overhead is of fundamental importance to teach quantum data to an algorithm. Recently, the quantum Wasserstein distance emerged from the theory of quantum optimal transport as a promising tool in this context. Here we show on general grounds that the quantum Wasserstein distance between two ground states of a quantum critical system exhibits critical scaling. We demonstrate this explicitly using known closed analytical expressions for the magnetic correlations in the transverse field Ising model, to numerically extract the critical exponents for the distance close to the quantum critical point, confirming our analytical derivation. Our results have implications for learning of ground states of quantum critical phases of matter.

quant-ph↗

arXiv2025

Nonexistence of maximally entangled mixed states for a fixed spectrum

The existence of a maximally entangled pure state is a cornerstone result of entanglement theory that has paramount consequences in quantum information theory. A natural generalization of this property is to consider whether a notion of maximal entanglement is possible among all states with the same spectrum (where the aforementioned case of pure states corresponds to the particular choice in which the spectrum is a delta distribution, i.e., rank-1 states). Despite positive evidence in the past that such a notion might exist at least in the case of two-qubit states, it was recently shown in [Phys. Rev. Lett. 133, 050202 (2024)] that the answer to the above question is negative. This reference proved this for particular choices of the spectrum in the case of rank-2 two-qubit density matrices. While this settles the problem in general, it still leaves open whether there are other choices of the spectrum outside the case of pure states where a maximally entangled state for a fixed spectrum might exist. In this work we extend this impossibility result to all rank-2 and rank-3 two-qubit states as well as for a large class of eigenvalue distributions in the case where the rank equals four.

quant-ph↗

arXiv2025

Quantum walk on a square lattice with identical particles

We investigate quantum superposition effects in two-dimensional quantum walks of identical particles with different statistics under particle exchange, starting from various different initial configurations. To characterize interparticle correlation dynamics, we focus on joint properties such as two-particle coincidence probabilities and the spread velocity of the interparticle distance. Regarding spatial modes as an environment for the particles internal degrees of freedom, we study the role played by the particle statistics using standard entanglement witnesses, showing that particles possessing fermionic statistics are more resistant to thermalize with their environment. We analyze the presence of multipartite entanglement in the system's degrees of freedom through the Quantum Fisher Information, revealing that fermionic states generated during the walk are better suited to perform quantum metrology tasks. Finally, we discuss the potential for implementing this model using integrated photonic circuits by exploiting $N$-partite entanglement between individual photons.

quant-ph↗

arXiv2025

A Quantum-Inspired Algorithm for Wave Simulation Using Tensor Networks

We present an efficient classical algorithm based on the construction of a unitary quantum circuit for simulating the Isotropic Wave Equation (IWE) in one, two, or three dimensions. Using an analogy with the massless Dirac equation, second order time and space derivatives in the IWE are reduced to first order, resulting in a Schrödinger equation of motion. Exact diagonalization of the unitary circuit in combination with Tensor Networks allows simulation of the wave equation with a resolution of $10^{13}$ grid points on a laptop. A method for encoding arbitrary analytical functions into diagonal Matrix Product Operators is employed to prepare and evolve a Matrix Product State (MPS) encoding the solution. Since the method relies on the Quantum Fourier Transform, which has been shown to generate small entanglement when applied to arbitrary MPSs, simulating the evolution of initial conditions with sufficiently low bond dimensions to high accuracy becomes highly efficient, up to the cost of Trotterized propagation and sampling of the wavefunction. We conclude by discussing possible extensions of the approach for carrying out Tensor Network simulations of other partial differential equations such as Maxwell's equations.

quant-ph↗

arXiv2024

Prolonging a discrete time crystal by quantum-classical feedback

Nonequilibrium phases of quantum matter featuring time crystalline eigenstate order have been realized recently on noisy intermediate-scale quantum (NISQ) devices. While ideal quantum time crystals exhibit collective subharmonic oscillations and spatiotemporal long-range order persisting for infinite times, the decoherence time of current NISQ devices sets a natural limit to the survival of these phases, restricting their observation to a shallow quantum circuit. Here we propose a time-periodic scheme that leverages quantum-classical feedback protocols in subregions of the system to enhance a time crystal signal significantly exceeding the decoherence time of the device. As a case of study, we demonstrate the survival of the many-body localized discrete time crystal phase in the one-dimensional periodically kicked Ising model, accounting for decoherence of the system with an environment. Based on classical simulation of quantum circuit realizations we find that this approach is suitable for implementation on existing quantum hardware and presents a prospective path to simulate complex quantum many-body dynamics that transcend the low depth limit of current digital quantum computers.

cond-mat.str-el↗

arXiv2023

Dynamically generated quadrupole polarization using Floquet adiabatic evolution

We investigate the nonequilibrium dynamics of the $S=1$ quantum spin chain subjected to a time-dependent external drive, where the driving frequency is adiabatically decreased as a function of time (``Floquet adiabatic evolution''). We show that when driving the rhombic anisotropy term (known as the ``two-axis countertwisting'' in the context of squeezed spin states) of a Néel antiferromagnet, we are able to induce an overall enhancement in the quadrupole polarization, while at the same time suppressing the staggered magnetization order. The system evolves into a new state with a net quadrupole moment and antiferroquadrupolar correlations. This state remains stable at long times once the driving frequency is kept constant. On the other hand, we find that we cannot achieve a quadrupole polarization for the symmetry-protected Haldane phase, which remains robust against such driving.

cond-mat.str-el↗

arXiv2022

Local density of states of the interacting resonant level model at zero temperature

We present results of the impurity local density of states of the interacting resonant level model at zero temperature. We concentrate on low-energy properties and predominantly use the numerical renormalisation group technique. As interaction is increased, we find that the resonance peak at zero energy disappears, while two new peaks at finite energy emerge. This is in the absence of any field breaking the resonance. We further show that the height of the spectral function does not scale in the same way as the width, and in fact defines a second distinct exponent. We back up our results with analytic strong-coupling calculations as well as an analytic diagrammatic renormalisation group calculation that rather surprisingly gets the second exponent exactly, even for strong interactions.

cond-mat.str-el↗

arXiv2019

Exact equilibrium results in the Interacting Resonant Level Model

We present exact results for the susceptibility of the interacting resonant level model in equilibrium. Detailed simulations using both the Numerical Renormalization Group and Density Matrix Renormalization Group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sine-Gordon model, one finds an analytic expression for the relevant energy scale $T_K$ with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level model does not correctly reproduce $T_K$ - however if the bare parameters in the model are renormalised, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case.

cond-mat.str-el↗