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See detailUnifying Quantum and Classical Speed Limits on Observables
García-Pintos, Luis Pedro; Nicholson, Schuyler B.; Green, Jason R. et al

in Physical Review X (2022)

The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables ... [more ▼]

The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit is divided into Mandelstam and Tamm’s original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, and both are generalized to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds on the speed of evolution.We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits and that a preferred basis of speed operators serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable. [less ▲]

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See detailProbing quantum chaos in multipartite systems
Cao, Zan; Xu, Zhenyu; Del Campo Echevarria, Adolfo UL

in Physical Review Research (2022)

Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed ... [more ▼]

Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting statistics of the local, total, and interaction energies. As in the spectral form factor, signatures of quantum chaos in the time domain dictate a dip-ramp-plateau structure in the characteristic function, i.e., the Fourier transform of the eigenvalue distribution. With this approach, we explore the fate of chaos in interacting subsystems that are locally maximally chaotic. Global quantum chaos can be suppressed at strong coupling, as illustrated with coupled copies of random-matrix Hamiltonians and of the Sachdev-Ye-Kitaev model. Our method is amenable to experimental implementation using single-qubit interferometry. [less ▲]

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See detailKibble-Zurek mechanism for nonequilibrium phase transitions in driven systems with quenched disorder
Reichhardt, C. J. O.; Del Campo Echevarria, Adolfo UL; Reichhardt, C.

in Communications Physics (2022)

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See detailSuper-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain
Yang, Jing UL; Pang, Shengshi; Del Campo Echevarria, Adolfo UL et al

in Physical Review Research (2022)

In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the the estimation of the ... [more ▼]

In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology. [less ▲]

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See detailVariational principle for optimal quantum controls in quantum metrology
Yang, Jing UL; Pang, Shengshi; Chen, Zekai et al

in Physical Review Letters (2022)

We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When ... [more ▼]

We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is limited, the exact optimal initial state and the optimal controls are, in general, dependent on the probe time, a feature missing in the unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, the problem can be approximately reduced to the unconstrained case via Floquet engineering. In particular, we find for magnetometry with a time-independent spin chain containing three-body interactions, even when the controls are restricted to one- and two-body interaction, that the Heisenberg scaling can still be approximately achieved. Our results open the door to investigate quantum metrology under a limited set of available controls, of relevance to many-body quantum metrology in realistic scenarios. [less ▲]

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See detailDigitized-counterdiabatic quantum approximate optimization algorithm
Chandarana, P.; Hegade, N. N.; Paul, K. et al

in Physical Review Research (2022)

The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ... [more ▼]

The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since the QAOA is an Ansatz-dependent algorithm, there is always a need to design Ansätze for better optimization. To this end, we propose a digitized version of the QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better Ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitized-CD QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms the standard QAOA in all cases we study. [less ▲]

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See detailBenchmarking quantum annealing dynamics: The spin-vector Langevin model
Subires, David; Gómez-Ruiz, Fernando J.; Ruiz-García, Antonia et al

in Physical Review Research (2022)

The classical spin-vector Monte Carlo (SVMC) model is a reference benchmark for the performance of a quantum annealer. Yet, as a Monte Carlo method, SVMC is unsuited for an accurate description of the ... [more ▼]

The classical spin-vector Monte Carlo (SVMC) model is a reference benchmark for the performance of a quantum annealer. Yet, as a Monte Carlo method, SVMC is unsuited for an accurate description of the annealing dynamics in real-time.We introduce the spin-vector Langevin (SVL) model as an alternative benchmark in which the time evolution is described by Langevin dynamics. The SVL model is shown to provide a more stringent test than the SVMC model for the identification of quantum signatures in the performance of quantum annealing devices, as we illustrate by describing the Kibble-Zurek scaling associated with the dynamics of symmetry breaking in the transverse field Ising model, recently probed using D-Wave machines. Specifically, we show that D-Wave data are reproduced by the SVL model. [less ▲]

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See detailDark solitons in a trapped gas of long-range interacting bosons
Beau, M.; Del Campo Echevarria, Adolfo UL; Frantzeskakis, D. J. et al

in Physical Review (2022)

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See detailParent Hamiltonians of Jastrow wavefunctions
Beau, Mathieu; Del Campo Echevarria, Adolfo UL

in SciPost Physics (2021)

We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian ... [more ▼]

We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus generalize the Calogero-Marchioro construction for the three-dimensional case to an arbitrary spatial dimension. The resulting family of models is further extended to include a one-body term representing an external potential, which gives rise to an additional long-range two-body interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of well-known systems such as the Calogero-Sutherland and Calogero-Moser models. We also introduce novel models, generalizing the McGuire many-body quantum bright soliton solution to higher dimensions and considering ground-states which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverse-engineered to construct models with a given potential, such as a pair-wise Yukawa potential, and to identify models governed exclusively by three-body interactions. [less ▲]

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See detailLimits to Perception by Quantum Monitoring with Finite Efficiency
García-Pintos, Luis Pedro; Del Campo Echevarria, Adolfo UL

in Entropy (2021)

We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds ... [more ▼]

We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent's perception of the system is altered by access to additional information We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain. [less ▲]

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See detailSuper-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain
Yang, Jing UL; Pang, Shengshi; Del Campo Echevarria, Adolfo UL et al

in Physical Review Research (2021)

In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction ... [more ▼]

In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology. [less ▲]

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See detailUhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results
Białończyk, Michał; Gomez-Ruiz, Fernando Javier; Del Campo Echevarria, Adolfo UL

in New Journal of Physics (2021)

We derive the exact expression for the Uhlmann fidelity between arbitrary thermal Gibbs states of the quantum XY model in a transverse field with finite system size. Using it, we conduct a thorough ... [more ▼]

We derive the exact expression for the Uhlmann fidelity between arbitrary thermal Gibbs states of the quantum XY model in a transverse field with finite system size. Using it, we conduct a thorough analysis of the fidelity susceptibility of thermal states for the Ising model in a transverse field.We compare the exact results with a common approximation that considers only the positive-parity subspace, which is shown to be valid only at high temperatures. The proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. We show that this enhancement persists in the thermodynamic limit and scales quadratically with the system size. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates, from which simple expressions are obtained for the thermal susceptibility and specific heat. [less ▲]

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See detailDelta-kick cooling, time-optimal control of scale-invariant dynamics, and shortcuts to adiabaticity assisted by kicks
Dupays, Léonce UL; Spierings, David C.; Steinberg, Aephraim M. et al

in Physical Review Research (2021)

Delta-kick cooling (DKC) is used to compress the momentum distribution of ultracold quantum matter. It combines expansion dynamics with the use of kick pulses, designed via classical methods, that bring ... [more ▼]

Delta-kick cooling (DKC) is used to compress the momentum distribution of ultracold quantum matter. It combines expansion dynamics with the use of kick pulses, designed via classical methods, that bring the system to rest.We introduce an exact approach to DKC for arbitrary scale-invariant dynamics of quantum gases, lifting the original restrictions to free evolution and noninteracting systems, to account for the control of atomic clouds in a time-dependent harmonic trap that can be either repulsive (inverted) or confining. We show that DKC assisted by a repulsive potential outperforms the conventional scheme, and that sudden trap-frequency quenches combined with DKC are equivalent to time-optimal bang-bang protocols.We further show that reverse engineering of the scale-invariant dynamics under smooth trap-frequency modulations can be combined with DKC to introduce a new class of shortcuts to adiabaticity assisted by kicks. [less ▲]

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See detailDistribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism
Mayo, Jack J.; Fan, Zhijie; Chern, Gia-Wei et al

in Physical Review Research (2021)

We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically ... [more ▼]

We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically found under Glauber dynamics, and the distribution of the number of kinks in the final state is shown to be consistent with a Poissonian distribution. The mean kink number, the variance, and the third centered moment take the same value and obey a universal power-law scaling with the quench time in which the temperature is varied. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics for moderate cooling times away from the asymptotic limit, when the kink-number distribution takes a binomial form. We analyze the relation of these results to physics beyond the Kibble-Zurek mechanism for critical dynamics, using the kink-number distribution to assess adiabaticity and its breakdown.We consider linear, nonlinear, and exponential cooling schedules, among which the last provides the most efficient shortcuts to cooling in a given quench time. The nonthermal behavior of the final state is established by considering the trace norm distance to a canonical Gibbs state. [less ▲]

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See detailExact thermal properties of free-fermionic spin chains
Białończyk, Michał; Gómez-Ruiz, Fernando Javier; Del Campo Echevarria, Adolfo UL

in SciPost Phys. (2021)

An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that ... [more ▼]

An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain. [less ▲]

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See detailDigitized-counterdiabatic quantum approximate optimization algorithm
Chandarana, P.; Hegade, N. N.; Paul, K. et al

in Physical Review Research (2021)

The quantum approximate optimization algorithm (QAOA) has proved to be an e ective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ... [more ▼]

The quantum approximate optimization algorithm (QAOA) has proved to be an e ective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since QAOA is an ansatz-dependent algorithm, there is always a need to design ansatz for better optimization. To this end, we propose a digitized version of QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitizedcounterdiabatic QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms standard QAOA in all cases we study. [less ▲]

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See detailUniversal statistics of vortices in a newborn holographic superconductor: beyond the Kibble-Zurek mechanism
Del Campo Echevarria, Adolfo UL; Gómez-Ruiz, Fernando Javier; Li, Zhi-Hong et al

in JHEP (2021)

Traversing a continuous phase transition at a finite rate leads to the breakdown of adiabatic dynamics and the formation of topological defects, as predicted by the celebrated Kibble-Zurek mechanism (KZM ... [more ▼]

Traversing a continuous phase transition at a finite rate leads to the breakdown of adiabatic dynamics and the formation of topological defects, as predicted by the celebrated Kibble-Zurek mechanism (KZM). We investigate universal signatures beyond the KZM, by characterizing the distribution of vortices generated in a thermal quench leading to the formation of a holographic superconductor. The full counting statistics of vortices is described by a binomial distribution, in which the mean value is dictated by the KZM and higher-order cumulants share the universal power-law scaling with the quench time. Extreme events associated with large fluctuations no longer exhibit a power-law behavior with the quench time and are characterized by a universal form of the Weibull distribution for different quench rates. [less ▲]

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See detailDark solitons in a trapped gas of long-range interacting bosons
Beau, M.; Del Campo Echevarria, Adolfo UL; Frantzeskakis, D. J. et al

in Physical Review X (2021)

We consider the interplay of repulsive short-range and long-range interactions in the dynamics of dark solitons, as prototypical coherent nonlinear excitations in a trapped quasi-1D Bose gas. Upon ... [more ▼]

We consider the interplay of repulsive short-range and long-range interactions in the dynamics of dark solitons, as prototypical coherent nonlinear excitations in a trapped quasi-1D Bose gas. Upon examining the form of the ground state, both the existence of the solitary waves and their stability properties are explored and corroborated by direct numerical simulations. We find that single- and multiple-dark-soliton states can exist and are generically robust in the presence of long-range interactions. We analyze the modes of vibration of such excitations and find that their respective frequencies are significantly upshifted as the strength of the long-range interactions is increased. Indeed, we find that a prefactor of the long-range interactions considered comparable to the trap strength may upshift the dark soliton oscillation frequency by an order of magnitude, in comparison to the well established one of /√2 in a trap of frequency . [less ▲]

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See detailProbing Quantum Speed Limits with Ultracold Gases
Del Campo Echevarria, Adolfo UL

in Physical Review Letters (2021)

Quantum speed limits (QSLs) rule the minimum time for a quantum state to evolve into a distinguishable state in an arbitrary physical process. These fundamental results constrain a notion of distance ... [more ▼]

Quantum speed limits (QSLs) rule the minimum time for a quantum state to evolve into a distinguishable state in an arbitrary physical process. These fundamental results constrain a notion of distance traveled by the quantum state, known as the Bures angle, in terms of the speed of evolution set by nonadiabatic energy fluctuations. I theoretically propose how to measure QSLs in an ultracold quantum gas confined in a timedependent harmonic trap. In this highly-dimensional system of continuous variables, quantum tomography is prohibited. Yet, QSLs can be probed whenever the dynamics is self-similar by measuring as a function of time the cloud size of the ultracold gas. This makes it possible to determine the Bures angle and energy fluctuations, as I discuss for various ultracold atomic systems. [less ▲]

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