Quantum reinforcement learning in the presence of thermal dissipation.

A study of the effect of thermal dissipation on quantum reinforcement learning is performed. For this purpose, a nondissipative quantum reinforcement learning protocol is adapted to the presence of thermal dissipation. Analytical calculations as well as numerical simulations are carried out, obtaining evidence that dissipation does not significantly degrade the performance of the quantum reinforcement learning protocol for sufficiently low temperatures, in some cases even being beneficial. Quantum reinforcement learning under realistic experimental conditions of thermal dissipation opens an avenue for the realization of quantum agents to be able to interact with a changing environment, as well as adapt to it, with many plausible applications inside quantum technologies and machine learning.

Toward Prediction of Financial Crashes with a D-Wave Quantum Annealer.

The prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can efficiently find optimal solutions. We experimentally explore a novel approach to this problem by using a D-Wave quantum annealer, benchmarking its performance for attaining a financial equilibrium. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed into a spin-1/2 Hamiltonian with at most, two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. The size of the simulation is mainly constrained by the necessity of a large number of physical qubits representing a logical qubit with the correct connectivity. Our experiment paves the way for the codification of this quantitative macroeconomics problem in quantum annealers.

One-Photon Solutions to the Multiqubit Multimode Quantum Rabi Model for Fast W-State Generation.

General solutions to the quantum Rabi model involve subspaces with an unbounded number of photons. However, for the multiqubit multimode case, we find special solutions with at most one photon for an arbitrary number of qubits and photon modes. Such solutions exist for arbitrary single qubit-photon coupling strength with constant eigenenergy, while still being qubit-photon entangled states. Taking advantage of their peculiarities and the reach of the ultrastrong coupling regime, we propose an adiabatic scheme for the fast and deterministic generation of a two-qubit Bell state and arbitrary single-photon multimode W states with nonadiabatic error less than 1%. Finally, we propose a superconducting circuit design to catch and release the W states, and shows the experimental feasibility of the multimode multiqubit quantum Rabi model.

Spin dynamics under the influence of elliptically rotating fields: Extracting the field topology from time-averaged quantities.

Systems that can be effectively described as a localized spin-s particle subject to time-dependent fields have attracted a great deal of interest due to, among other things, their relevance for quantum technologies. Establishing analytical relationships between the topological features of the applied fields and certain time-averaged quantities of the spin can provide important information for the theoretical understanding of these systems. Here, we address this question in the case of a localized spin-s particle subject to a static magnetic field coplanar to a coexisting elliptically rotating magnetic field. The total field periodically traces out an ellipse which encloses the origin of the coordinate system or not, depending on the values taken on by the static and the rotating components. As a result, two regimes with different topological properties characterized by the winding number of the total field emerge: the winding number is 1 if the origin lies inside the ellipse, and 0 if it lies outside. We show that the time average of the energy associated with the rotating component of the magnetic field is always proportional to the time average of the out-of-plane component of the expectation value of the spin. Moreover, the product of the signs of these two time-averaged quantities is uniquely determined by the topology of the total field and, consequently, provides a measurable indicator of this topology. We also propose an implementation of these theoretical results in a trapped-ion quantum system. Remarkably, our findings are valid in the totality of the parameter space and regardless of the initial state of the spin. In particular, when the system is prepared in a Floquet state, we demonstrate that the quasienergies, as a function of the driving amplitude at constant eccentricity, have stationary points at the topological transition boundary. The ability of the topological indicator proposed here to accurately locate the abrupt topological transition can have practical applications for the determination of unknown parameters appearing in the Hamiltonian. In addition, our predictions about the quasienergies can assist in the interpretation of conductance measurements in transport experiments with spin carriers in mesoscopic rings.

Experimental quantum simulation of fermion-antifermion scattering via boson exchange in a trapped ion.

Quantum field theories describe a variety of fundamental phenomena in physics. However, their study often involves cumbersome numerical simulations. Quantum simulators, on the other hand, may outperform classical computational capacities due to their potential scalability. Here we report an experimental realization of a quantum simulation of fermion-antifermion scattering mediated by bosonic modes, using a multilevel trapped ion, which is a simplified model of fermion scattering in both perturbative and non-perturbative quantum electrodynamics. The simulated model exhibits prototypical features in quantum field theory including particle pair creation and annihilation, as well as self-energy interactions. These are experimentally observed by manipulating four internal levels of a 171Yb+ trapped ion, where we encode the fermionic modes, and two motional degrees of freedom that simulate the bosonic modes. Our experiment establishes an avenue towards the efficient implementation of field modes, which may prove useful in studies of quantum field theories including non-perturbative regimes.

Measurement of linear response functions in Nuclear Magnetic Resonance.

We measure multi-time correlation functions of a set of Pauli operators on a two-level system, which can be used to retrieve its associated linear response functions. The two-level system is an effective spin constructed from the nuclear spins of 1H atoms in a solution of 13C-labeled chloroform. Response functions characterize the linear response of the system to a family of perturbations, allowing us to compute physical quantities such as the magnetic susceptibility of the effective spin. We use techniques exported from quantum information to measure time correlations on the two-level system. This approach requires the use of an ancillary qubit encoded in the nuclear spins of the 13C atoms and a sequence of controlled operations. Moreover, we demonstrate the ability of such a quantum platform to compute time-correlation functions of arbitrary order, which relate to higher-order corrections of perturbative methods. Particularly, we show three-time correlation functions for arbitrary times, and we also measure time correlation functions at fixed times up to tenth order.

Supervised Quantum Learning without Measurements.

We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation that introduces feedback in the dynamics and eliminates the necessity of intermediate measurements. The performance of the quantum algorithm is analyzed by comparing the results obtained in numerical simulations with the outcome of classical machine learning methods for the same problem. The use of time-delayed equations enhances the toolbox of the field of quantum machine learning, which may enable unprecedented applications in quantum technologies.

A Single-Ion Reservoir as a High-Sensitive Sensor of Electric Signals.

A single-ion reservoir has been tested, and characterized in order to be used as a highly sensitive optical detector of electric signals arriving at the trapping electrodes. Our system consists of a single laser-cooled 40Ca+ ion stored in a Paul trap with rotational symmetry. The performance is observed through the axial motion of the ion, which is equivalent to an underdamped and forced oscillator. Thus, the results can be projected also to Penning traps. We have found that, for an ion oscillator temperature T axial ≲ 10 mK in the forced-frequency range ω z = 2π × (80,200 kHz), the reservoir is sensitive to a time-varying electric field equivalent to an electric force of 5.3(2) neV/µm, for a measured quality factor Q = 3875(45), and a decay time constant γ z = 88(2) s-1. This method can be applied to measure optically the strength of an oscillating field or induced (driven) charge in this frequency range within times of tens of milliseconds. Furthermore the ion reservoir has been proven to be sensitive to electrostatic forces by measuring the ion displacement. Since the heating rate is below 0.3 µeV/s, this reservoir might be used as optical detector for any ion or bunch of charged particles stored in an adjacent trap.

Dispersive Regimes of the Dicke Model.

We study two dispersive regimes of the Dicke model in the dynamics of N two-level atoms interacting with a bosonic mode for long interaction times. Firstly, we analyze the model for the regime in which the qubit frequencies are equal and smaller than the mode frequency, and for values of the coupling strength similar or larger than the mode frequency, namely, the deep strong coupling regime. Secondly, we address an interaction that is dependent on the photon number, where the coupling strength is comparable to the geometric mean of the qubit and mode frequencies. We show that the associated dynamics is analytically tractable and provide useful frameworks with which to analyze the system behavior. In the deep strong coupling regime, we unveil the structure of unexpected resonances for specific values of the coupling, present for N ≥ 2, and in the photon-number-dependent regime we demonstrate that all the nontrivial dynamical behavior occurs in the atomic degrees of freedom for a given Fock state. We verify these assertions with numerical simulations of the qubit population and photon-statistic dynamics.

Basic protocols in quantum reinforcement learning with superconducting circuits.

Superconducting circuit technologies have recently achieved quantum protocols involving closed feedback loops. Quantum artificial intelligence and quantum machine learning are emerging fields inside quantum technologies which may enable quantum devices to acquire information from the outer world and improve themselves via a learning process. Here we propose the implementation of basic protocols in quantum reinforcement learning, with superconducting circuits employing feedback- loop control. We introduce diverse scenarios for proof-of-principle experiments with state-of-the-art superconducting circuit technologies and analyze their feasibility in presence of imperfections. The field of quantum artificial intelligence implemented with superconducting circuits paves the way for enhanced quantum control and quantum computation protocols.

A Study on Fast Gates for Large-Scale Quantum Simulation with Trapped Ions.

Large-scale digital quantum simulations require thousands of fundamental entangling gates to construct the simulated dynamics. Despite success in a variety of small-scale simulations, quantum information processing platforms have hitherto failed to demonstrate the combination of precise control and scalability required to systematically outmatch classical simulators. We analyse how fast gates could enable trapped-ion quantum processors to achieve the requisite scalability to outperform classical computers without error correction. We analyze the performance of a large-scale digital simulator, and find that fidelity of around 70% is realizable for π-pulse infidelities below 10-5 in traps subject to realistic rates of heating and dephasing. This scalability relies on fast gates: entangling gates faster than the trap period.

Digital-analog quantum simulation of generalized Dicke models with superconducting circuits.

We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi- Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.

Advanced-Retarded Differential Equations in Quantum Photonic Systems.

We propose the realization of photonic circuits whose dynamics is governed by advanced-retarded differential equations. Beyond their mathematical interest, these photonic configurations enable the implementation of quantum feedback and feedforward without requiring any intermediate measurement. We show how this protocol can be applied to implement interesting delay effects in the quantum regime, as well as in the classical limit. Our results elucidate the potential of the protocol as a promising route towards integrated quantum control systems on a chip.

Digital-Analog Quantum Simulation of Spin Models in Trapped Ions.

We propose a method to simulate spin models in trapped ions using a digital-analog approach, consisting in a suitable gate decomposition in terms of analog blocks and digital steps. In this way, we show that the quantum dynamics of an enhanced variety of spin models could be implemented with substantially less number of gates than a fully digital approach. Typically, analog blocks are built of multipartite dynamics providing the complexity of the simulated model, while the digital steps are local operations bringing versatility to it. Finally, we describe a possible experimental implementation in trapped-ion technologies.

Artificial Life in Quantum Technologies.

We develop a quantum information protocol that models the biological behaviours of individuals living in a natural selection scenario. The artificially engineered evolution of the quantum living units shows the fundamental features of life in a common environment, such as self-replication, mutation, interaction of individuals, and death. We propose how to mimic these bio-inspired features in a quantum-mechanical formalism, which allows for an experimental implementation achievable with current quantum platforms. This study paves the way for the realization of artificial life and embodied evolution with quantum technologies.

Time reversal and charge conjugation in an embedding quantum simulator.

A quantum simulator is an important device that may soon outperform current classical computations. A basic arithmetic operation, the complex conjugate, however, is considered to be impossible to be implemented in such a quantum system due to the linear character of quantum mechanics. Here, we present the experimental quantum simulation of such an unphysical operation beyond the regime of unitary and dissipative evolutions through the embedding of a quantum dynamics in the electronic multilevels of a (171)Yb(+) ion. We perform time reversal and charge conjugation, which are paradigmatic examples of antiunitary symmetry operators, in the evolution of a Majorana equation without the tomographic knowledge of the evolving state. Thus, these operations can be applied regardless of the system size. Our approach offers the possibility to add unphysical operations to the toolbox of quantum simulation, and provides a route to efficiently compute otherwise intractable quantities, such as entanglement monotones.

Quantum Emulation of Gravitational Waves.

Gravitational waves, as predicted by Einstein's general relativity theory, appear as ripples in the fabric of spacetime traveling at the speed of light. We prove that the propagation of small amplitude gravitational waves in a curved spacetime is equivalent to the propagation of a subspace of electromagnetic states. We use this result to propose the use of entangled photons to emulate the evolution of gravitational waves in curved spacetimes by means of experimental electromagnetic setups featuring metamaterials.