arXiv subjects

Juan José García-Ripoll

Publications and source records attributed to Juan José García-Ripoll.

At least 55 records · Page 3Linked to original sources

arXiv2022

Quantum Fourier analysis for multivariate functions and applications to a class of Schrödinger-type partial differential equations

In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schrödinger-type, Hamiltonian partial differential equations (PDEs), using space-efficient variational circuits, including the symmetries of the problem, and global and gradient-based optimizers. We use this algorithm to benchmark the performance of the representation techniques by means of the computation of the ground state in three PDEs, i.e., the one-dimensional quantum harmonic oscillator, and the transmon and flux qubits, studying how they would perform in ideal and near-term quantum computers. With the Fourier methods developed here, we obtain low infidelities of order $10^{-4}-10^{-5}$ using only three to four qubits, demonstrating the high compression of information in a quantum computer. Practical fidelities are limited by the noise and the errors of the evaluation of the cost function in real computers, but they can also be improved through error mitigation techniques.

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arXiv2021

Quantum variational optimization: The role of entanglement and problem hardness

Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this paper we study systematically the role of entanglement, the structure of the variational quantum circuit, and the structure of the optimization problem, in the success and efficiency of these algorithms. For this purpose, our study focuses on the variational quantum eigensolver (VQE) algorithm, as applied to quadratic unconstrained binary optimization (QUBO) problems on random graphs with tunable density. Our numerical results indicate an advantage in adapting the distribution of entangling gates to the problem's topology, specially for problems defined on low-dimensional graphs. Furthermore, we find evidence that applying conditional value at risk type cost functions improves the optimization, increasing the probability of overlap with the optimal solutions. However, these techniques also improve the performance of Ansätze based on product states (no entanglement), suggesting that a new classical optimization method based on these could outperform existing NISQ architectures in certain regimes. Finally, our study also reveals a correlation between the hardness of a problem and the Hamming distance between the ground- and first-excited state, an idea that can be used to engineer benchmarks and understand the performance bottlenecks of optimization methods.

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arXiv2021

Three-Josephson Junctions Flux Qubit Couplings

We analyze the coupling of two flux qubits with a general many-body projector into the low-energy subspace. Specifically, we extract the effective Hamiltonians that controls the dynamics of two qubits when they are coupled via a capacitor and/or via a Josephson junction. While the capacitor induces a static charge coupling tunable by design, the Josephson junction produces a magnetic-like interaction easily tunable by replacing the junction with a SQUID. Those two elements allow to engineer qubits Hamiltonians with $XX$, $YY$ and $ZZ$ interactions, including ultra-strongly coupled ones. We present an exhaustive numerical study for two three-Josephson junctions flux qubit that can be directly used in experimental work. The method developed here, namely the numerical tool to extract qubit effective Hamiltonians at strong coupling, can be applied to replicate our analysis for general systems of many qubits and any type of coupling.

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arXiv2021

Hybrid quantum-classical optimization for financial index tracking

Tracking a financial index boils down to replicating its trajectory of returns for a well-defined time span by investing in a weighted subset of the securities included in the benchmark. Picking the optimal combination of assets becomes a challenging NP-hard problem even for moderately large indices consisting of dozens or hundreds of assets, thereby requiring heuristic methods to find approximate solutions. Hybrid quantum-classical optimization with variational gate-based quantum circuits arises as a plausible method to improve performance of current schemes. In this work we introduce a heuristic pruning algorithm to find weighted combinations of assets subject to cardinality constraints. We further consider different strategies to respect such constraints and compare the performance of relevant quantum ansätze and classical optimizers through numerical simulations.

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arXiv2021

Ultrastrong capacitive coupling of flux qubits

A flux qubit can interact strongly when it is capacitively coupled to other circuit elements. This interaction can be separated in two parts, one acting on the qubit subspaces and one in which excited states mediate the interaction. The first term dominates the interaction between the flux qubit and an LC-resonator, leading to ultrastrong couplings of the form $σ^y(a+a^\dagger),$ which complement the inductive $σ^xi(a^\dagger-a)$ coupling. However, when coupling two flux qubits capacitively, all terms need to be taken into account, leading to complex non-stoquastic ultrastrong interaction of the $σ^yσ^y$, $σ^zσ^z$ and $σ^xσ^x$ type. Our theory explains all these interactions, describing them in terms of general circuit properties---coupling capacitances, qubit gaps, inductive, Josephson and capactive energies---, that apply to a wide variety of circuits and flux qubit designs.

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arXiv2021

Visualizing the emission of a single photon with frequency and time resolved spectroscopy

At the dawn of Quantum Physics, Wigner and Weisskopf obtained a full analytical description (a \textit{photon portrait}) of the emission of a single photon by a two-level system, using the basis of frequency modes (Weisskopf and Wigner, "Zeitschrift für Physik", 63, 1930). A direct experimental reconstruction of this portrait demands an accurate measurement of a time resolved fluorescence spectrum, with high sensitivity to the off-resonant frequencies and ultrafast dynamics describing the photon creation. In this work we demonstrate such an experimental technique in a superconducting waveguide Quantum Electrodynamics (wQED) platform, using single transmon qubit and two coupled transmon qubits as quantum emitters. In both scenarios, the photon portraits agree quantitatively with the predictions of the input-output theory and qualitatively with Wigner-Weisskopf theory. We believe that our technique allows not only for interesting visualization of fundamental principles, but may serve as a tool, e.g. to realize multi-dimensional spectroscopy in waveguide Quantum Electrodynamics.

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arXiv2021

Automatic design of quantum feature maps

We propose a new technique for the automatic generation of optimal ad-hoc ansätze for classification by using quantum support vector machine (QSVM). This efficient method is based on NSGA-II multiobjective genetic algorithms which allow both maximize the accuracy and minimize the ansatz size. It is demonstrated the validity of the technique by a practical example with a non-linear dataset, interpreting the resulting circuit and its outputs. We also show other application fields of the technique that reinforce the validity of the method, and a comparison with classical classifiers in order to understand the advantages of using quantum machine learning.

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arXiv2021

Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations

In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as low-entanglement states of the quantum register. These states can be efficiently created in a quantum computer, but they are also efficiently stored, manipulated and probed using Matrix-Product States techniques. Inspired by this idea, we present eight quantum-inspired numerical analysis algorithms, that include Fourier sampling, interpolation, differentiation and integration of partial derivative equations. These algorithms combine classical ideas -- finite-differences, spectral methods -- with the efficient encoding of quantum registers, and well known algorithms, such as the Quantum Fourier Transform. {When these heuristic methods work}, they provide an exponential speed-up over other classical algorithms, such as Monte Carlo integration, finite-difference and fast Fourier transforms (FFT). But even when they don't, some of these algorithms can be translated back to a quantum computer to implement a similar task.

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arXiv2021

Gaussian phase sensitivity of boson-sampling-inspired strategies

In this work we study the phase sensitivity of generic linear interferometric schemes using Gaussian resources and measurements. Our formalism is based on the Fisher information. This allows us to separate the contributions of the measurement scheme, the experimental imperfections, and auxiliary systems. We demonstrate the strength of this formalism using a broad class of multimode Gaussian states that includes well-known results from single- and two-mode metrology scenarios. Using this, we prove that input coherent states or squeezing beat the non-classical states proposed in preceding boson-sampling-inspired phase-estimation schemes. We also develop a novel polychromatic interferometric protocol, demonstrating an enhanced sensitivity with respect to two-mode squeezed-vacuum states, for which the ideal homodyne detection is formally shown to be optimal.

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arXiv2021

Remote Individual Addressing of Quantum Emitters with Chirped Pulses

We propose to use chirped pulses propagating near a bandgap to remotely address quantum emitters. We introduce a particular family of chirped pulses that dynamically self-compress to sub-wavelength spot sizes during their evolution in a medium with a quadratic dispersion relation. We analytically describe how the compression distance and width of the pulse can be tuned through its initial parameters. We show that the interaction of such pulses with a quantum emitter is highly sensitive to its position due to effective Landau-Zener processes induced by the pulse chirping. Our results propose pulse engineering as a powerful control and probing tool in the field of quantum emitters coupled to structured reservoirs.

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arXiv2021

Experimental reconstruction of the few-photon nonlinear scattering matrix from a single quantum dot in a nanophotonic waveguide

Coherent photon-emitter interfaces offer a way to mediate efficient nonlinear photon-photon interactions, much needed for quantum information processing. Here we experimentally study the case of a two-level emitter, a quantum dot, coupled to a single optical mode in a nanophotonic waveguide. We carry out few-photon transport experiments and record the statistics of the light to reconstruct the scattering matrix elements of 1- and 2-photon components. This provides direct insight to the complex nonlinear photon interaction that contains rich many-body physics.

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arXiv2020

Topological input-output theory for directional amplification

We present a topological approach to the input-output relations of photonic driven-dissipative lattices acting as directional amplifiers. Our theory relies on a mapping from the optical non-Hermitian coupling matrix to an effective topological insulator Hamiltonian. This mapping is based on the singular value decomposition of non-Hermitian coupling matrices, whose inverse matrix determines the linear input-output response of the system. In topologically non-trivial regimes, the input-output response of the lattice is dominated by singular vectors with zero singular values that are the equivalent of zero-energy states in topological insulators, leading to directional amplification of a coherent input signal. In such topological amplification regime, our theoretical framework allows us to fully characterize the amplification properties of the quantum device such as gain, bandwidth, added noise, and noise-to-signal ratio. We exemplify our ideas in a one-dimensional non-reciprocal photonic lattice, for which we derive fully analytical predictions. We show that the directional amplification is near quantum-limited with a gain growing exponentially with system size, $N$, while the noise-to-signal ratio is suppressed as $1/\sqrt{N}$. This points out to interesting applications of our theory for quantum signal amplification and single-photon detection.

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arXiv2019

Mediator assisted cooling in quantum annealing

We show a significant reduction of errors for an architecture of quantum annealers (QA) where bosonic modes mediate the interaction between qubits. These systems have a large redundancy in the subspace of solutions, supported by arbitrarily large bosonic occupations. We explain how this redundancy leads to a mitigation of errors when the bosonic modes operate in the ultrastrong coupling regime. Numerical simulations also predict a large increase of qubit coherence for a specific annealing problem with mediated interactions. We provide evidences that noise reduction occurs in more general types of quantum computers with similar architectures.

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arXiv2019

Single photons by quenching the vacuum

Heisenberg's uncertainty principle implies that the quantum vacuum is not empty but fluctuates. These fluctuations can be converted into radiation through nonadiabatic changes in the Hamiltonian. Here, we discuss how to control this vacuum radiation, engineering a single-photon emitter out of a two-level system (2LS) ultrastrongly coupled to a finite-band waveguide in a vacuum state. More precisely, we show the 2LS nonlinearity shapes the vacuum radiation into a nonGaussian superposition of even and odd cat states. When the 2LS bare frequency lays within the band gaps, this emission can be well approximated by individual photons. This picture is confirmed by a characterization of the ground and bound states, and a study of the dynamics with matrix product states and polaron Hamiltonian methods.

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arXiv2018

Correlated Dephasing Noise in Single-photon Scattering

We develop a theoretical framework to describe the scattering of photons against a two-level quantum emitter with arbitrary correlated dephasing noise. This is particularly relevant to waveguide-QED setups with solid-state emitters, such as superconducting qubits or quantum dots, which couple to complex dephasing environments in addition to the propagating photons along the waveguide. Combining input-output theory and stochastic methods, we predict the effect of correlated dephasing in single-photon transmission experiments with weak coherent inputs. We discuss homodyne detection and photon counting of the scattered photons and show that both measurements give the modulus and phase of the single-photon transmittance despite the presence of noise and dissipation. In addition, we demonstrate that these spectroscopic measurements contain the same information as standard time-resolved Ramsey interferometry, and thus they can be used to fully characterize the noise correlations without direct access to the emitter. The method is exemplified with paradigmatic correlated dephasing models such as colored Gaussian noise, white noise, telegraph noise, and 1/f-noise, as typically encountered in solid-state environments.

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arXiv2018

Quantum annealing in spin-boson model: from a perturbative to a ultrastrong mediated coupling

We study a quantum annealer where bosons mediate the Ising-type interactions between qubits. We compare the efficiency of ground state preparation for direct and mediated couplings, for which Ising and spin-boson Hamiltonian are employed respectively. This comparison is done numerically for a small frustrated antiferromagnet, with a careful choice of the optimal adiabatic passage that reveals the features of the boson-mediated interactions. Those features can be explained by taking into account what we called excited solutions: states with the same spin correlations as the ground-state but with a larger bosonic occupancy. For similar frequencies of the bosons and qubits, the performance of quantum annealing depends on how excited solutions interchange population with local spin errors. We report an enhancement of quantum annealing thanks to this interchange under certain circumstances.

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arXiv2017

Quantum Emulation of Molecular Force Fields: A Blueprint for a Superconducting Architecture

In this work, we propose a flexible architecture of microwave resonators with tunable couplings to perform quantum simulations of problems from the field of molecular chemistry. The architecture builds on the experience of the D-Wave design, working with nearly harmonic circuits instead of qubits. This architecture, or modifications of it, can be used to emulate molecular processes such as vibronic transitions. Furthermore, we discuss several aspects of these emulations, such as dynamical ranges of the physical parameters, quenching times necessary for diabaticity, and, finally, the possibility of implementing anharmonic corrections to the force fields by exploiting certain nonlinear features of superconducting devices.

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arXiv2017

Multiphoton Scattering Tomography with Coherent States

In this work we develop an experimental procedure to interrogate the single- and multiphoton scattering matrices of an unknown quantum system interacting with propagating photons. Our proposal requires coherent state laser or microwave inputs and homodyne detection at the scatterer's output, and provides simultaneous information about multiple ---elastic and inelastic--- segments of the scattering matrix. The method is resilient to detector noise and its errors can be made arbitrarily small by combining experiments at various laser powers. Finally, we show that the tomography of scattering has to be performed using pulsed lasers to efficiently gather information about the nonlinear processes in the scatterer.

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