arXiv subjects

Nicolás Quesada

Publications and source records attributed to Nicolás Quesada.

At least 55 records · Page 3Linked to original sources

arXiv2021

Exact and approximate continuous-variable gate decompositions

We gather and examine in detail gate decomposition techniques for continuous-variable quantum computers and also introduce some new techniques which expand on these methods. Both exact and approximate decomposition methods are studied and gate counts are compared for some common operations. While each having distinct advantages, we find that exact decompositions have lower gate counts whereas approximate techniques can cover decompositions for all continuous-variable operations but require significant circuit depth for a modest precision.

quant-ph↗

arXiv2020

Exact simulation of Gaussian Boson Sampling in polynomial space and exponential time

We introduce an exact classical algorithm for simulating Gaussian Boson Sampling (GBS). The complexity of the algorithm is exponential in the number of photons detected, which is itself a random variable. For a fixed number of modes, the complexity is in fact equivalent to that of calculating output probabilities, up to constant prefactors. The simulation algorithm can be extended to other models such as GBS with threshold detectors, GBS with displacements, and sampling linear combinations of Gaussian states. In the specific case of encoding non-negative matrices into a GBS device, our method leads to an approximate sampling algorithm with polynomial runtime. We implement the algorithm, making the code publicly available as part of Xanadu's The Walrus library, and benchmark its performance on GBS with random Haar interferometers and with encoded Erdős-Renyi graphs.

quant-ph↗

arXiv2020

Theory of high-gain twin-beam generation in waveguides: from Maxwell's equations to efficient simulation

We provide an efficient method for the calculation of high-gain, twin-beam generation in waveguides derived from a canonical treatment of Maxwell's equations. Equations of motion are derived that naturally accommodate photon generation via spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing (SFWM), and also include the effects of both self-phase modulation (SPM) of the pump, and of cross-phase modulation(XPM) of the twin beams by the pump. The equations we solve involve fields that evolve in space and are labelled by a frequency. We provide a proof that these fields satisfy bonafide commutation relations, and that in the distant past and future they reduce to standard time-evolving Heisenberg operators. Having solved for the input-output relations of these Heisenberg operators we also show how to construct the ket describing the quantum state of the twin-beams. Finally, we consider the example of high-gain SPDC in a waveguide with a flat nonlinearity profile, for which our approach provides an explicit solution that requires only a single matrix exponentiation.

quant-ph↗

arXiv2020

Fast optimization of parametrized quantum optical circuits

Parametrized quantum optical circuits are a class of quantum circuits in which the carriers of quantum information are photons and the gates are optical transformations. Classically optimizing these circuits is challenging due to the infinite dimensionality of the photon number vector space that is associated to each optical mode. Truncating the space dimension is unavoidable, and it can lead to incorrect results if the gates populate photon number states beyond the cutoff. To tackle this issue, we present an algorithm that is orders of magnitude faster than the current state of the art, to recursively compute the exact matrix elements of Gaussian operators and their gradient with respect to a parametrization. These operators, when augmented with a non-Gaussian transformation such as the Kerr gate, achieve universal quantum computation. Our approach brings two advantages: first, by computing the matrix elements of Gaussian operators directly, we don't need to construct them by combining several other operators; second, we can use any variant of the gradient descent algorithm by plugging our gradients into an automatic differentiation framework such as TensorFlow or PyTorch. Our results will find applications in quantum optical hardware research, quantum machine learning, optical data processing, device discovery and device design.

quant-ph↗

arXiv2020

Efficient sampling from shallow Gaussian quantum-optical circuits with local interactions

We prove that a classical computer can efficiently sample from the photon-number probability distribution of a Gaussian state prepared by using an optical circuit that is shallow and local. Our work generalizes previous known results for qubits to the continuous-variable domain. The key to our proof is the observation that the adjacency matrices characterizing the Gaussian states generated by shallow and local circuits have small bandwidth. To exploit this structure, we devise fast algorithms to calculate loop hafnians of banded matrices. Since sampling from deep optical circuits with exponential-scaling photon loss is classically simulable, our results pose a challenge to the feasibility of demonstrating quantum supremacy on photonic platforms with local interactions.

quant-ph↗

arXiv2020

Training Gaussian Boson Sampling Distributions

Gaussian Boson Sampling (GBS) is a near-term platform for photonic quantum computing. Applications have been developed which rely on directly programming GBS devices, but the ability to train and optimize circuits has been a key missing ingredient for developing new algorithms. In this work, we derive analytical gradient formulas for the GBS distribution, which can be used to train devices using standard methods based on gradient descent. We introduce a parametrization of the distribution that allows the gradient to be estimated by sampling from the same device that is being optimized. In the case of training using a Kullback-Leibler divergence or log-likelihood cost function, we show that gradients can be computed classically, leading to fast training. We illustrate these results with numerical experiments in stochastic optimization and unsupervised learning. As a particular example, we introduce the variational Ising solver, a hybrid algorithm for training GBS devices to sample ground states of a classical Ising model with high probability.

quant-ph↗

arXiv2020

Regimes of classical simulability for noisy Gaussian boson sampling

As a promising candidate for exhibiting quantum computational supremacy, Gaussian Boson Sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS --- in the form of an inequality between the input squeezing parameter, the overall transmission rate and the quality of photon detectors. Our result serves as a non-classicality test that must be passed by any quantum computationalsupremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss.

quant-ph↗

arXiv2019

Non-Hermitian engineering for brighter broadband pseudothermal light

We show that non-Hermitian engineering can play a positive role in quantum systems. This is in contrast to the widely accepted notion that optical losses are a foe that must be eliminated or, at least, minimized. We take advantage of the interplay between nonlinear interactions and loss to show that spectral-loss engineering can relax phase-matching conditions, enabling generation of broadband pseudothermal states at new frequencies. This opens the door for utilizing the full potential of semiconductor materials that exhibit giant nonlinearities but lack the necessary ingredients for achieving quasi-phase matching. This in turn may pave the way for building on-chip quantum light sources.

quant-ph↗

arXiv2019

Applications of Near-Term Photonic Quantum Computers: Software and Algorithms

Gaussian Boson Sampling (GBS) is a near-term platform for photonic quantum computing. Recent efforts have led to the discovery of GBS algorithms with applications to graph-based problems, point processes, and molecular vibronic spectra in chemistry. The development of dedicated quantum software is a key enabler in permitting users to program devices and implement algorithms. In this work, we introduce a new applications layer for the Strawberry Fields photonic quantum computing library. The applications layer provides users with the necessary tools to design and implement algorithms using GBS with only a few lines of code. This paper serves a dual role as an introduction to the software, supported with example code, and also a review of the current state of the art in GBS algorithms.

quant-ph↗

arXiv2019

Understanding high gain twin beam sources using cascaded stimulated emission

We present a new method for the spectral characterization of pulsed twin beam sources in the high gain regime, using cascaded stimulated emission. We show an implementation of this method for a ppKTP spontaneous parametric down-conversion source generating up to 60 photon pairs per pulse, and demonstrate excellent agreement between our experiments and our theory. This work enables the complete and accurate experimental characterization of high gain effects in parametric down conversion, including self and cross-phase modulation. Moreover, our theory allows the exploration of designs with the goal of improving the specifications of twin beam sources for application in quantum information, computation, sampling, and metrology.

quant-ph↗

arXiv2019

Point Processes with Gaussian Boson Sampling

Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of quantum computing to statistical modeling by establishing a connection between point processes and Gaussian Boson Sampling, an algorithm for special-purpose photonic quantum computers. We show that Gaussian Boson Sampling can be used to implement a class of point processes based on hard-to-compute matrix functions which, in general, are intractable to simulate classically. We also discuss situations where polynomial-time classical methods exist. This leads to a family of efficient quantum-inspired point processes, including a new fast classical algorithm for permanental point processes. We investigate the statistical properties of point processes based on Gaussian Boson Sampling and reveal their defining property: like bosons that bunch together, they generate collections of points that form clusters. Finally, we discuss several additional properties of these point processes which we illustrate with example applications.

quant-ph↗

arXiv2019

A faster hafnian formula for complex matrices and its benchmarking on a supercomputer

We introduce new and simple algorithms for the calculation of the number of perfect matchings of complex weighted, undirected graphs with and without loops. Our compact formulas for the hafnian and loop hafnian of $n \times n $ complex matrices run in $O(n^3 2^{n/2})$ time, are embarrassingly parallelizable and, to the best of our knowledge, are the fastest exact algorithms to compute these quantities. Despite our highly optimized algorithm, numerical benchmarks on the Titan supercomputer with matrices up to size $56 \times 56$ indicate that one would require the 288000 CPUs of this machine for about a month and a half to compute the hafnian of a $100 \times 100$ matrix.

cs.DS↗

arXiv2019

Strawberry Fields: A Software Platform for Photonic Quantum Computing

We introduce Strawberry Fields, an open-source quantum programming architecture for light-based quantum computers, and detail its key features. Built in Python, Strawberry Fields is a full-stack library for design, simulation, optimization, and quantum machine learning of continuous-variable circuits. The platform consists of three main components: (i) an API for quantum programming based on an easy-to-use language named Blackbird; (ii) a suite of three virtual quantum computer backends, built in NumPy and TensorFlow, each targeting specialized uses; and (iii) an engine which can compile Blackbird programs on various backends, including the three built-in simulators, and -- in the near future -- photonic quantum information processors. The library also contains examples of several paradigmatic algorithms, including teleportation, (Gaussian) boson sampling, instantaneous quantum polynomial, Hamiltonian simulation, and variational quantum circuit optimization.

quant-ph↗

arXiv2019

Broadband pseudothermal states with tunable spectral coherence generated via nonlinear optics

It is well known that the reduced state of a two-mode squeezed vacuum state is a thermal state---i.e. a state whose photon-number statistics obey a geometric distribution. More exotic \emph{broadband} states can be realized as the reduced state of two spectrally-entangled beams generated using nonlinear optics. We show that these broadband "pseudothermal" states are tensor products of states in spectral Schmidt modes, whose photon-number statistics obey a geometric distribution. We study the spectral and temporal coherence properties of these states and show that their spectral coherence can be tuned---from perfect coherence to complete incoherence---by adjusting the pump spectral width. In the limit of a cw pump, these states are tensor products of true thermal states, but with different temperatures at each frequency. This could be an interesting state of light for investigating the interplay between spectral, temporal, and photon-number coherences.

quant-ph↗

arXiv2018

Franck-Condon factors by counting perfect matchings of graphs with loops

We show that the Franck-Condon Factor (FCF) associated to a transition between initial and final vibrational states in two different potential energy surfaces, having $N$ and $M$ vibrational quanta, respectively, is equivalent to calculating the number of perfect matchings of a weighted graph with loops that has $P = N+M$ vertices. This last quantity is the loop hafnian of the (symmetric) adjacency matrix of the graph which can be calculated in $O(P^3 2^{P/2})$ steps. In the limit of small numbers of vibrational quanta per normal mode our loop hafnian formula significantly improves the speed at which FCFs can be calculated. Our results more generally apply to the calculation of the matrix elements of a bosonic Gaussian unitary between two multimode Fock states having $N$ and $M$ photons in total and provide a useful link between certain calculations of quantum chemistry, quantum optics and graph theory.

quant-ph↗

arXiv2018

Gaussian Boson Sampling using threshold detectors

We study what is arguably the most experimentally appealing Boson Sampling architecture: Gaussian states sampled with threshold detectors. We show that in this setting, the probability of observing a given outcome is related to a matrix function that we name the Torontonian, which plays an analogous role to the permanent or the Hafnian in other models. We also prove that, provided that the probability of observing two or more photons in a single output mode is sufficiently small, our model remains intractable to simulate classically under standard complexity-theoretic conjectures. Finally, we leverage the mathematical simplicity of the model to introduce a physically motivated, exact sampling algorithm for all Boson Sampling models that employ Gaussian states and threshold detectors.

quant-ph↗

arXiv2018

Classical benchmarking of Gaussian Boson Sampling on the Titan supercomputer

Gaussian Boson Sampling is a model of photonic quantum computing where single-mode squeezed states are sent through linear-optical interferometers and measured using single-photon detectors. In this work, we employ a recent exact sampling algorithm for GBS with threshold detectors to perform classical simulations on the Titan supercomputer. We determine the time and memory resources as well as the amount of computational nodes required to produce samples for different numbers of modes and detector clicks. It is possible to simulate a system with 800 optical modes postselected on outputs with 20 detector clicks, producing a single sample in roughly two hours using $40\%$ of the available nodes of Titan. Additionally, we benchmark the performance of GBS when applied to dense subgraph identification, even in the presence of photon loss. We perform sampling for several graphs containing as many as 200 vertices. Our findings indicate that large losses can be tolerated and that the use of threshold detectors is preferable over using photon-number-resolving detectors postselected on collision-free outputs.

quant-ph↗

arXiv2018

Continuous-variable quantum neural networks

We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field. This circuit contains a layered structure of continuously parameterized gates which is universal for CV quantum computation. Affine transformations and nonlinear activation functions, two key elements in neural networks, are enacted in the quantum network using Gaussian and non-Gaussian gates, respectively. The non-Gaussian gates provide both the nonlinearity and the universality of the model. Due to the structure of the CV model, the CV quantum neural network can encode highly nonlinear transformations while remaining completely unitary. We show how a classical network can be embedded into the quantum formalism and propose quantum versions of various specialized model such as convolutional, recurrent, and residual networks. Finally, we present numerous modeling experiments built with the Strawberry Fields software library. These experiments, including a classifier for fraud detection, a network which generates Tetris images, and a hybrid classical-quantum autoencoder, demonstrate the capability and adaptability of CV quantum neural networks.

quant-ph↗