arXiv subjects

Nicolás Quesada

Publications and source records attributed to Nicolás Quesada.

At least 37 records · Page 2Linked to original sources

arXiv2024

Photon-number moments and cumulants of Gaussian states

We develop closed-form expressions for the moments and cumulants of Gaussian states when measured in the photon-number basis. We express the photon-number moments of a Gaussian state in terms of the loop Hafnian, a function that when applied to a $(0,1)$-matrix representing the adjacency of a graph, counts the number of its perfect matchings. Similarly, we express the photon-number cumulants in terms of the Montrealer, a newly introduced matrix function that when applied to a $(0,1)$-matrix counts the number of Hamiltonian cycles of that graph. Based on these graph-theoretic connections, we show that the calculation of photon-number moments and cumulants are #P-hard. Moreover, we provide an exponential time algorithm to calculate Montrealers (and thus cumulants), matching well-known results for Hafnians. We then demonstrate that when a uniformly lossy interferometer is fed in every input with identical single-mode Gaussian states with zero displacement, all the odd-order cumulants but the first one are zero. Finally, we employ the expressions we derive to study the distribution of cumulants up to the fourth order for different input states in a Gaussian boson sampling setup where $K$ identical states are fed into an $\ell$-mode interferometer. We analyze the dependence of the cumulants as a function of the type of input state, squeezed, lossy squeezed, squashed, or thermal, and as a function of the number of non-vacuum inputs. We find that thermal states perform much worse than other classical states, such as squashed states, at mimicking the photon-number cumulants of lossy or lossless squeezed states.

quant-ph↗

arXiv2024

Linear cross-entropy certification of quantum computational advantage in Gaussian Boson Sampling

Validation of quantum advantage claims in the context of Gaussian Boson Sampling (GBS) currently relies on providing evidence that the experimental samples genuinely follow their corresponding ground truth, i.e., the theoretical model of the experiment that includes all the possible losses that the experimenters can account for. This approach to verification has an important drawback: it is necessary to assume that the ground truth distributions are computationally hard to sample, that is, that they are sufficiently close to the distribution of the ideal, lossless experiment, for which there is evidence that sampling, either exactly or approximately, is a computationally hard task. This assumption, which cannot be easily confirmed, opens the door to classical algorithms that exploit the noise in the ground truth to efficiently simulate the experiments, thus undermining any quantum advantage claim. In this work, we argue that one can avoid this issue by validating GBS implementations using their corresponding ideal distributions directly. We explain how to use a modified version of the linear cross-entropy, a measure that we call the LXE score, to find reference values that help us assess how close a given GBS implementation is to its corresponding ideal model. Finally, we analytically compute the score that would be obtained by a lossless GBS implementation.

quant-ph↗

arXiv2024

Etching Properties of PIN-PMN-PT and its Integration in Electro-Optic Phase Modulators

We investigate the etching characteristics of PIN-PMN-PT crystals, exploring various wet etching solutions, reactive ion etching gases, and ion beam etching. The etch rate and surface roughness are systematically measured for each method. A process flow to obtain PIN-PMN-PT thin films is described and performed to later build a single mode rib waveguide. An integrated electro-optic phase modulator is fabricated by depositing electrodes on the sides of the waveguides. The electro-optic coefficient implied in our phase modulators is the $r_{51}/r_{42}$. The performances are tested achieving a $V_πL$ of 19.2 V$\cdot$cm.

physics.optics↗

arXiv2024

Beyond the parametric approximation: pump depletion, entanglement and squeezing in macroscopic down-conversion

We study the dynamics of the pump mode in the down-conversion Hamiltonian using the cumulant expansion method, perturbation theory, and the full numerical simulation of systems with a pump mean photon number of up to one hundred thousand. We particularly focus on the properties of the pump-mode such as depletion, entanglement, and squeezing for an experimentally relevant initial state in which the pump mode is initialized in a coherent state. Through this analysis, we obtain the short-time behaviour of various quantities and derive timescales at which the above-mentioned features, which cannot be understood through the parametric approximation, originate in the system. We also provide an entanglement witness involving moments of bosonic operators that can capture the entanglement of the pump mode. Finally, we study the photon-number statistics of the pump and the signal/idler modes to understand the general behaviour of these modes for experimentally relevant time scales.

quant-ph↗

arXiv2024

Perfect pulsed inline twin-beam squeezers

Perfect inline squeezers are both spectrally pure and have identical input and output temporal modes, allowing one to squeeze an arbitrary input quantum state in the sole input mode on which the device acts, while the quantum states of any other modes are unaffected. We study theoretically how to obtain a perfect pulsed inline squeezer in twin-beam systems by considering three commonly used configurations: unpoled single pass, poled single pass, and poled double pass. By obtaining analytical relations between the input and output temporal modes from the Bloch-Messiah decomposition of the discretized Heisenberg-picture propagator, we find that a double pass structure produces a perfect pulsed inline squeezer when operated in a frequency degenerate, symmetric group-velocity matched type-II configuration.

quant-ph↗

arXiv2024

Riemannian optimization of photonic quantum circuits in phase and Fock space

We propose a framework to design and optimize generic photonic quantum circuits composed of Gaussian objects (pure and mixed Gaussian states, Gaussian unitaries, Gaussian channels, Gaussian measurements) as well as non-Gaussian effects such as photon-number-resolving measurements. In this framework, we parametrize a phase space representation of Gaussian objects using elements of the symplectic group (or the unitary or orthogonal group in special cases), and then we transform it into the Fock representation using a single linear recurrence relation that computes the Fock amplitudes of any Gaussian object recursively. We also compute the gradient of the Fock amplitudes with respect to phase space parameters by differentiating through the recurrence relation. We can then use Riemannian optimization on the symplectic group to optimize M-mode Gaussian objects, avoiding the need to commit to particular realizations in terms of fundamental gates. This allows us to "mod out" all the different gate-level implementations of the same circuit, which now can be chosen after the optimization has completed. This can be especially useful when looking to answer general questions, such as bounding the value of a property over a class of states or transformations, or when one would like to worry about hardware constraints separately from the circuit optimization step. Finally, we make our framework extendable to non-Gaussian objects that can be written as linear combinations of Gaussian ones, by explicitly computing the change in global phase when states undergo Gaussian transformations. We implemented all of these methods in the freely available open-source library MrMustard, which we use in three examples to optimize the 216-mode interferometer in Borealis, and 2- and 3-modes circuits (with Fock measurements) to produce cat states and cubic phase states.

quant-ph↗

arXiv2024

Matrix decompositions in Quantum Optics: Takagi/Autonne, Bloch-Messiah/Euler, Iwasawa, and Williamson

In this note we summarize four important matrix decompositions commonly used in quantum optics, namely the Takagi/Autonne, Bloch-Messiah/Euler, Iwasawa, and Williamson decompositions. The first two of these decompositions are specialized versions of the singular-value decomposition when applied to symmetric or symplectic matrices. The third factors any symplectic matrix in a unique way in terms of matrices that belong to different subgroups of the symplectic group. The last one instead gives the symplectic diagonalization of real, positive definite matrices of even size. While proofs of the existence of these decompositions exist in the literature, we focus on providing explicit constructions to implement these decompositions using standard linear algebra packages and functionalities such as singular-value, polar, Schur and QR decompositions, and matrix square roots and inverses.

quant-ph↗

arXiv2023

Classical models may be a better explanation of the Jiuzhang 1.0 Gaussian Boson Sampler than its targeted squeezed light model

Recently, Zhong et al. performed landmark Gaussian boson sampling experiments with up to 144 modes using threshold detectors. The authors claim to have achieved quantum computational advantage with the implementation of these experiments, named Jiuzhang 1.0 and Jiuzhang 2.0. Their experimental results are validated against several classical hypotheses and adversaries using tests such as the comparison of statistical correlations between modes, Bayesian hypothesis testing and the Heavy Output Generation (HOG) test. We propose an alternative classical hypothesis for the validation of these experiments using the probability distribution of mixtures of coherent states sent into a lossy interferometer; these input mixed states, which we term squashed states, have vacuum fluctuations in one quadrature and excess fluctuations in the other. We find that for configurations in the high photon number density regime, the comparison of statistical correlations does not tell apart the ground truth of the experiment (two-mode squeezed states sent into an interferometer) from our alternative hypothesis. The Bayesian test indicates that, for all configurations excepting Jiuzhang 1.0, the ground truth is a more likely explanation of the experimental data than our alternative hypothesis. A similar result is obtained for the HOG test: for all configurations of Jiuzhang 2.0, the test indicates that the experimental samples have higher ground truth probability than the samples obtained form our alternative distribution; for Jiuzhang 1.0 the test is inconclusive. Our results provide a new hypothesis that should be considered in the validation of future GBS experiments, and shed light into the need to identify proper metrics to verify quantum advantage in the context of GBS. They also indicate that a classical explanation of the Jiuzhang 1.0 experiment, lacking any quantum features, has not been ruled out.

quant-ph↗

arXiv2023

Quantum-inspired classical algorithm for graph problems by Gaussian boson sampling

We present a quantum-inspired classical algorithm that can be used for graph-theoretical problems, such as finding the densest $k$-subgraph and finding the maximum weight clique, which are proposed as applications of a Gaussian boson sampler. The main observation from Gaussian boson samplers is that a given graph's adjacency matrix to be encoded in a Gaussian boson sampler is nonnegative, which does not necessitate quantum interference. We first provide how to program a given graph problem into our efficient classical algorithm. We then numerically compare the performance of ideal and lossy Gaussian boson samplers, our quantum-inspired classical sampler, and the uniform sampler for finding the densest $k$-subgraph and finding the maximum weight clique and show that the advantage from Gaussian boson samplers is not significant in general. We finally discuss the potential advantage of a Gaussian boson sampler over the proposed sampler.

quant-ph↗

arXiv2023

Custom nonlinearity profile for integrated quantum light sources

Heralded single-photon sources are a fundamental building block for optical quantum technologies. These sources need to be unfiltered and integrated to have good scalability and avoid unnecessary losses. To attain this goal, it is necessary to control the effective nonlinearity seen by the fields as they mix and propagate in a waveguide source. In this paper, we introduce a method to design nonlinear waveguides with arbitrarily shaped effective nonlinearity profiles. The method takes advantage of the fact that the second order nonlinear response is a tensor quantity and thus the local effective nonlinearity of a material depends on the propagation direction of the fields participating in the interaction. Thus, by locally changing the propagation direction of the fields we can modulate the wave-mixing process. Our methods allows for the waveguide fabrication process to be significantly simplified: The material structure of the waveguide is made by a single crystal, no longer needing oriented patterning (OP) or periodic poling (PP). We use our method to design waveguides with a nonlinearity profile that is Gaussian in the propagation length, allowing to generate perfectly pure heralded single photons.

physics.optics↗

arXiv2023

Waveguided sources of consistent, single-temporal-mode squeezed light: the good, the bad, and the ugly

We study theoretically how the brightness of pumps, with fixed profiles, affects the temporal mode structure of squeezed states generated by fixed parametric waveguided sources. We find that the temporal modes of these squeezed states can be partially mismatched and thus distinguishable, which is undesirable when using these states as resources for quantum computing or heralded state generation. By studying common frequency filtering techniques used experimentally, we find that although one can regain indistinguishability it comes at the price of potentially greatly reducing the purity of the state. We consider three different source configurations: unapodized single pass, apodized single pass, and apodized double pass. We find that the double pass configuration produces optimal results with almost perfectly indistinguishable states over varying degrees of brightness.

quant-ph↗

arXiv2022

The Complexity of Bipartite Gaussian Boson Sampling

Gaussian boson sampling is a model of photonic quantum computing that has attracted attention as a platform for building quantum devices capable of performing tasks that are out of reach for classical devices. There is therefore significant interest, from the perspective of computational complexity theory, in solidifying the mathematical foundation for the hardness of simulating these devices. We show that, under the standard Anti-Concentration and Permanent-of-Gaussians conjectures, there is no efficient classical algorithm to sample from ideal Gaussian boson sampling distributions (even approximately) unless the polynomial hierarchy collapses. The hardness proof holds in the regime where the number of modes scales quadratically with the number of photons, a setting in which hardness was widely believed to hold but that nevertheless had no definitive proof. Crucial to the proof is a new method for programming a Gaussian boson sampling device so that the output probabilities are proportional to the permanents of submatrices of an arbitrary matrix. This technique is a generalization of Scattershot BosonSampling that we call BipartiteGBS. We also make progress towards the goal of proving hardness in the regime where there are fewer than quadratically more modes than photons (i.e., the high-collision regime) by showing that the ability to approximate permanents of matrices with repeated rows/columns confers the ability to approximate permanents of matrices with no repetitions. The reduction suffices to prove that GBS is hard in the constant-collision regime.

quant-ph↗

arXiv2022

Threshold detection statistics of bosonic states

In quantum photonics, threshold detectors, distinguishing between vacuum and one or more photons, such as superconducting nanowires and avalanche photodiodes, are routinely used to measure Fock and Gaussian states of light. Despite being the standard measurement scheme, there is no general closed form expression for measurement probabilities with threshold detectors, unless accepting coarse approximations or combinatorially scaling summations. Here, we present new matrix functions to fill this gap. We develop the Bristolian and the loop Torontonian functions for threshold detection of Fock and displaced Gaussian states, respectively, and connect them to each other and to existing matrix functions. By providing a unified picture of bosonic statistics for most quantum states of light, we provide novel tools for the design and analysis of photonic quantum technologies.

quant-ph↗

arXiv2022

PennyLane: Automatic differentiation of hybrid quantum-classical computations

PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.

quant-ph↗

arXiv2022

Universal quantum circuits for quantum chemistry

Universal gate sets for quantum computing have been known for decades, yet no universal gate set has been proposed for particle-conserving unitaries, which are the operations of interest in quantum chemistry. In this work, we show that controlled single-excitation gates in the form of Givens rotations are universal for particle-conserving unitaries. Single-excitation gates describe an arbitrary $U(2)$ rotation on the two-qubit subspace spanned by the states $|01\rangle, |10\rangle$, while leaving other states unchanged -- a transformation that is analogous to a single-qubit rotation on a dual-rail qubit. The proof is constructive, so our result also provides an explicit method for compiling arbitrary particle-conserving unitaries. Additionally, we describe a method for using controlled single-excitation gates to prepare an arbitrary state of a fixed number of particles. We derive analytical gradient formulas for Givens rotations as well as decompositions into single-qubit and CNOT gates. Our results offer a unifying framework for quantum computational chemistry where every algorithm is a unique recipe built from the same universal ingredients: Givens rotations.

quant-ph↗

arXiv2021

Quantum Algorithm for Simulating Molecular Vibrational Excitations

The excitation of vibrational modes in molecules affects the outcome of chemical reactions, for example by providing molecules with sufficient energy to overcome activation barriers. In this work, we introduce a quantum algorithm for simulating molecular vibrational excitations during vibronic transitions. We discuss how a special-purpose quantum computer can be programmed with molecular data to optimize a vibronic process such that desired modes get excited during the transition. We investigate the effect of such excitations on selective bond dissociation in pyrrole and butane during photochemical and mechanochemical vibronic transitions. The results are discussed with respect to experimental observations and classical simulations. We also introduce quantum-inspired classical algorithms for simulating molecular vibrational excitations in special cases where only a limited number of modes are of interest.

quant-ph↗

arXiv2021

Quadratic speedup for simulating Gaussian boson sampling

We introduce an algorithm for the classical simulation of Gaussian boson sampling that is quadratically faster than previously known methods. The complexity of the algorithm is exponential in the number of photon pairs detected, not the number of photons, and is directly proportional to the time required to calculate a probability amplitude for a pure Gaussian state. The main innovation is to use auxiliary conditioning variables to reduce the problem of sampling to computing pure-state probability amplitudes, for which the most computationally-expensive step is calculating a loop hafnian. We implement and benchmark an improved loop hafnian algorithm and show that it can be used to compute pure-state probabilities, the dominant step in the sampling algorithm, of up to 50-photon events in a single workstation, i.e., without the need of a supercomputer.

quant-ph↗

arXiv2021

Fast simulation of bosonic qubits via Gaussian functions in phase space

Bosonic qubits are a promising route to building fault-tolerant quantum computers on a variety of physical platforms. Studying the performance of bosonic qubits under realistic gates and measurements is challenging with existing analytical and numerical tools. We present a novel formalism for simulating classes of states that can be represented as linear combinations of Gaussian functions in phase space. This formalism allows us to analyze and simulate a wide class of non-Gaussian states, transformations and measurements. We demonstrate how useful classes of bosonic qubits -- Gottesman-Kitaev-Preskill (GKP), cat, and Fock states -- can be simulated using this formalism, opening the door to investigating the behaviour of bosonic qubits under Gaussian channels and measurements, non-Gaussian transformations such as those achieved via gate teleportation, and important non-Gaussian measurements such as threshold and photon-number detection. Our formalism enables simulating these situations with levels of accuracy that are not feasible with existing methods. Finally, we use a method informed by our formalism to simulate circuits critical to the study of fault-tolerant quantum computing with bosonic qubits but beyond the reach of existing techniques. Specifically, we examine how finite-energy GKP states transform under realistic qubit phase gates; interface with a CV cluster state; and transform under non-Clifford T gate teleportation using magic states. We implement our simulation method as a part of the open-source Strawberry Fields Python library.

quant-ph↗