Quantum computational advantage with a programmable photonic processor.

A quantum computer attains computational advantage when outperforming the best classical computers running the best-known algorithms on well-defined tasks. No photonic machine offering programmability over all its quantum gates has demonstrated quantum computational advantage: previous machines1,2 were largely restricted to static gate sequences. Earlier photonic demonstrations were also vulnerable to spoofing3, in which classical heuristics produce samples, without direct simulation, lying closer to the ideal distribution than do samples from the quantum hardware. Here we report quantum computational advantage using Borealis, a photonic processor offering dynamic programmability on all gates implemented. We carry out Gaussian boson sampling4 (GBS) on 216 squeezed modes entangled with three-dimensional connectivity5, using a time-multiplexed and photon-number-resolving architecture. On average, it would take more than 9,000 years for the best available algorithms and supercomputers to produce, using exact methods, a single sample from the programmed distribution, whereas Borealis requires only 36 µs. This runtime advantage is over 50 million times as extreme as that reported from earlier photonic machines. Ours constitutes a very large GBS experiment, registering events with up to 219 photons and a mean photon number of 125. This work is a critical milestone on the path to a practical quantum computer, validating key technological features of photonics as a platform for this goal.

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 nonclassicality test that must be passed by any quantum computational supremacy 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.

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.

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

We show that the Franck-Condon Factor (FCF) associated with 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(P32P/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.

Why you should not use the electric field to quantize in nonlinear optics.

We show that using the electric field as a quantization variable in nonlinear optics leads to incorrect expressions for the squeezing parameters in spontaneous parametric down-conversion (SPDC) and conversion rates in frequency conversion. This observation is related to the fact that if the electric field is written as a linear combination of bosonic creation and annihilation operators one cannot satisfy Maxwell's equations in a nonlinear dielectric.

High efficiency in mode-selective frequency conversion.

Frequency conversion (FC) is an enabling process in many quantum information protocols. Recently, it has been observed that upconversion efficiencies in single-photon, mode-selective FC are limited to around 80%. In this Letter, we argue that these limits can be understood as time-ordering corrections (TOCs) that modify the joint conversion amplitude of the process. Furthermore, using a simple scaling argument, we show that recently proposed cascaded FC protocols that overcome the aforementioned limitations act as "attenuators" of the TOCs. This observation allows us to argue that very similar cascaded architectures can be used to attenuate TOCs in photon generation via spontaneous parametric downconversion. Finally, by using the Magnus expansion, we argue that the TOCs, which are usually considered detrimental for FC efficiency, can also be used to increase the efficiency of conversion in partially mode-selective FC.

Time-ordering effects in the generation of entangled photons using nonlinear optical processes.

We study the effects of time ordering in photon generation processes such as spontaneous parametric down-conversion (SPDC) and four wave mixing (SFWM). The results presented here are used to construct an intuitive picture that allows us to predict when time-ordering effects significantly modify the joint spectral amplitude (JSA) of the photons generated in SPDC and SFWM. These effects become important only when the photons being generated lie with the pump beam that travels through the nonlinear material for a significant amount of time. Thus sources of spectrally separable photons are ideal candidates for the observation of modifications of the JSA due to time ordering.

Quantum computational advantage via high-dimensional Gaussian boson sampling.

Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and demonstrations face challenges. Experimentally, current implementations of Gaussian boson sampling (GBS) lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make progress in improving both the theoretical evidence and experimental prospects. We provide evidence for the hardness of GBS, comparable to the strongest theoretical proposals for QCA. We also propose a QCA architecture we call high-dimensional GBS, which is programmable and can be implemented with low loss using few optical components. We show that particular algorithms for simulating GBS are outperformed by high-dimensional GBS experiments at modest system sizes. This work thus opens the path to demonstrating QCA with programmable photonic processors.

Density operator of a system pumped with polaritons: a Jaynes-Cummings-like approach.

We investigate the effects of considering two different incoherent excitation mechanisms on microcavity quantum dot systems modeled using the Jaynes-Cummings Hamiltonian. When the system is incoherently pumped with polaritons it is able to sustain a large number of photons inside the cavity with Poisson-like statistics in the stationary limit, and it also leads to a separable exciton-photon state. We also investigate the effects of both types of pumpings (excitonic and polaritonic) in the emission spectrum of the cavity. We show that the polaritonic pumping considered here is unable to modify the dynamical regimes of the system at variance with the excitonic pumping. Finally, we obtain a closed form expression for the negativity of the density matrices that the quantum master equation considered here generates.

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 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 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 analyze properties of these point processes for homogeneous and inhomogeneous state spaces, describe methods to control cluster location, and illustrate how to encode correlation matrices.

Strong coupling of two interacting excitons confined in a nanocavity-quantum dot system.

We present a study of the strong coupling between radiation and matter, considering a system of two quantum dots, which are in mutual interaction and interact with a single mode of light confined in a semiconductor nanocavity. We take into account dissipative mechanisms such as the escape of the cavity photons, decay of the quantum dot excitons by spontaneous emission, and independent exciton pumping. It is shown that the mutual interaction between the dots can be measured off-resonance only if the strong coupling condition is reached. Using the quantum regression theorem, a reasonable definition of the dynamical coupling regimes is introduced in terms of the complex Rabi frequency. Finally, the emission spectrum for relevant conditions is presented and compared with the above definition, demonstrating that the interaction between the excitons does not affect the strong coupling.