We provide general sufficient conditions for the efficient classical simulation of quantum-optics experiments that involve inputting states to a quantum process and making measurements at the output. The first condition is based on the negativity of phase-space quasiprobability distributions (PQDs) of the output state of the process and the output measurements; the second one is based on the negativity of PQDs of the input states, the output measurements, and the transition function associated with the process. We show that these conditions provide useful practical tools for investigating the effects of imperfections in implementations of boson sampling. In particular, we apply our formalism to boson-sampling experiments that use single-photon or spontaneous-parametric-down-conversion sources and on-off photodetectors. Considering simple models for loss and noise, we show that above some threshold for the probability of random counts in the photodetectors, these boson-sampling experiments are classically simulatable. We identify mode mismatching as the major source of error contributing to random counts and suggest that this is the chief challenge for implementations of boson sampling of interesting size.
We provide general sufficient conditions for the efficient classical simulation of quantum-optics experiments that involve inputting states to a quantum process and making measurements at the output. The first condition is based on the negativity of phase-space quasiprobability distributions (PQDs) of the output state of the process and the output measurements; the second one is based on the negativity of PQDs of the input states, the output measurements, and the transition function associated with the process. We show that these conditions provide useful practical tools for investigating the effects of imperfections in implementations of boson sampling. In particular, we apply our formalism to boson-sampling experiments that use single-photon or spontaneous-parametric-down-conversion sources and on-off photodetectors. Considering simple models for loss and noise, we show that above some threshold for the probability of random counts in the photodetectors, these boson-sampling experiments are classically simulatable. We identify mode mismatching as the major source of error contributing to random counts and suggest that this is the chief challenge for implementations of boson sampling of interesting size.
We provide general sufficient conditions for the efficient classical simulation of quantum-optics experiments that involve inputting states to a quantum process and making measurements at the output.The first condition is based on the negativity of phase-space quasiprobability distributions (PQDs) of the output state of the process and the output measurements; the second one is based on the negativity of PQDs of the input states, the output measurements, and the transition function associated with the process.We show that these conditions provide useful practical tools for investigating the effects of imperfections in implementations of boson sampling.In particular, we apply our formalism to boson-sampling experiments that use single-photon or spontaneous-parametric-down-conversion sources and on-off photodetectors.Considering simple models for loss and noise, we show that above some threshold for the probability of random counts in the photodetectors, these boson-sampling experiments are classically simulatable.We identify mode mismatching as the major source of error contributing to random counts and suggest that this is the chief challenge for implementations of boson sampling of interesting size.
Linear-optical platforms provide a promising route to demonstrate quantum computational advantage, particularly through the boson sampling problem. While a boson sampling system should be large enough to show the quantum advantage, the size of the boson sampling problem is often restricted by experimental constraints. In particular, as a boson sampling system is scaled up, experimental constraints can limit its effective problem size to permit efficient classical simulation. In this paper, we investigate the theoretical scalability bounds for boson sampling systems under practical experimental conditions, including photon loss, mode mismatch, and input state error. We employ non-negativity conditions for phase-space quasiprobability distribution functions to analyze these effects. In addition, we introduce two device-level metrics, the boson sampling score which measures the usable capacity of a given device and the boson sampling volume which provides a common hardware-level benchmark for comparing different platforms and assessing their access to an advantage-relevant problem size regime. Our results provide fundamental insights into the performance of boson sampling systems under realistic experimental conditions and offer practical guidelines for scaling up boson sampling systems.
Boson sampling, a computational problem conjectured to be hard to simulate on a classical machine, is a promising candidate for an experimental demonstration of quantum advantage using bosons. However, inevitable experimental noise and imperfections, such as loss in the interferometer and random counts at the detectors, could challenge the sampling task from entering the regime where quantum advantage is achievable. In this work we introduce higher-order nonlinearities as a means to enhance the computational complexity of the problem and the protocol's robustness against noise, i.e., to increase the noise threshold that allows us to perform an efficient classical simulation of the problem. Using a phase-space method based on the negativity volume of the relevant quasiprobability distributions, we establish a necessary nonclassicality condition that any experimental proof of quantum advantage must satisfy. Our results indicate that the addition of single-mode Kerr nonlinearity at the input-state preparation level, while retaining a linear-optical evolution, makes the boson-sampling protocol more robust against noise and consequently relaxes the constraints on the noise parameters required to show quantum advantage.
Abstract Quasiprobability representations are important tools for analyzing a quantum system, such as a quantum state or a quantum circuit. In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear optical circuit using quasiprobability distributions. Notably, we can reduce the negativity bound of a circuit from exponential to at most polynomial for specific cases by modulating the shapes of quasiprobability distributions thanks to the symmetry of the linear optical transformation in the phase space. Consequently, our scheme provides an efficient estimation of outcome probabilities within an additive-error whose precision depends on the classicality of the input state. When the classicality is high enough, we reach a polynomial-time estimation algorithm of a probability within a multiplicative-error by an efficient sampling from a log-concave function. By choosing appropriate input states and measurements, our results provide plenty of quantum-inspired classical algorithms for approximating various matrix functions beating best-known results. Moreover, we give sufficient conditions for the classical simulability of Gaussian Boson sampling using our approximating algorithm for any (marginal) outcome probability under the poly-sparse condition.
This thesis presents results under the topics of quantum correlations and quantum information processing using linear-optical networks. The first part of this thesis concerns with quantum correlations, specially in Gaussian states, which play a central role as resource in quantum protocols. The second part is about quantum information processing using linear-optical networks that are of great practical interest due to their simple physical realization. In the first part, we present a measurement-based method for verifying nonzero quantum discord, a measure of quantum correlations, in bipartite systems that can be used for both continuous and discrete-variable systems. Based on this method, we show that the only bipartite Gaussian states with zero quantum discord are product states. We also present a simple and efficient experimental method for verifying quantum correlations in Gaussian states using homodyne measurements. Moreover, we introduce an operational measure for quantifying quantum correlations in Gaussian states that is purely based on Gaussian measurements. We then illustrate the operational significance of the measure in terms of a Gaussian quantum protocol. In the second part, we present results on linear quantum-optics experiments, specifically boson sampling, an intermediate model of quantum computation that can be implemented using single-photon states, linear-optical networks, and photodetectors. We first present an efficient experimental method for characterization of linear-optical networks, which is essential for practical implementation of boson sampling. We show that using coherent states one can directly measure all the nontrivial phases and moduli of the matrix describing the network. Next, we consider the problem of boson sampling with Gaussian states. We derive a general formula for calculating the output photon-counting probabilities. We show that for input thermal states, sampling from the output probability distribution can be efficiently classically simulated. Using this, we find that permanents of positive-semidefinite Hermitian matrices can be approximated to within a multiplicative error in BPPNP. We also discuss boson sampling with squeezed vacuum states. Finally, we provide a sufficient condition for the efficient classical simulation of the general sampling problem using linear-quantum optics, which involves a multimode input quantum state to a linear-optical network and set of measurements at the output. This condition is based on the phase-space quasiprobability distributions, and suggests that negativity is a quantum resource. We apply this condition to implementations of boson sampling using single-photon or spontaneous parametric down-conversion sources. We show that above some threshold for loss and noise in the experiment, boson sampling is classically simulatable.