Related papers: Marginal probabilities in boson samplers with arbi…
Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in…
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors,…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
When the problem of boson sampling was first proposed, it was assumed that little or no photon collisions occur. However, modern experimental realizations rely on setups where collisions are quite common, i.e. the number of photons $M$…
A lossless beam-splitter has certain (complex-valued) probability amplitudes for sending an incoming photon into one of two possible directions. We use elementary laws of classical and quantum optics to obtain general relations among the…
We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can…
Linear optical quantum circuits with photon number resolving (PNR) detectors are used for both Gaussian Boson Sampling (GBS) and for the preparation of non-Gaussian states such as Gottesman-Kitaev-Preskill (GKP), cat and NOON states. They…
Photonic interference is a key quantum resource for optical quantum computation, and in particular for so-called boson sampling machines. In interferometers with certain symmetries, genuine multiphoton quantum interference effectively…
Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…
We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. For various quantum algorithms, in particular in the context of quantum chemistry, it is crucial to have energy…
We introduce the problem of *shadow tomography*: given an unknown $D$-dimensional quantum mixed state $\rho$, as well as known two-outcome measurements $E_{1},\ldots,E_{M}$, estimate the probability that $E_{i}$ accepts $\rho$, to within…
It is known that, by accounting for the multiboson interferences up to a finite order, the output distribution of noisy Boson Sampling, with distinguishability of bosons serving as noise, can be approximately sampled from in a time…
We introduce a computational problem of distinguishing between the output of an ideal coarse-grained boson sampler and the output of a true random number generator, as a resource for cryptographic schemes, which are secure against…
Photonic quantum computing has recently emerged as a promising candidate for fault-tolerant quantum computing by photonic qubits. These protocols make use of nondeterministic gates, enabling universal quantum computation. However, the…
Boson sampling is a problem for which quantum devices could prove to go beyond classical computing using only linear optics and photon preparation and counting. While theoretically important, there is a lack of practical applications for…
Photonic architectures are one of the leading platforms for demonstrating quantum computational advantage, with Boson Sampling and Gaussian Boson Sampling as the primary schemes. Yet, we lack for these photonic primitives a systematic…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
There are two common settings in a quantum-state discrimination problem. One is minimum-error discrimination where a wrong guess (error) is allowed and the discrimination success probability is maximized. The other is unambiguous…
Boson-sampling has been presented as a simplified model for linear optical quantum computing. In the boson-sampling model, Fock states are passed through a linear optics network and sampled via number-resolved photodetection. It has been…
Quantum machine learning seeks a computational advantage in data processing by evaluating functions of quantum states, such as their similarity, that can be classically intractable to compute. For quantum advantage to be possible, however,…