Related papers: Quantum rejection sampling
Randomness is an indispensable resource in modern science and information technology. Fortunately, an experimentally simple procedure exists to generate randomness with well-characterized devices: measuring a quantum system in a basis…
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…
Boson Sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be…
We propose a novel modular debiasing technique applicable to any discrete random source, addressing the fundamental challenge of reliably extracting high-quality randomness from inherently imperfect physical processes. The method involves…
This paper studies quantum supervised learning for classical inference from quantum states. In this model, a learner has access to a set of labeled quantum samples as the training set. The objective is to find a quantum measurement that…
Quantum error mitigation techniques can reduce noise on current quantum hardware without the need for fault-tolerant quantum error correction. For instance, the quasiprobability method simulates a noise-free quantum computer using a noisy…
Uniform sampling and approximate counting are fundamental primitives for modern database applications, ranging from query optimization to approximate query processing. While recent breakthroughs have established optimal sampling and…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
A universal and fault tolerant scheme for quantum computation is proposed which utilizes a class of error correcting codes that is based on the detection of spontaneous emission (of, e.g., photons, phonons, and ripplons). The scheme is…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
In relative entropy coding, a sender aims to design a stochastic code such that, on input $X \sim P_X$, the receiver can generate a sample $Y \sim P_{Y \mid X}$. It is a standard result that (1) this requires at least $I(X; Y)$ bits, (2)…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
In former work, we showed that a quantum algorithm is the sum over the histories of a classical algorithm that knows in advance 50% of the information about the solution of the problem - each history is a possible way of getting the…
Quantum Signal Processing (QSP) is a technique that can be used to implement a polynomial transformation $P(x)$ applied to the eigenvalues of a unitary $U$, essentially implementing the operation $P(U)$, provided that $P$ satisfies some…
Curve samplers are sampling algorithms that proceed by viewing the domain as a vector space over a finite field, and randomly picking a low-degree curve in it as the sample. Curve samplers exhibit a nice property besides the sampling…
This work develops a powerful and versatile framework for determining acceptance ratios in Metropolis-Hastings type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which…
We develop an adaptive method for quantum state preparation that utilizes randomness as an essential component and that does not require classical optimization. Instead, a cost function is minimized to prepare a desired quantum state…
Hypothesis exclusion is an information-theoretic task in which an experimenter aims at ruling out a false hypothesis from a finite set of known candidates, and an error occurs if and only if the hypothesis being ruled out is the ground…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
We study the problems of quantum tomography and shadow tomography using measurements performed on individual, identical copies of an unknown $d$-dimensional state. We first revisit a known lower bound due to Haah et al. (2017) on quantum…