Related papers: Quantum algorithm for Discrete Gaussian Sampling
We present a new quantum algorithm for estimating the mean of a real-valued random variable obtained as the output of a quantum computation. Our estimator achieves a nearly-optimal quadratic speedup over the number of classical i.i.d.…
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…
We describe and analyze a simple algorithm for sampling from the solution $\mathbf{x}^* := \mathbf{A}^+\mathbf{b}$ to a linear system $\mathbf{A}\mathbf{x} = \mathbf{b}$. We assume access to a sampler which allows us to draw indices…
In this work we show that the hardness of the Learning with Errors problem with errors taken from the discrete Gaussian distribution implies the hardness of the Learning with Errors problem with errors taken from the symmetric Skellam…
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…
We present a fairly general framework for reducing $(\varepsilon, \delta)$ differentially private (DP) statistical estimation to its non-private counterpart. As the main application of this framework, we give a polynomial time and…
We present the first explicit connection between quantum computation and lattice problems. Namely, we show a solution to the Unique Shortest Vector Problem (SVP) under the assumption that there exists an algorithm that solves the hidden…
We present a quantum augmented variant of the dual lattice attack on the Learning with Errors (LWE) problem, using classical memory with quantum random access (QRACM). Applying our results to lattice parameters from the literature, we find…
Gaussian Processes (GPs) are a powerful tool for probabilistic modeling, but their performance is often constrained in complex, large-scale real-world domains due to the limited expressivity of classical kernels. Quantum computing offers…
Boson Sampling represents a promising witness of the supremacy of quantum systems as a resource for the solution of computational problems. The classical hardness of Boson Sampling has been related to the so called Permanent-of-Gaussians…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
We pose a generalized Boson Sampling problem. Strong evidence exists that such a problem becomes intractable on a classical computer as a function of the number of Bosons. We describe a quantum optical processor that can solve this problem…
Lattice-based cryptography relies on generating random bases which are difficult to fully reduce. Given a lattice basis (such as the private basis for a cryptosystem), all other bases are related by multiplication by matrices in…
Differential cryptanalysis is one of the most popular methods in attacking block ciphers. However, there still some limitations in traditional differential cryptanalysis. On the other hand, researches of quantum algorithms have made great…
We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we…
In this paper, we show new algorithms, hardness results and applications for $\sf{S|LWE\rangle}$ and $\sf{C|LWE\rangle}$ with real Gaussian, Gaussian with linear or quadratic phase terms, and other related amplitudes. Let $n$ be the…
Public-key cryptography algorithms have evolved towards increasing computational complexity to hide desired messages, which is accelerating with the development of the Internet and quantum computing. This paper introduces a novel public-key…
We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian…
Combinatorial optimization is an important application targeted by quantum computing. However, near-term hardware constraints make quantum algorithms unlikely to be competitive when compared to high-performing classical heuristics on large…