Related papers: The Power of Quantum Fourier Sampling
We describe an efficient, scalable Gaussian boson sampler based on a classical description of squeezed quantum light and a deterministic model of single-photon detectors that click when the incident amplitude falls above a given threshold.…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$.…
Quantum computers promise significant speedups in solving problems intractable for conventional computers but, despite recent progress, remain limited in scaling and availability. Therefore, quantum software and hardware development heavily…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
Gaussian Boson Sampling (GBS) generate random samples of photon-click patterns from a class of probability distributions that are hard for a classical computer to sample from. Despite heroic demonstrations for quantum supremacy using GBS,…
Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly…
The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a…
We investigate the probabilistic cloning and purification of quantum states. The performance of these probabilistic operations is quantified by the average fidelity between the ideal and actual output states. We provide a simple formula for…
Recent work by Bravyi, Gosset, and Koenig showed that there exists a search problem that a constant-depth quantum circuit can solve, but that any constant-depth classical circuit with bounded fan-in cannot. They also pose the question: Can…
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
It has been proven that Boson sampling is a much promising model of optical quantum computation, which has been applied to designing quantum computer successfully, such as "Jiuzhang". However, the meaningful randomness of Boson sampling…
Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to…
We introduce collapsed compilation, a novel approximate inference algorithm for discrete probabilistic graphical models. It is a collapsed sampling algorithm that incrementally selects which variable to sample next based on the partial…
From the existence of an efficient quantum algorithm for factoring, it is likely that quantum computation is intrinsically more powerful than classical computation. At present, the best upper bound known for the power of quantum computation…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
Boson sampling, thought to be intractable classically, can be solved by a quantum machine composed of merely generation, linear evolution and detection of single photons. Such an analog quantum computer for this specific problem provides a…
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to…