Related papers: The Computational Complexity of Linear Optics
Linear optics quantum computing (LOQC) is a promising approach to implementing scalable quantum computation (QC). However, this approach has very demanding physical resource requirements. Recently, Aaronson & Arkhipov showed that a…
There is a natural relationship between Jones polynomials and quantum computation. We use this relationship to show that the complexity of evaluating relative-error approximations of Jones polynomials can be used to bound the classical…
Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they…
Recent astonishing experiments with quantum computers have demonstrated unambiguously the existence of a quantum multiverse, where calculations of mind-boggling complexity are effortlessly computed in just a few minutes. Here, we…
We demonstrate how boson sampling with photons of partial distinguishability can be expressed in terms of interference of fewer photons. We use this observation to propose a classical algorithm to simulate the output of a boson sampler fed…
Computational physics is an important tool for analysing, verifying, and -- at times -- replacing physical experiments. Nevertheless, simulating quantum systems and analysing quantum data has so far resisted an efficient classical treatment…
Single photons, manipulated using integrated linear optics, constitute a promising platform for universal quantum computation. A series of increasingly efficient proposals have shown linear-optical quantum computing to be formally scalable.…
This note reviews the model of computation generated by photonic circuits, comprising edges that are traversed by photons in a single time-bin and vertices given by idealised lossless beam splitters and phase shifters. The circuit model is…
BosonSampling is the leading candidate for demonstrating quantum computational advantage in photonic systems. While we have recently seen many impressive experimental demonstrations, there is still a formidable distance between the…
Photonics is a promising architecture for the realisation of quantum information processing, since the two-photon interaction, or non-linearity, necessary to build logical gates can efficiently be realised by the use of interference with…
Over the last decade, researchers have studied the synergy between quantum computing (QC) and classical machine learning (ML) algorithms. However, measurements in QC often disturb or destroy quantum states, requiring multiple repetitions of…
Boson sampling has emerged as an important tool to demonstrate the difference between quantum and classical computers and has attracted the interest of experimentalists and theoreticians. In this work we study Boson sampling from general,…
Quantum computing promises to exploit the laws of quantum mechanics for processing information in ways fundamentally different from today's classical computers, leading to unprecedented efficiency. One-way quantum computation, sometimes…
We introduce an exact classical algorithm for simulating Gaussian Boson Sampling (GBS). The complexity of the algorithm is exponential in the number of photons detected, which is itself a random variable. For a fixed number of modes, the…
Output probability distributions of several sub-universal quantum computing models cannot be classically efficiently sampled unless some unlikely consequences occur in classical complexity theory, such as the collapse of the polynomial-time…
We introduce a connection between a near-term quantum computing device, specifically a Gaussian boson sampler, and the graph isomorphism problem. We propose a scheme where graphs are encoded into quantum states of light, whose properties…
Quantum generative modeling has emerged as a promising application of quantum computers, aiming to model complex probability distributions beyond the reach of classical methods. In practice, however, training such models often requires…
It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
Quantum computing involving physical systems with continuous degrees of freedom, such as the quantum states of light, has recently attracted significant interest. However, a well-defined quantum complexity theory for these bosonic…