Related papers: The Classical Complexity of Boson Sampling
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…
Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research…
Sampling from probability distributions of quantum circuits is a fundamentally and practically important task which can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In the present work, we examine…
In a sampling problem, we are given an input x, and asked to sample approximately from a probability distribution D_x. In a search problem, we are given an input x, and asked to find a member of a nonempty set A_x with high probability. (An…
Optical losses are the main obstacle to demonstrating a quantum advantage via boson sampling without leaving open the possibility of classical spoofing. We propose a method for generating low-depth optical circuits suitable for boson…
Boson sampling can provide strong evidence that the computational power of a quantum computer outperforms a classical one via currently feasible linear optics experiments. However, how to identify an actual boson sampling device against any…
Boson sampling is the problem of generating a quantum bit stream whose average is the permanent of a $n\times n$ matrix. The bitstream is created as the output of a prototype quantum computing device with $n$ input photons. It is a…
Interference of multiple photons via a linear-optical network has profound applications for quantum foundation, quantum metrology and quantum computation. Particularly, a boson sampling experiment with a moderate number of photons becomes…
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
Gaussian boson sampling (GBS) is considered a candidate problem for demonstrating quantum advantage. We propose an algorithm for approximate classical simulation of a lossy GBS instance. The algorithm relies on the Taylor series expansion,…
Quantum computers are unnecessary for exponentially-efficient computation or simulation if the Extended Church-Turing thesis---a foundational tenet of computer science---is correct. The thesis would be directly contradicted by a physical…
Hard optimization problems are often approached by finding approximate solutions. Here, we highlight the concept of proportional sampling and discuss how it can be used to improve the performance of stochastic algorithms for optimization.…
Recent claims of achieving exponential quantum advantage have attracted attention to Gaussian boson sampling (GBS), a potential application of which is dense subgraph finding. We investigate the effects of sources of error including loss…
Gaussian boson sampling (GBS) is not only a feasible protocol for demonstrating quantum computational advantage, but also mathematically associated with certain graph-related and quantum chemistry problems. In particular, it is proposed…
Quantum computer, harnessing quantum superposition to boost a parallel computational power, promises to outperform its classical counterparts and offer an exponentially increased scaling. The term "quantum advantage" was proposed to mark…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…
Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon number distribution of a linear optical interferometric network, which is fed…
Achieving a quantum computational advantage regime, and thus providing evidence against the extended Church-Turing thesis, remains one of the key challenges of modern science. Boson sampling seems to be a very promising platform in this…
Simon's problem plays an important role in the history of quantum algorithms, as it inspired Shor to discover the celebrated quantum algorithm solving integer factorization in polynomial time. Besides, the quantum algorithm for Simon's…