Related papers: The power of quantum circuits in sampling
The classical communication complexity of testing closeness of discrete distributions has recently been studied by Andoni, Malkin and Nosatzki (ICALP'19). In this problem, two players each receive $t$ samples from one distribution over…
Giving a convincing experimental evidence of the quantum supremacy over classical simulations is a challenging goal. Noise is considered to be the main problem in such a demonstration, hence it is urgent to understand the effect of noise.…
We explore potential quantum speedups for the fundamental problem of testing the properties of closeness and $k$-wise uniformity of probability distributions. Closeness testing is the problem of distinguishing whether two $n$-dimensional…
Communication scenarios between two parties can be implemented by first encoding messages into some states of a physical system which acts as the physical medium of the communication and then decoding the messages by measuring the state of…
Given a quantum Markovian noise model, we study the maximum dimension of a classical or quantum system that can be stored for arbitrarily large time. We show that, unlike the fixed time setting, in the limit of infinite time, the classical…
Quantum computers are believed to bring computational advantages in simulating quantum many body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems…
The impressive progress in quantum hardware in the last years has raised the interest of the quantum computing community in harvesting the computational power of such devices. However, in the absence of error correction, these devices can…
Simon as extended by Brassard and H{\o}yer shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine infinitely often. The present paper shows that there are tasks on which…
Current quantum computers suffer from a limited number of qubits and high error rates, limiting practical applicability. Different techniques exist to mitigate these effects and run larger algorithms. In this work, we analyze one of these…
One of the core challenges of research in quantum computing is concerned with the question whether quantum advantages can be found for near-term quantum circuits that have implications for practical applications. Motivated by this mindset,…
Peaked quantum circuits, whose output distribution is sharply concentrated on a single bitstring, have emerged as a promising candidate for verifiable quantum advantage, as the correctness of the quantum output can be checked by simply…
We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…
In this work, we propose a new way to (non-interactively, verifiably) demonstrate Quantum Advantage by solving the average-case $\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) multivariate quadratic…
The distance of a classical or quantum code is a key figure of merit which reflects its capacity to detect errors. Quantum LDPC code families have considerable promise in reducing the overhead required for fault-tolerant quantum…
A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…
Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In this work, we present classical sampling algorithms for single-photon and…
With the current rate of progress in quantum computing technologies, systems with more than 50 qubits will soon become reality. Computing ideal quantum state amplitudes for circuits of such and larger sizes is a fundamental step to assess…
As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
Channel simulation algorithms can efficiently encode random samples from a prescribed target distribution $Q$ and find applications in machine learning-based lossy data compression. However, algorithms that encode exact samples usually have…