Related papers: A framework for robust quantum speedups in practic…

The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage…

The identification of causal relations is a cornerstone of the scientific method. Traditional approaches to this task are based on classical statistics. However, such classical approaches do not apply in the quantum domain, where a broader…

Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and…

One of the outstanding challenges in contemporary science and technology is building a quantum computer that is useful in applications. By starting from an estimate of the algorithm success rate, we can explicitly connect gate fidelity to…

Quantum-enhanced Markov chain Monte Carlo, an algorithm in which configurations are proposed through a measured quantum quench and accepted or rejected by a classical algorithm, has been proposed as a possible method for robust quantum…

We consider whether trainable quantum unitaries can be used to discover quantum speed-ups for classical problems. Using methods recently developed for training quantum neural nets, we consider Simon's problem, for which there is a known…

The ability to identify cause-effect relations is an essential component of the scientific method. The identification of causal relations is generally accomplished through statistical trials where alternative hypotheses are tested against…

We introduce a classical-quantum hybrid approach to computation, allowing for a quadratic performance improvement in the decision process of a learning agent. In particular, a quantum routine is described, which encodes on a quantum…

The maximal evolution speed of any quantum system can be expressed by the quantum speed limit time. In this paper, we consider a model in which the system has a correlation with the environment. The influence of the initial correlation…

For many problems, quantum algorithms promise speedups over their classical counterparts. However, these results predominantly rely on asymptotic worst-case analysis, which overlooks significant overheads due to error correction and the…

This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…

Optimizing quantum circuits is critical for enhancing computational speed and mitigating errors caused by quantum noise. Effective optimization must be achieved without compromising the correctness of the computations. This survey explores…

Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the…

Simulating complex molecules and materials is an anticipated application of quantum devices. With strong quantum advantage demonstrated in artificial tasks, we examine how such advantage translates into modeling physical problems of…

The advent of quantum algorithms has initiated a discourse on the potential for quantum speedups for optimization problems. However, several factors still hinder a practical realization of the potential benefits. These include the lack of…

Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms…

Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…

We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…

Motivated by notions of quantum heuristics and by average-case rather than worst-case algorithmic analysis, we define quantum computational advantage in terms of individual problem instances. Inspired by the classical notions of Kolmogorov…