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Quantum computers are believed to surpass the classical ones. Moreover, it is claimed that this belief reaches the level of a mathematically proven fact within the oracle model of computation. Here we impair the whole class of the so-called…
Quantum computing promises exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (non-quantum) CAD, such as…
This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…
Quantum computing is of high interest because it promises to perform at least some kinds of computations much faster than classical computers. Arute et al. 2019 (informally, "the Google Quantum Team") report the results of experiments that…
In this Perspective article, we explore some of the promising spin and topology material platforms (e.g. spins in semi- and superconductors, skyrmionic, topological and 2D materials) being developed for such quantum components as qubits,…
This work develops tools to understand how quantum information spreads, scrambles, and is reshaped by measurements in many-body systems. First, I study scrambling and pseudorandomness in the Brownian Sachdev-Ye-Kitaev (SYK) model,…
Non-classical features of quantum systems can degrade when subjected to environment and noise. Here, we ask a fundamental question: What is the minimum amount of time it takes for a quantum system to exhibit non-classical features in the…
Recent experiments completed by collaborating research groups from Google, NASA Ames, UC Santa Barbara, and others provided compelling evidence that quantum supremacy has finally been achieved on a superconducting quantum processor. The…
The quantum information science community has seen a surge in new algorithmic developments across scientific domains. These developments have demonstrated polynomial or better improvements in computational and space complexity,…
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…
Over the last two decades, tremendous advances have been made for constructing large-scale quantum computers. In particular, the quantum processor architecture based on superconducting qubits has become the leading candidate for scalable…
We consider how to forecast progress in the domain of quantum computing. For this purpose we collect a dataset of quantum computer systems to date, scored on their physical qubits and gate error rate, and we define an index combining both…
To date, a conclusive detection of quantum speedup remains elusive. Recently, a team by Google Inc.~[V.~S.~Denchev {\em et al}., Phys.~Rev.~X {\bf 6}, 031015 (2016)] proposed a weak-strong cluster model tailored to have tall and narrow…
It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the…
This article is devoted to the study of which appears as the most famous paradoxes of quantum theory (Schrodinger cat, EPR argument and Aspect experiments, delayed choice experiments and retrocausality problems). Through these experiments,…
We propose an application for near-term quantum devices: namely, generating cryptographically certified random bits, to use (for example) in proof-of-stake cryptocurrencies. Our protocol repurposes the existing "quantum supremacy"…
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…
Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to…