Related papers: The Quantum PCP Conjecture
Quantum Computing (QC) claims to improve the efficiency of solving complex problems, compared to classical computing. When QC is integrated with Machine Learning (ML), it creates a Quantum Machine Learning (QML) system. This paper aims to…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…
Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper,…
Quantum theory revolutionised physics by introducing a new fundamental constant and a new mathematical framework to describe the observed phenomena at the atomic scale. These new concepts run counter to our familiar notions of classical…
Randomness is an intrinsic feature of quantum theory. The outcome of any quantum measurement will be random, sampled from a probability distribution that is defined by the measured quantum state. The task of sampling from a prescribed…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
Machine learning is frequently listed among the most promising applications for quantum computing. This is in fact a curious choice: Today's machine learning algorithms are notoriously powerful in practice, but remain theoretically…
From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedankenexperiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced…
Nyquist-Shannon sampling theorem, instrumental in classical telecommunication technologies, is extended to quantum systems supporting a unitary representation of a finite group $G$. Two main ideas from the classical theory having natural…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged…
We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and…
Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the…
Is the universe digital or analog? In this essay I argue that both classical and quantum physics include limits that prevent us from definitively answering that question. That quantum physics does so is no surprise. That classical physics…
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…
Here we show that the concepts behind such terms as entanglement, qubits, quantum gates, quantum error corrections, unitary time evolution etc., which are usually ascribed to quantum systems, can be adequately realized on a set of coupled…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…
In this review we discuss intriguing properties of apparently classical optical fields, that go beyond purely classical context and allow us to speak about quantum characteristics of such fields and about their applications in quantum…
From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a…