Related papers: Statistical mechanics of classical and quantum com…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…
Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness and coherence are arguably of great significance. We introduce…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a…
Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete problems for the complexity classes NP and QMA which are believed to be intractable for classical and quantum computers, respectively. Statistical ensembles of…
Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most…
A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device, with comparable time and memory resources, is performing a computation that is impossible for classical computers.…
Quantum computing is currently gaining significant attention, not only from the academic community but also from industry, due to its potential applications across several fields for addressing complex problems. For any practical problem…
The science of complex networks is a new interdisciplinary branch of science which has arisen recently on the interface of physics, biology, social and computer sciences, and others. Its main goal is to discover general laws governing the…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
A longstanding goal in quantum information science is to demonstrate quantum computations that cannot be feasibly reproduced on a classical computer. Such demonstrations mark major milestones: they showcase fine control over quantum systems…
We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories. In this model, distinguishable particles start out with known momenta and…
The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question: {\it When and how will quantum computers outperform classical computers?} The next milestone is undoubtedly…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…
(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…