Related papers: Classical-Quantum Mixing in the Random 2-Satisfiab…
In this paper we show that the performance of the quantum adiabatic algorithm is determined by phase transitions in underlying problem in the presence of transverse magnetic field $\Gamma$. We show that the quantum version of random…
We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_*(k)$ such that a random $k$-SAT formula of clause density $\alpha$ is with…
We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…
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.…
Classical verification of quantum learning allows classical clients to reliably leverage quantum computing advantages by interacting with untrusted quantum servers. Yet, current quantum devices available in practice suffers from a variety…
Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…
A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…
We study a quantum version of the sequential game illustrating problems connected with making rational decisions. We compare the results that the two models (quantum and classical) yield. In the quantum model intransitivity gains importance…
The field of Quantum Computing has gathered significant popularity in recent years and a large number of papers have studied its effectiveness in tackling many tasks. We focus in particular on Quantum Annealing (QA), a meta-heuristic solver…
The $\Sigma$-QMAC problem is introduced, involving $S$ servers, $K$ classical ($\mathbb{F}_d$) data streams, and $T$ independent quantum systems. Data stream ${\sf W}_k, k\in[K]$ is replicated at a subset of servers…
The random 3-satisfiability (3-SAT) problem is in the unsatisfiable (UNSAT) phase when the clause density $\alpha$ exceeds a critical value $\alpha_s \approx 4.267$. However, rigorously proving the unsatisfiability of a given large 3-SAT…
The k-local Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k<=2. It was known that the problem is QMA-complete for any…
With the rapid development of quantum computers, quantum algorithms have been studied extensively. However, quantum algorithms tackling statistical problems are still lacking. In this paper, we propose a novel non-oracular quantum adaptive…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…
Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the…
We study the correlation structure of separable and classical states in 2x2- and 2x3-dimensional quantum systems with fixed spectra. Even for such simple systems the maximal correlation - as measured by mutual information - over the set of…
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors,…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when it…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…