Related papers: The Entangled Quantum Polynomial Hierarchy Collaps…
By means of the Ehrhart theory of inside-out polytopes we establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen, on a polygonal convex board. The number of ways…
We begin by establishing structural results for several fundamental quantum complexity classes: p/mBQP, p/mQ(C)MA, $\text{p/mQSZK}_{\text{hv}}$, p/mQIP, p/mBQP/qpoly, p/mBQP/poly, and p/mPSPACE. This includes identifying complete problems,…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…
The problem of the relationship between entanglement and two-qubit systems in which it is embedded is central to the quantum information theory. This paper suggests that the concurrence hierarchy as an entanglement measure provides an…
Using the information content of correlations between multipartite systems, together with the notion of partitioning, we show that some general results about the evolution of correlations in quantum systems can be derived with only…
It is widely believed that quantum mechanics cannot exhibit chaos, since unitarity of time evolution ensures that distances between quantum states are preserved. However, a parallel argument can be constructed in classical mechanics that…
In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems, showed that all these problems are either in P or NP-complete, and gave a…
We consider a dominance order on positive vectors induced by the elementary symmetric polynomials. Under this dominance order we provide conditions that yield simple proofs of several monotonicity questions. Notably, our approach yields a…
The degree of a polynomial representing (or approximating) a function f is a lower bound for the number of quantum queries needed to compute f. This observation has been a source of many lower bounds on quantum algorithms. It has been an…
Shared entanglement can significantly amplify classical correlations between systems interacting over a limited quantum channel. A natural avenue is to use entanglement of the same dimension as the channel because this allows for unitary…
In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…
Quantum walk (QW) utilizes its internal quantum states to decide the displacement, thereby introducing single-particle entanglement between the internal and positional degrees of freedom. By simulating three variants of QW with the…
Bell-inequality violations establish that two systems share some quantum entanglement. We give a simple test to certify that two systems share an asymptotically large amount of entanglement, n EPR states. The test is efficient: unlike…
We study holographic models related to global quantum quenches in finite size systems. The holographic set up describes naturally a CFT, which we consider on a circle and a sphere. The enhanced symmetry of the conformal group on the circle…
We define rewinding operators that invert quantum measurements. Then, we define complexity classes ${\sf RwBQP}$, ${\sf CBQP}$, and ${\sf AdPostBQP}$ as sets of decision problems solvable by polynomial-size quantum circuits with a…
Quantum Machine Learning (QML) has emerged as a promising framework for exploring how quantum dynamics may enhance data processing tasks. Here we investigate Quantum Extreme Learning Machines (QELMs), a quantum analogue of classical Extreme…
Quantum walks are powerful tools for building quantum search algorithms or quantum sampling algorithms named the construction of quantum stationary state. However, the success probability of those algorithms are all far away from 1.…
Downward collapse (a.k.a. upward separation) refers to cases where the equality of two larger classes implies the equality of two smaller classes. We provide an unqualified downward collapse result completely within the polynomial…
To detect frauds from some internal participants or external attackers, some verifiable threshold quantum secret sharing schemes have been proposed. In this paper, we present a new verifiable threshold structure based on a single qubit…