Related papers: Quantum NP and a Quantum Hierarchy
This paper proves the polynomial equivalence of a broad class of definitions of quantum computational complexity. We study right-invariant metrics on the unitary group -- often called `complexity geometries' following the definition of…
A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket…
Over the last decade, Quantum Computing hardware has rapidly developed and become a very intriguing, promising, and active research field among scientists worldwide. To achieve the desired quantum functionalities, quantum algorithms require…
The quantification of the quantumness of a quantum ensemble has theoretical and practical significance in quantum information theory. We propose herein a class of measures of the quantumness of quantum ensembles using the unitary similarity…
The polynomial hierarchy has been widely studied in classical complexity theory. In this paper, we will generalize some commonly known results about the polynomial hierarchy to a version of the hierarchy extended to promise problems. This…
The Quantum Satisfiability problem (QSAT) is the generalization of the canonical NP-complete problem - Boolean Satisfiability. (k,s)-QSAT is the following variant of the problem: given a set of projectors of rank 1, acting non-trivially on…
In building a quantum information processor (QIP), the challenge is to coherently control a large quantum system well enough to perform an arbitrary quantum algorithm and to be able to correct errors induced by decoherence. Nuclear magnetic…
We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub, and Smale for…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…
Quantum Computers, one fully realized, can represent an exponential boost in computing power. However, the computational power of the current quantum computers, referred to as Noisy Internediate Scale Quantum, or NISQ, is severely limited…
We propose an operational definition of complementarity, pinning down the concept originally introduced by Bohr. Two properties of a system are considered complementary if they cannot be simultaneously well defined. We further show that,…
This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known…
Hybrid classical quantum learning is often bottlenecked by communication overhead and approximation error from generic variational ansatzes. In this study, we introduce Neural Native Quantum Arithmetic (NNQA), which compiles classically…
The widely held belief that BQP strictly contains BPP raises fundamental questions: Upcoming generations of quantum computers might already be too large to be simulated classically. Is it possible to experimentally test that these systems…
Recently the theory of communication developed by Shannon has been extended to the quantum realm by exploiting the rules of quantum theory. This latter stems on complex vector spaces. However complex (as well as real) numbers are just…
The main goal of this master's thesis is to introduce Quantum Natural Language Processing (QNLP) in a way understandable by both the NLP engineer and the quantum computing practitioner. QNLP is a recent application of quantum computing that…
We first discuss a framework for discrete quantum processes (DQP). It is shown that the set of q-probability operators is convex and its set of extreme elements is found. The property of consistency for a DQP is studied and the quadratic…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
Quantum signal processing (QSP) is a methodology for constructing polynomial transformations of a linear operator encoded in a unitary. Applied to an encoding of a state $\rho$, QSP enables the evaluation of nonlinear functions of the form…