Related papers: On Perfect Completeness for QMA

We construct a unitary oracle relative to which $\mathbf{BQP}=\mathbf{QCMA}$ but quantum-computation-classical-communication (QCCC) commitments and QCCC multiparty non-interactive key exchange exist. We also construct a unitary oracle…

The canonical problem for the class Quantum Merlin-Arthur (QMA) is that of estimating ground state energies of local Hamiltonians. Perhaps surprisingly, [Ambainis, CCC 2014] showed that the related, but arguably more natural, problem of…

Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…

We present a new quantum complexity class, called MQ^2, which is contained in AWPP. This class has a compact and simple mathematical definition, involving only polynomial-time computable functions and a unitarity condition. It contains both…

Classical probability theory is based on assumptions which are often violated in practice. Therefore quantum probability is a proposed alternative not only in quantum physics, but also in other sciences. However, so far it mostly criticizes…

We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified…

We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: (*) Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In…

This work investigates the relationships between quantum state synthesis complexity classes (a recent concept in computational complexity that focuses on the complexity of preparing quantum states) and traditional decision complexity…

While quantum mechanics (QM) is covered at length in introductory physics textbooks, the concept of quantum entanglement is typically not covered at all, despite its importance in the rapidly growing area of quantum information science and…

We have unified quantum and classical computing in open quantum systems called qACP which is a quantum generalization of process algebra ACP. But, an axiomatization for quantum and classical processes with an assumption of closed quantum…

We present new results on realtime alternating, private alternating, and quantum alternating automaton models. Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable. Then, we…

We describe Kitaev's result from 1999, in which he defines the complexity class QMA, the quantum analog of the class NP, and shows that a natural extension of 3-SAT, namely local Hamiltonians, is QMA complete. The result builds upon the…

This paper investigates the role of interaction and coins in public-coin quantum interactive proof systems (also called quantum Arthur-Merlin games). While prior works focused on classical public coins even in the quantum setting, the…

The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…

We show that any quantum algorithm to decide whether a function f:[n]->[n] is a permutation or far from a permutation must make Omega(n^{1/3}/w) queries to f, even if the algorithm is given a w-qubit quantum witness in support of f being a…

Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…

Question Answering (QA) has proved to be an arduous challenge in the area of natural language processing (NLP) and artificial intelligence (AI). Many attempts have been made to develop complete solutions for QA as well as improving…

A composite quantum system has properties that are incompatible with every property of its parts. The existence of such global properties incompatible with all local properties constitutes what I call "mereological holism"--the distinctive…

The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating this question to…

A foundational question in quantum computational complexity asks how much more useful a quantum state can be in a given task than a comparable, classical string. Aaronson and Kuperberg showed such a separation in the presence of a quantum…