Related papers: QIP $ \subseteq $ AM(2QCFA)
We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…
"Quantitative languages are extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the…
We study a model of one-way quantum automaton where only measurement operations are allowed (MOn-1qfa). We give an algebraic characterization of LMO, showing that the syntactic monoids of the languages in LMO are exactly the literal…
I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic…
Answer Set Programming with Quantifiers ASP(Q) extends Answer Set Programming (ASP) to allow for declarative and modular modeling of problems from the entire polynomial hierarchy. The first implementation of ASP(Q), called qasp, was based…
It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of…
Quantum finite automata (QFAs) literature offers an alternative mathematical model for studying quantum systems with finite memory. As a superiority of quantum computing, QFAs have been shown exponentially more succinct on certain problems…
Any technology for quantum information processing (QIP) must embody within it quantum bits (qubits) and maintain control of their key quantum properties of superposition and entanglement. Typical QIP schemes envisage an array of physical…
Quantum machine learning seeks to leverage quantum computers to improve upon classical machine learning algorithms. Currently, robust uncertainty quantification methods remain underdeveloped in the quantum domain, despite the critical need…
1-way quantum finite state automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. We introduce 2-tape…
We present a representation for linguistic structure that we call a Fock-space representation, which allows us to embed problems in language processing into small quantum devices. We further develop a formalism for understanding both…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…
A proof of quantumness (PoQ) allows a classical verifier to efficiently test if a quantum machine is performing a computation that is infeasible for any classical machine. In this work, we propose a new approach for constructing PoQ…
We provide a new, quantum inspired, proof for the celebrated claim of [LFKN92] that $P^{\#P} \subseteq IP$. The protocol is fundamentally different from the original sum-check protocol of [LFKN92, Sha92], as well as from variants of this…
Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata…
We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…
In recent years, the number of hybrid algorithms that combine quantum and classical computations has been continuously increasing. These two approaches to computing can mutually enhance each others' performances thus bringing the promise of…
We introduce a simple sub-universal quantum computing model, which we call the Hadamard-classical circuit with one-qubit (HC1Q) model. It consists of a classical reversible circuit sandwiched by two layers of Hadamard gates, and therefore…
A critical step in experimental quantum information processing (QIP) is to implement control of quantum systems protected against decoherence via informational encodings, such as quantum error correcting codes, noiseless subsystems and…