Related papers: Debates with small transparent quantum verifiers
In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a…
In classical Arthur-Merlin games, the class of languages whose membership proofs can be verified by Arthur using logarithmic space (AM(log-space)) coincides with the class P \cite{Co89}. In this note, we show that if Arthur has a fixed-size…
A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify the quantum advantage of an untrusted prover. That is, a quantum prover can correctly answer the verifier's challenges and…
Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…
This paper gives the first formal treatment of a quantum analogue of multi-prover interactive proof systems. It is proved that the class of languages having quantum multi-prover interactive proof systems is necessarily contained in NEXP,…
Despite theoretical promise, debate as a scalable oversight protocol has produced mixed empirical results: gains in some settings, and null effects in others, especially when the judge does not have information hidden from it. We study…
Our preferences depend on the circumstances in which we reveal them. We will introduce a dependency which allows us to illustrate the relation between the possibility of winning of particular candidates in a quantum election and the type of…
We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
We study the capabilities of probabilistic finite-state machines that act as verifiers for certificates of language membership for input strings, in the regime where the verifiers are restricted to toss some fixed nonzero number of coins…
Quantum correlations provide dramatic advantage over the corresponding classical resources in several communication tasks. However a broad class of probabilistic theories exists that attributes greater success than quantum theory in many of…
We study the ability of efficient quantum verifiers to decide properties of exponentially large subsets given either a classical or quantum witness. We develop a general framework that can be used to prove that QCMA machines, with only…
In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an (information-theoretically secure) streaming proof with a…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…
In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…
A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device, with comparable time and memory resources, is performing a computation that is impossible for classical computers.…
A language L has a property tester if there exists a probabilistic algorithm that given an input x only asks a small number of bits of x and distinguishes the cases as to whether x is in L and x has large Hamming distance from all y in L.…
Hybrid quantum-classical classifiers promise to positively impact critical aspects of natural language processing tasks, particularly classification-related ones. Among the possibilities currently investigated, quantum transfer learning,…
In recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine.…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Quantum Merlin-Arthur proof systems are believed to be stronger than both their classical counterparts and ``stand-alone'' quantum computers when Arthur is assumed to operate in $\Omega(\log n)$ space. No hint of such an advantage over…