Related papers: On Perfect Completeness for QMA
This paper presents stronger methods of achieving perfect completeness in quantum interactive proofs. First, it is proved that any problem in QMA has a two-message quantum interactive proof system of perfect completeness with constant…
Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…
We give an alternative proof of PreciseQMA = PSPACE, first proved by Fefferman and Lin (Innov. Theor. Comp. Sci. 2018), where PreciseQMA is the class Quantum Merlin-Arthur with inverse exponential completeness-soundness gap. We adapt the…
We prove that it is impossible to construct perfect-complete quantum public-key encryption (QPKE) with classical keys from quantumly secure one-way functions (OWFs) in a black-box manner, resolving a long-standing open question in quantum…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
We consider the power of various quantum complexity classes with the restriction that states and operators are defined over a real, rather than complex, Hilbert space. It is well know that a quantum circuit over the complex numbers can be…
We show that computational problem of testing the behaviour of quantum circuits is hard for the class of problems known as QMA that can be verified efficiently with a quantum computer. This result is a generalization of the techniques…
We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of…
A long-standing open problem in quantum complexity theory is whether ${\sf QMA}$, the quantum analogue of ${\sf NP}$, is equal to ${\sf QMA}_1$, its one-sided error variant. We show that ${\sf QMA}={\sf QMA}^{\infty}= {\sf QMA}_1^{\infty}$,…
Decision problems are the problems whose answer is either YES or NO. As the quantum analogue of $\mathsf{NP}$ (nondeterministic polynomial time), the class $\mathsf{QMA}$ (quantum Merlin-Arthur) contains the decision problems whose YES…
Quantum entanglement is a fundamental property of quantum mechanics and plays a crucial role in quantum computation and information. We study entanglement via the lens of computational complexity by considering quantum generalizations of…
We present evidence that there exist quantum computations that can be carried out in constant depth, using 2-qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically…
The class MA consists of languages that can be efficiently verified by classical probabilistic verifiers using a single classical certificate, and the class QMA consists of languages that can be efficiently verified by quantum verifiers…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
It is a long-standing open question in quantum complexity theory whether the definition of $\textit{non-deterministic}$ quantum computation requires quantum witnesses $(\textsf{QMA})$ or if classical witnesses suffice $(\textsf{QCMA})$. We…
Relational quantum queries are sometimes capable to effectively decide between collections of mutually exclusive elementary cases without completely resolving and determining those individual instances. Thereby the set of mutually exclusive…
We define a problem "exact non-identity check": Given a classical description of a quantum circuit with an ancilla system, determine whether it is strictly equivalent to the identity or not. We show that this problem is NQP-complete. In a…
{\it Learning finite automata} (termed as {\it model learning}) has become an important field in machine learning and has been useful realistic applications. Quantum finite automata (QFA) are simple models of quantum computers with finite…
Many problems of industrial interest are NP-complete, and quickly exhaust resources of computational devices with increasing input sizes. Quantum annealers (QA) are physical devices that aim at this class of problems by exploiting quantum…
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…