Related papers: QIP $ \subseteq $ AM(2QCFA)
This paper considers the following problem. Two mixed-state quantum circuits Q and R are given, and the goal is to determine which of two possibilities holds: (i) Q and R act nearly identically on all possible quantum state inputs, or (ii)…
In this article we introduce a new complexity class called PQMA_log(2). Informally, this is the class of languages for which membership has a logarithmic-size quantum proof with perfect completeness and soundness which is polynomially close…
We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five entangled provers, (ii) the verifier sends a classical message on O(log n) bits…
We study three variants of multi-prover quantum Merlin-Arthur proof systems. We first show that the class of problems that can be efficiently verified using polynomially many quantum proofs, each of logarithmic-size, is exactly MQA (also…
It is known that for some languages quantum finite automata are more efficient than classical counterparts. Particularly, a QFA recognizing the language $MOD_p$ has an exponential advantage over the classical finite automata. However, the…
{\it Two-way quantum automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous in 2002. In this paper we study state succinctness of 2QCFA. For any $m\in {\mathbb{Z}}^+$ and any $\epsilon<1/2$, we show…
In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…
qPCF is a paradigmatic quantum programming language that ex- tends PCF with quantum circuits and a quantum co-processor. Quantum circuits are treated as classical data that can be duplicated and manipulated in flexible ways by means of a…
If two classical provers share an entangled state, the resulting interactive proof system is significantly weakened [quant-ph/0404076]. We show that for the case where the verifier computes the XOR of two binary answers, the resulting proof…
We study a model where two opposing provers debate over the membership status of a given string in a language, trying to convince a weak verifier whose coins are visible to all. We show that the incorporation of just two qubits to an…
This paper studies quantum Arthur-Merlin games, which are Arthur-Merlin games in which Arthur and Merlin can perform quantum computations and Merlin can send Arthur quantum information. As in the classical case, messages from Arthur to…
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…
An open question in quantum complexity theory is whether or not the class $\operatorname{MIP}^{co}$, consisting of languages that can be efficiently verified using interacting provers sharing quantum resources according to the quantum…
This paper proves one of the open problem posed by Beigi et al. in arXiv:1004.0411v2. We consider quantum interactive proof systems where in the beginning the verifier and prover send messages to each other with the combined length of all…
Interactive proofs (IP) model a world where a verifier delegates computation to an untrustworthy prover, verifying the prover's claims before accepting them. IP protocols have applications in areas such as verifiable computation…
Multi Prover Interactive Proof systems (MIPs)were first presented in a cryptographic context, but ever since they were used in various fields. Understanding the power of MIPs in the quantum context raises many open problems, as there are…
Quantum multiprover interactive proof systems with entanglement MIP* are much more powerful than its classical counterpart MIP (Babai et al. '91, Ji et al. '20): while MIP = NEXP, the quantum class MIP* is equal to RE, a class including the…
The classical channel remote state preparation (ccRSP) is an important two-party primitive in quantum cryptography. Alice (classical polynomial-time) and Bob (quantum polynomial-time) exchange polynomial rounds of classical messages, and…
We show that every language in QMA admits a classical-verifier, quantum-prover zero-knowledge argument system which is sound against quantum polynomial-time provers and zero-knowledge for classical (and quantum) polynomial-time verifiers.…
Complexity class containments involving interactive proof classes are famously nonrelativizing: although $\mathsf{IP} = \mathsf{PSPACE}$, Fortnow and Sipser showed that that there exists an oracle relative to which $\mathsf{coNP}…