Related papers: Quantum Proofs
In this paper we propose a definition for (honest verifier) quantum statistical zero-knowledge interactive proof systems and study the resulting complexity class, which we denote QSZK. We prove several facts regarding this class that…
Quantum finite automata have been studied intensively since their introduction in late 1990s as a natural model of a quantum computer with finite-dimensional quantum memory space. This paper seeks their direct application to interactive…
Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow…
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…
Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 a study on the computational power of quantum interactive proof systems…
Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output…
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…
Quantum computers are expected to offer substantial speedups over their classical counterparts and to solve problems that are intractable for classical computers. Beyond such practical significance, the concept of quantum computation opens…
We present a classical interactive protocol that verifies the validity of a quantum witness state for the local Hamiltonian problem. It follows from this protocol that approximating the non-local value of a multi-player one-round game to…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
The class of languages having polynomial-time classical or quantum interactive proof systems ($\mathsf{IP}$ or $\mathsf{QIP}$, respectively) is identical to $\mathsf{PSPACE}$. We show that $\mathsf{PSPACE}$ (and so $\mathsf{QIP}$) is subset…
We define the notion of a proof of knowledge in the setting where the verifier is classical, but the prover is quantum, and where the witness that the prover holds is in general a quantum state. We establish simple properties of our…
Using the measurement-based quantum computation model, we construct interactive proofs with non-communicating quantum provers and a classical verifier. Our construction gives interactive proofs for all languages in BQP with a polynomial…
This paper studies the complexity classes QZK and HVQZK of problems having a quantum computational zero-knowledge proof system and an honest-verifier quantum computational zero-knowledge proof system, respectively. The results proved in…
We initiate the study of non-interactive zero-knowledge (NIZK) arguments for languages in QMA. Our first main result is the following: if Learning With Errors (LWE) is hard for quantum computers, then any language in QMA has an NIZK…
Verification of quantum computation is a task to efficiently check whether an output given from a quantum computer is correct. Existing verification protocols conducted between a quantum computer to be verified and a verifier necessitate…
Bit commitment schemes are at the basis of modern cryptography. Since information-theoretic security is impossible both in the classical and the quantum regime, we need to look at computationally secure commitment schemes. In this paper, we…
We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the pi-calculus with primitives for measurement…
Suppose that a polynomial-time mixed-state quantum circuit, described as a sequence of local unitary interactions followed by a partial trace, generates a quantum state shared between two parties. One might then wonder, does this quantum…
QMA and QCMA are possible quantum analogues of the complexity class NP. In QCMA the verifier is a quantum program and the proof is classical. In contrast, in QMA the proof is also a quantum state. We show that two known QMA-complete…