Related papers: Quantum Proofs
We initiate the study of quantum Interactive Oracle Proofs (qIOPs), a generalization of both quantum Probabilistically Checkable Proofs and quantum Interactive Proofs, as well as a quantum analogue of classical Interactive Oracle Proofs. In…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
The widely held belief that BQP strictly contains BPP raises fundamental questions: if we cannot efficiently compute predictions for the behavior of quantum systems, how can we test their behavior? In other words, is quantum mechanics…
The widely held belief that BQP strictly contains BPP raises fundamental questions: Upcoming generations of quantum computers might already be too large to be simulated classically. Is it possible to experimentally test that these systems…
The way entanglement influences the power of quantum and classical multi-prover interactive proof systems is a long-standing open question. We show that the class of languages recognized by quantum multi-prover interactive proof systems,…
Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a…
This paper proves that the computational power of quantum interactive proof systems, with a double-exponentially small gap in acceptance probability between the completeness and soundness cases, is precisely characterized by EXP, the class…
We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
Complexity theory typically focuses on the difficulty of solving computational problems using classical inputs and outputs, even with a quantum computer. In the quantum world, it is natural to apply a different notion of complexity, namely…
Whereas quantum complexity theory has traditionally been concerned with problems arising from classical complexity theory (such as computing boolean functions), it also makes sense to study the complexity of inherently quantum operations…
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.…
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…
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…
Zero-knowledge and multi-prover systems are both central notions in classical and quantum complexity theory. There is, however, little research in quantum multi-prover zero-knowledge systems. This paper studies complexity-theoretical…
This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA=QCMA. We prove three results about this question. First, we give a "quantum oracle separation" between QMA and QCMA. More…
We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof…
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…
The ultimate goal of the classicality programme is to quantify the amount of quantumness of certain processes. Here, classicality is studied for a restricted type of process: quantum information processing (QIP). Under special conditions,…
We identify a formal connection between physical problems related to the detection of separable (unentangled) quantum states and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum…