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Efficient zero-knowledge proofs (ZKPs) have been restricted to NP statements so far, whereas they exist for all statements in PSPACE. This work presents the first practical zero-knowledge (ZK) protocols for PSPACE-complete statements by…
We consider quantum search algorithms that have access to a noisy oracle that, for every oracle call, with probability $p>0$ completely depolarizes the query registers, while otherwise working properly. Previous results had not ruled out…
We construct perfect zero-knowledge probabilistically checkable proofs (PZK-PCPs) for every language in #P. This is the first construction of a PZK-PCP for any language outside BPP. Furthermore, unlike previous constructions of…
Quantum computation requires large classical datasets to be embedded into quantum states in order to exploit quantum parallelism. However, this embedding requires considerable resources. It would therefore be desirable to avoid it, if…
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…
Zero-Knowledge Proofs (ZKPs) are a cryptographic primitive that allows a prover to demonstrate knowledge of a secret value to a verifier without revealing anything about the secret itself. ZKPs have shown to be an extremely powerful tool,…
We prove two sets of results concerning computational complexity classes. The first concerns a variation of the random oracle hypothesis posed by Bennett and Gill after they showed that relative to a randomly chosen oracle, P not equal NP…
In this work we study oblivious complexity classes. These classes capture the power of interactive proofs where the prover(s) are only given the input size rather than the actual input. In particular, we study the connections between the…
Shared control problems involve a robot learning to collaborate with a human. When learning a shared control policy, short communication between the agents can often significantly reduce running times and improve the system's accuracy. We…
Recent advances in artificial intelligence (AI), particularly deep learning, have led to widespread adoption across various applications. Yet, a fundamental challenge persists: how can we verify the correctness of AI model inference when…
Zero-knowledge proofs (ZKPs) have evolved from being a theoretical concept providing privacy and verifiability to having practical, real-world implementations, with SNARKs (Succinct Non-Interactive Argument of Knowledge) emerging as one of…
We study the algorithmic task of learning Boolean disjunctions in the distribution-free agnostic PAC model. The best known agnostic learner for the class of disjunctions over $\{0, 1\}^n$ is the $L_1$-polynomial regression algorithm,…
Let a Boolean function be available as a black-box (oracle) and one likes to devise an algorithm to test whether it has certain property or it is $\epsilon$-far from having that property. The efficiency of the algorithm is judged by the…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
We study the complexity of problems solvable in deterministic polynomial time with access to an NP or Quantum Merlin-Arthur (QMA)-oracle, such as $P^{NP}$ and $P^{QMA}$, respectively. The former allows one to classify problems more finely…
We describe a general framework for regarding oracle-assisted quantum algorithms as tools for discriminating between unitary transformations. We apply this to the Deutsch-Jozsa problem and derive all possible quantum algorithms which solve…
A proof is concurrent zero-knowledge if it remains zero-knowledge when many copies of the proof are run in an asynchronous environment, such as the Internet. It is known that zero-knowledge is not necessarily preserved in such an…
Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves…
Zero-knowledge proofs have always provided a clear solution when it comes to conveying information from a prover to a verifier or vice versa without revealing essential information about the process. Advancements in zero-knowledge have…
We study the power of quantum witnesses under perfect completeness. We construct a classical oracle relative to which a language lies in $\mathsf{QMA}_1$ but not in $\mathsf{QCMA}$ when the $\mathsf{QCMA}$ verifier is only allowed…