Related papers: Oracle Separations Between Quantum and Non-interac…
This paper positively solves the quantum subroutine problem for fully quantum oracles. The quantum subroutine problem asks whether a quantum computer with an efficiently computable oracle can be efficiently simulated by a non-oracle quantum…
The $P$ versus $NP$ problem is still unsolved. But there are several oracles with $P$ unequal $NP$ relative to them. Here we will prove, that $P\not=NP$ relative to a $P$-complete oracle. In this paper, we use padding arguments as the proof…
We develop a framework for learning from noisy quantum experiments in which fault-tolerant devices access uncharacterized systems through noisy couplings. Introducing the complexity class $\textsf{NBQP}$ ("noisy BQP''), we model noisy…
Zero-knowledge proofs (zk-Proofs) are communication protocols by which a prover can demonstrate to a verifier that it possesses a solution to a given public problem without revealing the content of the solution. Arbitrary computations can…
A Zero-Knowledge Protocol (ZKP) allows one party to convince another party of a fact without disclosing any extra knowledge except the validity of the fact. For example, it could be used to allow a customer to prove their identity to a…
As Artificial Intelligence (AI) systems, particularly those based on machine learning (ML), become integral to high-stakes applications, their probabilistic and opaque nature poses significant challenges to traditional verification and…
We construct a publicly-verifiable non-interactive zero-knowledge argument system for QMA with the following properties. 1. Transparent setup. Our protocol only requires a uniformly random string (URS) setup. The only prior…
In a proof of knowledge (PoK), a verifier becomes convinced that a prover possesses privileged information. In combination with zero-knowledge proof systems, PoKs play an important role in security protocols such as in digital signatures…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
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…
The Quantum Oracle Classification (QOC) problem is to classify a function, given only quantum black box access, into one of several classes without necessarily determining the entire function. Generally, QOC captures a very wide range of…
We give an oracle separation between QMA and QCMA for quantum algorithms that have bounded adaptivity in their oracle queries; that is, the number of rounds of oracle calls is small, though each round may involve polynomially many queries…
The complexity class Quantum Statistical Zero-Knowledge ($\mathsf{QSZK}$), introduced by Watrous (FOCS 2002) and later refined in Watrous (SICOMP, 2009), has the best known upper bound $\mathsf{QIP(2)} \cap \text{co-}\mathsf{QIP(2)}$, which…
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…
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…
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…
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 quantum algorithm for an oracle problem can be understood as a quantum strategy for a player in a two-player zero-sum game in which the other player is constrained to play classically. I formalize this correspondence and give examples of…
We investigate the existence of constant-round post-quantum black-box zero-knowledge protocols for $\mathbf{NP}$. As a main result, we show that there is no constant-round post-quantum black-box zero-knowledge argument for $\mathbf{NP}$…
The oracle identification problem (OIP) is, given a set $S$ of $M$ Boolean oracles out of $2^{N}$ ones, to determine which oracle in $S$ is the current black-box oracle. We can exploit the information that candidates of the current oracle…