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Neural networks are increasingly employed in safety-critical domains. This has prompted interest in verifying or certifying logically encoded properties of neural networks. Prior work has largely focused on checking existential properties,…
We propose a set of Bell-type nonlocal games that can be used to prove an unconditional quantum advantage in an objective and hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure 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…
Distributed quantum systems and especially the Quantum Internet have the ever-increasing potential to fully demonstrate the power of quantum computation. This is particularly true given that developing a general-purpose quantum computer is…
We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a…
We construct a quantumness witness following the work of Alicki and van Ryn (AvR) in "A simple test of quantumness for a single system" [J. Phys. A: Math. Theor., vol. 41, 062001 (2008)]. The AvR test is designed to detect quantumness. We…
The behavior of entangled quantum systems can generally not be explained as being determined by shared classical randomness. In the first part of this paper, we propose a simple game for n players demonstrating this non-local property of…
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 $L \in \textbf{P}$…
Recent works have shown that tokenisation is NP-complete. However, these works assume tokenisation is applied to inputs with unboundedly large alphabets -- an unrealistic assumption, given that in practice tokenisers operate over fixed-size…
Nonlocal games are a foundational tool for understanding entanglement and constructing quantum protocols in settings with multiple spatially separated quantum devices. In this work, we continue the study initiated by Kalai et al. (STOC '23)…
We show that if a language $L$ admits a public-coin unambiguous interactive proof (UIP) with round complexity $\ell$, where $a$ bits are communicated per round, then the batch language $L^{\otimes k}$, i.e. the set of $k$-tuples of…
Quantum entanglement is a fundamental property of quantum mechanics and plays a crucial role in quantum computation and information. We study entanglement via the lens of computational complexity by considering quantum generalizations of…
We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. This contains circuits giving rise to the second level of the Fourier Hierarchy, the lowest…
We study the quantum moment problem: Given a conditional probability distribution together with some polynomial constraints, does there exist a quantum state rho and a collection of measurement operators such that (i) the probability of…
Answer set programming (ASP) is a well-established logic programming language that offers an intuitive, declarative syntax for problem solving. In its traditional application, a fixed ASP program for a given problem is designed and the…
In this paper, we look at good-for-games Rabin automata that recognise a Muller language (a language that is entirely characterised by the set of letters that appear infinitely often in each word). We establish that minimal such automata…
Authentication is a well-studied area of classical cryptography: a sender S and a receiver R sharing a classical private key want to exchange a classical message with the guarantee that the message has not been modified by any third party…
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…
Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be…
We show that, for any language in NP, there is an entanglement-resistant constant-bit two-prover interactive proof system with a constant completeness vs. soundness gap. The previously proposed classical two-prover constant-bit interactive…