Related papers: Approximation, Proof Systems, and Correlations in …
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
We show that computational problem of testing the behaviour of quantum circuits is hard for the class of problems known as QMA that can be verified efficiently with a quantum computer. This result is a generalization of the techniques…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
Quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems. Considerable progress has been made in the development of a physical quantum annealer, motivating the study of methods to…
In this Letter we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. We find that entanglement can be classified in the framework…
One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more…
The polynomial-time hierarchy ($\mathrm{PH}$) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as $\mathrm{PH}$ does not collapse). Here, we study whether two…
Quantum nondeterministic distributed computing was recently introduced as dQMA (distributed quantum Merlin-Arthur) protocols by Fraigniaud, Le Gall, Nishimura and Paz (ITCS 2021). In dQMA protocols, with the help of quantum proofs and local…
In this paper, we propose a method to probe entanglement in a theoretically inaccessible quantum system with either a discrete or continuous basis. Our approach leverages insights into the entanglement distribution within a four-partite…
We study the notion of zero-knowledge secure against quantum polynomial-time verifiers (referred to as quantum zero-knowledge) in the concurrent composition setting. Despite being extensively studied in the classical setting, concurrent…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
Entanglement, a defining property of quantum mechanics in which two physical subsystems cannot be seen as independent entities, challenges our everyday experience and classical intuition. However, only such strong quantum correlations…
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate…
This thesis explores foundational aspects of quantum information theory and quantum cryptography. First, we investigate quantum correlations in interactive settings, including the CHSH and graph isomorphism games. We aim to distinguish…
The past decade has witnessed significant advancements in quantum hardware, encompassing improvements in speed, qubit quantity, and quantum volume-a metric defining the maximum size of a quantum circuit effectively implementable on…
We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to…
Quantum programs exhibit inherent non-deterministic behavior, which poses more significant challenges for error discovery compared to classical programs. While several testing methods have been proposed for quantum programs, they often…
Characterising the correlations that arise from locally measuring a single part of a joint quantum system is one of the main problems of quantum information theory. The seminal work [M. Navascu\'es et al., New J. Phys. 10, 073013 (2008)],…
Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of scientific and industrial contexts - has been identified as one of the core potential fields of applicability of quantum computers. It…