Related papers: The Detectability Lemma and Quantum Gap Amplificat…
It is a general belief that all fundamental interactions need to be quantized. However, all attempts to develop a quantum theory of gravity presented various problems, leading to a recent active debate about how to probe its quantum nature.…
In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the…
The $k$-local Hamiltonian problem is a central model for quantum many-body systems and Hamiltonian complexity. Semidefinite programming and noncommutative sum-of-squares hierarchies provide systematic certificates for ground-state energies,…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
It has been argued that the entropy of de Sitter space corresponds to the entanglement between disconnected regions computable by switching on a replica parameter $q$ modeled by the quotient dS$/\mathbb{Z}_q$. Within this framework, we show…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
We study the complexity of a classic problem in computational topology, the homology problem: given a description of some space $X$ and an integer $k$, decide if $X$ contains a $k$-dimensional hole. The setting and statement of the homology…
Standard approaches to quantum statistical inference rely on measurements that induce a collapse of the wave function, effectively consuming the quantum state to extract information. In this work, we investigate the fundamental limits of…
Quantum walk (QW) utilizes its internal quantum states to decide the displacement, thereby introducing single-particle entanglement between the internal and positional degrees of freedom. By simulating three variants of QW with the…
Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms…
In this paper, we provide a simple framework for deriving one-shot achievable bounds for some problems in quantum information theory. Our framework is based on the joint convexity of the exponential of the collision relative entropy, and is…
The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition…
Entanglement is often regarded as an inherently quantum feature. We show that this does not have to be the case: under restricted operational access, classical correlations can appear nonseparable when expressed in the formalism of quantum…
This is the second of the two related papers analysing origins and possible explanations of a paradoxical phenomenon of the quantum potential (QP). It arises in quantum mechanics'(QM) of a particle in the Riemannian $n$-dimensional…
Quantum annealing aims at finding optimal solutions to complex optimization problems using a suitable quantum many body Hamiltonian encoding the solution in its ground state. To find the solution one typically evolves the ground state of a…
Quantum systems may contain underlying correlations which are inaccessible to computationally bounded observers. We capture this distinction through a framework that analyses bipartite states only using efficiently implementable quantum…
Communication complexity is a fundamental aspect of information science, concerned with the amount of communication required to solve a problem distributed among multiple parties. The standard quantification of one-way communication…
Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs…
The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error…
Quantum physics enables parameter estimation with precisions beyond the capability of classical sensors. Quantum criticality is a key resource for this quantum-enhanced sensing, but experimental realization has been challenging due to the…