Related papers: Approximation, Proof Systems, and Correlations in …
Correlations between spacelike separated measurements on entangled quantum systems are stronger than any classical correlations and are at the heart of numerous quantum technologies. In practice, however, spacelike separation is often not…
Quantifying unknown quantum entanglement experimentally is a difficult task, but also becomes more and more necessary because of the fast development of quantum engineering. Machine learning provides practical solutions to this fundamental…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction…
Quantum computers have the potential to provide an advantage over classical computers in a number of areas. Numerous metrics to benchmark the performance of quantum computers, ranging from their individual hardware components to entire…
QMA (Quantum Merlin-Arthur) is the quantum analogue of the class NP. There are a few QMA-complete problems, most notably the ``Local Hamiltonian'' problem introduced by Kitaev. In this dissertation we show some new QMA-complete problems.…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition--------quantum coherence or quantum superposition. In this paper, we attempt to give an alternative…
I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic…
We begin by establishing structural results for several fundamental quantum complexity classes: p/mBQP, p/mQ(C)MA, $\text{p/mQSZK}_{\text{hv}}$, p/mQIP, p/mBQP/qpoly, p/mBQP/poly, and p/mPSPACE. This includes identifying complete problems,…
We define a general formulation of quantum PCPs, which captures adaptivity and multiple unentangled provers, and give a detailed construction of the quantum reduction to a local Hamiltonian with a constant promise gap. The reduction turns…
Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of…
Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
In the minimal scenario of quantum correlations, two parties can choose from two observables with two possible outcomes each. Probabilities are specified by four marginals and four correlations. The resulting four-dimensional convex body of…
The absolute/relative debate on the nature of space and time is ongoing for thousands of years. Here we attempt to investigate space and time from the information theoretic point of view to understand spatial and temporal correlations under…
This thesis offers novel strategies for the measurement of quantum correlations present in controllable quantum systems, as well as for a full-fledged implementation of the models of light-matter interaction through which these correlations…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…