Related papers: A Dequantized Algorithm for the Guided Local Hamil…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number 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…
The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution…
A broad range of quantum optimisation problems can be phrased as the question whether a specific system has a ground state at zero energy, i.e.\ whether its Hamiltonian is frustration free. Frustration-free Hamiltonians, in turn, play a…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…
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…
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…
The Quantum Lov\'asz Local Lemma (QLLL) [AKS12] establishes non-constructively that any quantum system constrained by a local Hamiltonian has a zero-energy ground state, if the local Hamiltonian terms overlap only in a certain restricted…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…
With physical quantum computers becoming increasingly accessible, research on their applications across various fields has advanced rapidly. In this paper, we present the first study of quantum cosmology conducted on physical quantum…
Combinatorial optimization is a challenging problem applicable in a wide range of fields from logistics to finance. Recently, quantum computing has been used to attempt to solve these problems using a range of algorithms, including…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
The QMA-completeness of the local Hamiltonian problem is a landmark result of the field of Hamiltonian complexity that studies the computational complexity of problems in quantum many-body physics. Since its proposal, substantial effort has…
Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core…
Combinatorial optimization problems that arise in science and industry typically have constraints. Yet the presence of constraints makes them challenging to tackle using both classical and quantum optimization algorithms. We propose a new…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…