Related papers: Quantum simulators, continuous-time automata, and …
While LDPC codes have been demonstrated with desirable error correcting properties, this has come at a cost of diverging from the geometrical constraints of many hardware platforms. Viewing codes as the groundspace of a Hamiltonian, we…
We present a general procedure for constructing lattices of qubits with a Hamiltonian composed of nearest-neighbour two-body interactions such that the ground state encodes a cluster state. We give specific details for lattices in one-,…
We study the computation power of lattices composed of two dimensional systems (qubits) on which translationally invariant global two-qubit gates can be performed. We show that if a specific set of 6 global two qubit gates can be performed,…
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…
Here we present a problem related to the local Hamiltonian problem (identifying whether the ground state energy falls within one of two ranges) which is restricted to being translationally invariant. We prove that for problems with a fixed…
A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY…
We present a simple quantum many-body system - a two-dimensional lattice of qubits with a Hamiltonian composed of nearest-neighbor two-body interactions - such that the ground state is a universal resource for quantum computation using…
While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum…
Current quantum devices execute specific tasks that are hard for classical computers and have the potential to solve problems such as quantum simulation of material science and chemistry, even without error correction. For practical…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state minimizes the energy of each local term…
We develop circuit implementations for digital-level quantum Hamiltonian dynamics simulation algorithms suitable for implementation on a reconfigurable quantum computer, such as trapped ions. Our focus is on the co-design of a problem, its…
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…
It is known that three fundamental questions regarding local Hamiltonians -- approximating the ground state energy (the Local Hamiltonian problem), simulating local measurements on the ground space (APX-SIM), and deciding if the low energy…
Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one…
Many computationally hard problems can be encoded in quantum Hamiltonians. The solution to these problems is given by the ground states of these Hamiltonians. A state-of-the-art algorithm for finding the ground state of a Hamiltonian is the…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
Despite progress in quantum Hamiltonian complexity, little is known about the computational complexity of quantum physics at the thermodynamic limit. Even defining the problem is not straight forward. We study the complexity of estimating…
Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on…