Related papers: Local Hamiltonians in Quantum Computation
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.…
A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply…
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…
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes…
A typical goal of a quantum simulation is to find the energy levels and eigenstates of a given Hamiltonian. This can be realized by adiabatically varying the system control parameters to steer an initial eigenstate into the eigenstate of…
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian,…
Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyse a particular class of qauntum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on…
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…
This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically,…
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
We delve into the use of photonic quantum computing to simulate quantum mechanics and extend its application towards quantum field theory. We develop and prove a method that leverages this form of Continuous-Variable Quantum Computing…
The success of adiabatic quantum computation (AQC) depends crucially on the ability to maintain the quantum computer in the ground state of the evolution Hamiltonian. The computation process has to be sufficiently slow as restricted by the…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…
Adiabatic quantum computation provides an alternative approach to quantum computation using a time-dependent Hamiltonian. The time evolution of entanglement during the adiabatic quantum search algorithm is studied, and its relevance as a…
We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time…
The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems which support Hamiltonian evolution, rather…
An explicit algorithm for the travelling salesman problem is constructed in the framework of adiabatic quantum computation, AQC. The initial Hamiltonian for the AQC process admits canonical coherent states as the ground state, and the…