66 research outputs found
Quantum Walks, Quantum Gates and Quantum Computers
The physics of quantum walks on graphs is formulated in Hamiltonian language,
both for simple quantum walks and for composite walks, where extra discrete
degrees of freedom live at each node of the graph. It is shown how to map
between quantum walk Hamiltonians and Hamiltonians for qubit systems and
quantum circuits; this is done for both a single- and multi-excitation coding,
and for more general mappings. Specific examples of spin chains, as well as
static and dynamic systems of qubits, are mapped to quantum walks, and walks on
hyperlattices and hypercubes are mapped to various gate systems. We also show
how to map a quantum circuit performing the quantum Fourier transform, the key
element of Shor's algorithm, to a quantum walk system doing the same. The
results herein are an essential preliminary to a Hamiltonian formulation of
quantum walks in which coupling to a dynamic quantum environment is included.Comment: 17 pages, 10 figure
Exact Entanglement Dynamics of Two Spins in Finite Baths
We consider the buildup and decay of two-spin entanglement through phase
interactions in a finite environment of surrounding spins, as realized in
quantum computing platforms based on arrays of atoms, molecules, or nitrogen
vacancy centers. The non-Markovian dephasing caused by the spin environment
through Ising-type phase interactions can be solved exactly and compared to an
effective Markovian treatment based on collision models. In a first case study
on a dynamic lattice of randomly hopping spins, we find that non-Markovianity
boosts the dephasing rate caused by nearest neighbour interactions with the
surroundings, degrading the maximum achievable entanglement. However, we also
demonstrate that additional three-body interactions can mitigate this
degradation, and that randomly timed reset operations performed on the two-spin
system can help sustain a finite average amount of steady-state entanglement.
In a second case study based on a model nuclear magnetic resonance system, we
elucidate the role of bath correlations at finite temperature on non-Markovian
dephasing. They speed up the dephasing at low temperatures while slowing it
down at high temperatures, compared to an uncorrelated bath, which is related
to the number of thermally accessible spin configurations with and without
interactions.Comment: 11 pages, 8 figure
Quantum walks and quantum search on graphene lattices
This thesis details research I have carried out in the field of quantum walks, which are the quantum analogue of classical random walks. Quantum walks have been shown to offer a significant speed-up compared to classical random walks for certain tasks and for this reason there has been considerable interest in their use in algorithmic settings, as well as in experimental demonstrations of such phenomena.
One of the most interesting developments in quantum walk research is their application to spatial searches, where one searches for a particular site of some network or lattice structure. There has been much work done on the creation of discrete- and continuous-time quantum walk search algorithms on various lattice types. However, it has remained an issue that continuous-time searches on two-dimensional lattices have required the inclusion of additional memory in order to be effective, memory which takes the form of extra internal degrees of freedom for the walker.
In this work, we describe how the need for extra degrees of freedom can be negated by utilising a graphene lattice, demonstrating that a continuous-time quantum search in the experimentally relevant regime of two-dimensions is possible. This is achieved through alternative methods of marking a particular site to previous searches, creating a quantum search protocol at the Dirac point in graphene.
We demonstrate that this search mechanism can also be adapted to allow state transfer across the lattice. These two processes offer new methods for channelling information across lattices between specific sites and supports the possibility of graphene devices which operate at a single-atom level. Recent experiments on microwave analogues of graphene that adapt these ideas, which we will detail, demonstrate the feasibility of realising the quantum search and transfer mechanisms on graphene
Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator
We study a 2-D disordered time-discrete quantum walk based on 1-D
`generalized elephant quantum walk' where an entangling coin operator is
assumed and which paves the way to a new set of properties. We show that
considering a given disorder in one direction, it is possible to control the
degree of spreading and entanglement in the other direction. This observation
helps assert that the random quantum walks of this ilk serve as a controllable
decoherence channel with the degree of randomness being the tunable parameter
and highlight the role of dimensionality in quantum systems regarding
information and transport.Comment: 16 pages, 19 figure
Quantum walks and quantum search on graphene lattices
This thesis details research I have carried out in the field of quantum walks, which are the quantum analogue of classical random walks. Quantum walks have been shown to offer a significant speed-up compared to classical random walks for certain tasks and for this reason there has been considerable interest in their use in algorithmic settings, as well as in experimental demonstrations of such phenomena.
One of the most interesting developments in quantum walk research is their application to spatial searches, where one searches for a particular site of some network or lattice structure. There has been much work done on the creation of discrete- and continuous-time quantum walk search algorithms on various lattice types. However, it has remained an issue that continuous-time searches on two-dimensional lattices have required the inclusion of additional memory in order to be effective, memory which takes the form of extra internal degrees of freedom for the walker.
In this work, we describe how the need for extra degrees of freedom can be negated by utilising a graphene lattice, demonstrating that a continuous-time quantum search in the experimentally relevant regime of two-dimensions is possible. This is achieved through alternative methods of marking a particular site to previous searches, creating a quantum search protocol at the Dirac point in graphene.
We demonstrate that this search mechanism can also be adapted to allow state transfer across the lattice. These two processes offer new methods for channelling information across lattices between specific sites and supports the possibility of graphene devices which operate at a single-atom level. Recent experiments on microwave analogues of graphene that adapt these ideas, which we will detail, demonstrate the feasibility of realising the quantum search and transfer mechanisms on graphene
Developing Quantum Algorithms for NISQ Hardware
When designing quantum algorithms, we typically abstract away the full capabilities
of the underlying hardware. For near-term applications of quantum hardware, it is
not clear that this is justified. In this thesis, I develop techniques to exploit the greater
underlying control over qubit interactions available in principle in most quantum
hardware. I derive analytic circuit identities for efficiently synthesising multi-qubit
evolutions from two-qubit interactions. I apply these techniques to Hamiltonian
simulation and quantum phase estimation, two of the most important algorithms
within the field of quantum computing. I analyse these techniques under a standard
error model where errors occur per gate, and an error model with a constant error
rate per unit time. For both Hamiltonian simulation and quantum phase estimation I
explore a concrete numerical example: the 2D spin Fermi-Hubbard model
Many Body Quantum Chaos
This editorial remembers Shmuel Fishman, one of the founding fathers of the research field "quantum chaos", and puts into context his contributions to the scientific community with respect to the twelve papers that form the special issue
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