



@article {1221,
	title = {Universal computation by multi-particle quantum walk},
	journal = {Science},
	volume = {339},
	year = {2013},
	month = {2013/02/14},
	pages = {791 - 794},
	abstract = {  A quantum walk is a time-homogeneous quantum-mechanical process on a graph
defined by analogy to classical random walk. The quantum walker is a particle
that moves from a given vertex to adjacent vertices in quantum superposition.
Here we consider a generalization of quantum walk to systems with more than one
walker. A continuous-time multi-particle quantum walk is generated by a
time-independent Hamiltonian with a term corresponding to a single-particle
quantum walk for each particle, along with an interaction term. Multi-particle
quantum walk includes a broad class of interacting many-body systems such as
the Bose-Hubbard model and systems of fermions or distinguishable particles
with nearest-neighbor interactions. We show that multi-particle quantum walk is
capable of universal quantum computation. Since it is also possible to
efficiently simulate a multi-particle quantum walk of the type we consider
using a universal quantum computer, this model exactly captures the power of
quantum computation. In principle our construction could be used as an
architecture for building a scalable quantum computer with no need for
time-dependent control.
},
	doi = {10.1126/science.1229957},
	url = {http://arxiv.org/abs/1205.3782v2},
	author = {Andrew M. Childs and David Gosset and Zak Webb}
}
@article {1205,
	title = {Universal computation by quantum walk},
	journal = {Physical Review Letters},
	volume = {102},
	year = {2009},
	month = {2009/5/4},
	abstract = {  In some of the earliest work on quantum mechanical computers, Feynman showed
how to implement universal quantum computation by the dynamics of a
time-independent Hamiltonian. I show that this remains possible even if the
Hamiltonian is restricted to be a sparse matrix with all entries equal to 0 or
1, i.e., the adjacency matrix of a low-degree graph. Thus quantum walk can be
regarded as a universal computational primitive, with any desired quantum
computation encoded entirely in some underlying graph. The main idea of the
construction is to implement quantum gates by scattering processes.
},
	doi = {10.1103/PhysRevLett.102.180501},
	url = {http://arxiv.org/abs/0806.1972v1},
	author = {Andrew M. Childs}
}
@article {1251,
	title = {Unified derivations of measurement-based schemes for quantum computation},
	journal = {Physical Review A},
	volume = {71},
	year = {2005},
	month = {2005/3/17},
	abstract = {  We present unified, systematic derivations of schemes in the two known
measurement-based models of quantum computation. The first model (introduced by
Raussendorf and Briegel [Phys. Rev. Lett., 86, 5188 (2001)]) uses a fixed
entangled state, adaptive measurements on single qubits, and feedforward of the
measurement results. The second model (proposed by Nielsen [Phys. Lett. A, 308,
96 (2003)] and further simplified by Leung [Int. J. Quant. Inf., 2, 33 (2004)])
uses adaptive two-qubit measurements that can be applied to arbitrary pairs of
qubits, and feedforward of the measurement results. The underlying principle of
our derivations is a variant of teleportation introduced by Zhou, Leung, and
Chuang [Phys. Rev. A, 62, 052316 (2000)]. Our derivations unify these two
measurement-based models of quantum computation and provide significantly
simpler schemes.
},
	doi = {10.1103/PhysRevA.71.032318},
	url = {http://arxiv.org/abs/quant-ph/0404132v2},
	author = {Andrew M. Childs and Debbie W. Leung and Michael A. Nielsen}
}
@article {1261,
	title = {Universal simulation of Hamiltonian dynamics for qudits},
	journal = {Physical Review A},
	volume = {66},
	year = {2002},
	month = {2002/8/30},
	abstract = {  What interactions are sufficient to simulate arbitrary quantum dynamics in a
composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial
solution to this problem in the form of an efficient algorithm to simulate any
desired two-body Hamiltonian evolution using any fixed two-body entangling
N-qubit Hamiltonian, and local unitaries. We extend this result to the case
where the component systems have D dimensions. As a consequence we explain how
universal quantum computation can be performed with any fixed two-body
entangling N-qudit Hamiltonian, and local unitaries.
},
	doi = {10.1103/PhysRevA.66.022317},
	url = {http://arxiv.org/abs/quant-ph/0109064v2},
	author = {Michael A. Nielsen and Michael J. Bremner and Jennifer L. Dodd and Andrew M. Childs and Christopher M. Dawson}
}
@article {1260,
	title = {Universal simulation of Markovian quantum dynamics},
	journal = {Physical Review A},
	volume = {64},
	year = {2001},
	month = {2001/11/9},
	abstract = {  Although the conditions for performing arbitrary unitary operations to
simulate the dynamics of a closed quantum system are well understood, the same
is not true of the more general class of quantum operations (also known as
superoperators) corresponding to the dynamics of open quantum systems. We
propose a framework for the generation of Markovian quantum dynamics and study
the resources needed for universality. For the case of a single qubit, we show
that a single nonunitary process is necessary and sufficient to generate all
unital Markovian quantum dynamics, whereas a set of processes parametrized by
one continuous parameter is needed in general. We also obtain preliminary
results for the unital case in higher dimensions.
},
	doi = {10.1103/PhysRevA.64.062302},
	url = {http://arxiv.org/abs/quant-ph/0008070v2},
	author = {Dave Bacon and Andrew M. Childs and Isaac L. Chuang and Julia Kempe and Debbie W. Leung and Xinlan Zhou}
}
@article {1207,
	title = {Universal quantum computation with two-level trapped ions},
	journal = {Physical Review A},
	volume = {63},
	year = {2000},
	month = {2000/12/11},
	abstract = {  Although the initial proposal for ion trap quantum computation made use of an
auxiliary internal level to perform logic between ions, this resource is not
necessary in principle. Instead, one may perform such operations directly using
sideband laser pulses, operating with an arbitrary (sufficiently small)
Lamb-Dicke parameter. We explore the potential of this technique, showing how
to perform logical operations between the internal state of an ion and the
collective motional state and giving explicit constructions for a
controlled-not gate between ions.
},
	doi = {10.1103/PhysRevA.63.012306},
	url = {http://arxiv.org/abs/quant-ph/0008065v1},
	author = {Andrew M. Childs and Isaac L. Chuang}
}
