



@article {1206,
	title = {On the relationship between continuous- and discrete-time quantum walk},
	journal = {Communications in Mathematical Physics},
	volume = {294},
	year = {2010},
	month = {2009/10/10},
	pages = {581 - 603},
	abstract = {  Quantum walk is one of the main tools for quantum algorithms. Defined by
analogy to classical random walk, a quantum walk is a time-homogeneous quantum
process on a graph. Both random and quantum walks can be defined either in
continuous or discrete time. But whereas a continuous-time random walk can be
obtained as the limit of a sequence of discrete-time random walks, the two
types of quantum walk appear fundamentally different, owing to the need for
extra degrees of freedom in the discrete-time case.
  In this article, I describe a precise correspondence between continuous- and
discrete-time quantum walks on arbitrary graphs. Using this correspondence, I
show that continuous-time quantum walk can be obtained as an appropriate limit
of discrete-time quantum walks. The correspondence also leads to a new
technique for simulating Hamiltonian dynamics, giving efficient simulations
even in cases where the Hamiltonian is not sparse. The complexity of the
simulation is linear in the total evolution time, an improvement over
simulations based on high-order approximations of the Lie product formula. As
applications, I describe a continuous-time quantum walk algorithm for element
distinctness and show how to optimally simulate continuous-time query
algorithms of a certain form in the conventional quantum query model. Finally,
I discuss limitations of the method for simulating Hamiltonians with negative
matrix elements, and present two problems that motivate attempting to
circumvent these limitations.
},
	doi = {10.1007/s00220-009-0930-1},
	url = {http://arxiv.org/abs/0810.0312v3},
	author = {Andrew M. Childs}
}
@article {1238,
	title = {Reversible simulation of bipartite product Hamiltonians},
	journal = {IEEE Transactions on Information Theory},
	volume = {50},
	year = {2004},
	month = {2004/06/01},
	pages = {1189 - 1197},
	abstract = {  Consider two quantum systems A and B interacting according to a product
Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used
to simulate each other reversibly (i.e., without efficiency losses) with the
help of local unitary operations and local ancillas. Accordingly, all non-local
features of a product Hamiltonian -- including the rate at which it can be used
to produce entanglement, transmit classical or quantum information, or simulate
other Hamiltonians -- depend only upon a single parameter. We identify this
parameter and use it to obtain an explicit expression for the entanglement
capacity of all product Hamiltonians. Finally, we show how the notion of
simulation leads to a natural formulation of measures of the strength of a
nonlocal Hamiltonian.
},
	doi = {10.1109/TIT.2004.828069},
	url = {http://arxiv.org/abs/quant-ph/0303097v1},
	author = {Andrew M. Childs and Debbie W. Leung and Guifre Vidal}
}
@article {1249,
	title = {Realization of quantum process tomography in NMR},
	journal = {Physical Review A},
	volume = {64},
	year = {2001},
	month = {2001/6/13},
	abstract = {  Quantum process tomography is a procedure by which the unknown dynamical
evolution of an open quantum system can be fully experimentally characterized.
We demonstrate explicitly how this procedure can be implemented with a nuclear
magnetic resonance quantum computer. This allows us to measure the fidelity of
a controlled-not logic gate and to experimentally investigate the error model
for our computer. Based on the latter analysis, we test an important assumption
underlying nearly all models of quantum error correction, the independence of
errors on different qubits.
},
	doi = {10.1103/PhysRevA.64.012314},
	url = {http://arxiv.org/abs/quant-ph/0012032v1},
	author = {Andrew M. Childs and Isaac L. Chuang and Debbie W. Leung}
}
@article {1209,
	title = {Robustness of adiabatic quantum computation},
	journal = {Physical Review A},
	volume = {65},
	year = {2001},
	month = {2001/12/14},
	abstract = {  We study the fault tolerance of quantum computation by adiabatic evolution, a
quantum algorithm for solving various combinatorial search problems. We
describe an inherent robustness of adiabatic computation against two kinds of
errors, unitary control errors and decoherence, and we study this robustness
using numerical simulations of the algorithm.
},
	doi = {10.1103/PhysRevA.65.012322},
	url = {http://arxiv.org/abs/quant-ph/0108048v1},
	author = {Andrew M. Childs and Edward Farhi and John Preskill}
}
