54,316 research outputs found
Surface code implementation of block code state distillation
State distillation is the process of taking a number of imperfect copies of a
particular quantum state and producing fewer better copies. Until recently, the
lowest overhead method of distilling states |A>=(|0>+e^{i\pi/4}|1>)/\sqrt{2}
produced a single improved |A> state given 15 input copies. New block code
state distillation methods can produce k improved |A> states given 3k+8 input
copies, potentially significantly reducing the overhead associated with state
distillation. We construct an explicit surface code implementation of block
code state distillation and quantitatively compare the overhead of this
approach to the old. We find that, using the best available techniques, for
parameters of practical interest, block code state distillation does not always
lead to lower overhead, and, when it does, the overhead reduction is typically
less than a factor of three.Comment: 26 pages, 28 figure
Data Structures in Classical and Quantum Computing
This survey summarizes several results about quantum computing related to
(mostly static) data structures. First, we describe classical data structures
for the set membership and the predecessor search problems: Perfect Hash tables
for set membership by Fredman, Koml\'{o}s and Szemer\'{e}di and a data
structure by Beame and Fich for predecessor search. We also prove results about
their space complexity (how many bits are required) and time complexity (how
many bits have to be read to answer a query). After that, we turn our attention
to classical data structures with quantum access. In the quantum access model,
data is stored in classical bits, but they can be accessed in a quantum way: We
may read several bits in superposition for unit cost. We give proofs for lower
bounds in this setting that show that the classical data structures from the
first section are, in some sense, asymptotically optimal - even in the quantum
model. In fact, these proofs are simpler and give stronger results than
previous proofs for the classical model of computation. The lower bound for set
membership was proved by Radhakrishnan, Sen and Venkatesh and the result for
the predecessor problem by Sen and Venkatesh. Finally, we examine fully quantum
data structures. Instead of encoding the data in classical bits, we now encode
it in qubits. We allow any unitary operation or measurement in order to answer
queries. We describe one data structure by de Wolf for the set membership
problem and also a general framework using fully quantum data structures in
quantum walks by Jeffery, Kothari and Magniez
- …