Vol.16 No.3&4, March
1, 2016
Research Articles:
Information cost of quantum
communication protocols
(pp01810196)
Iordanis
Kerenidis, Mathieu Lauriere, Francois Le Gall, Mathys Rennela
In twoparty quantum communication complexity, Alice and Bob receive
some classical inputs and wish to compute some function that depends on
both these inputs, while minimizing the communication. This model
has found numerous applications in many areas of computer science. One
notion that has received a lot of attention recently is the information
cost of the protocol, namely how much information the players reveal
about their inputs when they run the protocol. In the quantum world, it
is not straightforward to define a notion of quantum information cost.
We study two different notions and analyze their relation. We also
provide new quantum protocols for the Inner Product function and for
Private Information Retrieval, and show that protocols for Private
Information Retrieval whose classical or quantum information cost for
the user is zero can have exponentially different information cost for
the server.
Quantum algorithms and circuits
for scientific computing
(pp01970236)
Mihir
K. Bhaskar, Stuart Hadfield, Anargyros Papageorgiou, and Iasonas Petras
Quantum algorithms for scientific computing require modules
implementing fundamental functions, such as the square root, the
logarithm, and others. We require algorithms that have a wellcontrolled
numerical error, that are uniformly scalable and reversible (unitary),
and that can be implemented efficiently. We present quantum algorithms
and circuits for computing the square root, the natural logarithm, and
arbitrary fractional powers. We provide performance guarantees in terms
of their worstcase accuracy and cost. We further illustrate their
performance by providing tests comparing them to the respective floating
point implementations found in widely used numerical software.
On the relation between a graph
code and a graph state
(pp02370250)
Yongsoo
Hwang and Jun Heo
A graph state and a graph code respectively are defined based on a
mathematical simple graph. In this work, we examine a relation between a
graph state and a graph code both obtained from the same graph, and show
that a graph state is a superposition of logical qubits of the related
graph code. By using the relation, we first discuss that a local
complementation which has been used for a graph state can be useful for
searching locally equivalent stabilizer codes, and second provide a
method to find a stabilizer group of a graph code.
Commuting quantum circuits with
few outputs are unlikely to be classically simulatable
(pp02510270)
Yasuhiro
Takahashi, Seiichiro Tani, Takeshi Yamazaki, and Kazuyuki Tanaka
We study the classical simulatability of commuting quantum circuits
with $n$ input qubits and $O(\log n)$ output qubits, where a quantum
circuit is classically simulatable if its output probability
distribution can be sampled up to an exponentially small additive error
in classical polynomial time. Our main result is that there exists a
commuting quantum circuit that is not classically simulatable unless the
polynomial hierarchy collapses to the third level. This is the first
formal evidence that a commuting quantum circuit is not classically
simulatable even when the number of output qubits is $O(\log n)$. Then,
we consider a generalized version of the circuit and clarify the
condition under which it is classically simulatable. Lastly, using a
proof similar to that of the main result, we provide an evidence that a
slightly extended Clifford circuit is not classically simulatable.
Dense quantum communication
using single and twoparticle operations on sixparticle cluster state
(pp02710290)
Parminder
S. Bhatia
Theory of controlled tripartite quantum
dense coding for the transmission of fourbinary bits between two
distinct locations is presented. The entanglement resource for this
transmission is provided by a sixqubit cluster state. Theoretical
detail of an encoder that can encode sixteen different operations and a
fourbit binary decoder required for this transmission is discussed. We
show that in the absence of availability of any fourstate analyzer
decoding can be reduced to singleparticle and twoparticle Bellstate
measurements (). In our
scheme, Bellstate measurements ()
performed during decoding, result in Bellpairs, which along with
singleparticle projections are used to unambiguously discriminate all
sixteen encoding operations. Proposed experiment to verify theory of
tripartite quantum dense coding scheme, using photonic entanglement, is
also briefly discussed. Success probability of the scheme is determined.
In addition, longdistance implementation of this tripartite quantum
dense coding scheme is discussed. Faulttolerant quantum repeaters used
in this longdistance scheme are based on quantum errorcorrection,
which is achieved with the aid of CalderbankShorSteane ()
encoding.
Universality of beamsplitters
(pp02910312)
Adam
Sawicki
We consider the problem of building an arbitrary $N\times N$ real
orthogonal operator using a finite set, $S$, of elementary quantum
optics gates operating on $m\leq N$ modes  the problem of universality
of $S$ on $N$ modes. In particular, we focus on the universality problem
of an $m$mode beamsplitter. Using methods of control theory and some
properties of rotations in three dimensions, we prove that any
nontrivial real 2mode and `almost' any nontrivial real $3$mode
beamsplitter is universal on $m\geq3$ modes.
Renyi and Tsallis formulations
of noisedisturbance tradeoff relations
(pp03130331)
Alexey
E. Rastegin
We address an informationtheoretic approach to noise and
disturbance in quantum measurements. Properties of corresponding
probability distributions are characterized by means of both the R\'{e}nyi
and
Tsallis entropies. Related informationtheoretic measures of noise and
disturbance are introduced. These definitions are based on the concept
of conditional entropy. To motivate introduced measures, some important
properties of the conditional R\'{e}nyi and Tsallis entropies are
discussed. There exist several formulations of entropic uncertainty
relations for a pair of observables. Tradeoff relations for noise and
disturbance are derived on the base of known formulations of such a
kind.
Squash 2: a hierarchical
scalable quantum mapper considering ancilla sharing
(pp03320356)
Mohammad
J. Dousti, Alireza Shafaei, and Massoud Pedram
We present a multicore reconfigurable quantum processor
architecture, called Requp, which supports a hierarchical
approach to mapping a quantum algorithm while sharing physical and
logical ancilla qubits. Each core is capable of performing any quantum
instruction. Moreover, we introduce a scalable quantum mapper, called
\textit{Squash~2}, which divides a given quantum circuit into a number
of quantum moduleseach module is divided into k parts such
that each part will run on one of k available cores. Experimental
results demonstrate that Squash~2 can handle largescale quantum
algorithms while providing an effective mechanism for sharing ancilla
qubits.
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