560 research outputs found
Session Communication and Integration
The scenario-based specification of a large distributed system is usually
naturally decomposed into various modules. The integration of specification
modules contrasts to the parallel composition of program components, and
includes various ways such as scenario concatenation, choice, and nesting. The
recent development of multiparty session types for process calculi provides
useful techniques to accommodate the protocol modularisation, by encoding
fragments of communication protocols in the usage of private channels for a
class of agents. In this paper, we extend forgoing session type theories by
enhancing the session integration mechanism. More specifically, we propose a
novel synchronous multiparty session type theory, in which sessions are
separated into the communicating and integrating levels. Communicating sessions
record the message-based communications between multiple agents, whilst
integrating sessions describe the integration of communicating ones. A
two-level session type system is developed for pi-calculus with syntactic
primitives for session establishment, and several key properties of the type
system are studied. Applying the theory to system description, we show that a
channel safety property and a session conformance property can be analysed.
Also, to improve the utility of the theory, a process slicing method is used to
help identify the violated sessions in the type checking.Comment: A short version of this paper is submitted for revie
Reasoning about Cardinal Directions between Extended Objects
Direction relations between extended spatial objects are important
commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model,
known as Cardinal Direction Calculus (CDC), for representing direction
relations between connected plane regions. CDC is perhaps the most expressive
qualitative calculus for directional information, and has attracted increasing
interest from areas such as artificial intelligence, geographical information
science, and image retrieval. Given a network of CDC constraints, the
consistency problem is deciding if the network is realizable by connected
regions in the real plane. This paper provides a cubic algorithm for checking
consistency of basic CDC constraint networks, and proves that reasoning with
CDC is in general an NP-Complete problem. For a consistent network of basic CDC
constraints, our algorithm also returns a 'canonical' solution in cubic time.
This cubic algorithm is also adapted to cope with cardinal directions between
possibly disconnected regions, in which case currently the best algorithm is of
time complexity O(n^5)
Optimal universal programmable detectors for unambiguous discrimination
We discuss the problem of designing unambiguous programmable discriminators
for any n unknown quantum states in an m-dimensional Hilbert space. The
discriminator is a fixed measurement that has two kinds of input registers: the
program registers and the data register. The quantum state in the data register
is what users want to identify, which is confirmed to be among the n states in
program registers. The task of the discriminator is to tell the users which
state stored in the program registers is equivalent to that in the data
register. First, we give a necessary and sufficient condition for judging an
unambiguous programmable discriminator. Then, if , we present an optimal
unambiguous programmable discriminator for them, in the sense of maximizing the
worst-case probability of success. Finally, we propose a universal unambiguous
programmable discriminator for arbitrary n quantum states.Comment: 7 page
Parallel Quantum Algorithm for Hamiltonian Simulation
We study how parallelism can speed up quantum simulation. A parallel quantum
algorithm is proposed for simulating the dynamics of a large class of
Hamiltonians with good sparse structures, called uniform-structured
Hamiltonians, including various Hamiltonians of practical interest like local
Hamiltonians and Pauli sums. Given the oracle access to the target sparse
Hamiltonian, in both query and gate complexity, the running time of our
parallel quantum simulation algorithm measured by the quantum circuit depth has
a doubly (poly-)logarithmic dependence
on the simulation precision . This presents an exponential
improvement over the dependence of
previous optimal sparse Hamiltonian simulation algorithm without parallelism.
To obtain this result, we introduce a novel notion of parallel quantum walk,
based on Childs' quantum walk. The target evolution unitary is approximated by
a truncated Taylor series, which is obtained by combining these quantum walks
in a parallel way. A lower bound is
established, showing that the -dependence of the gate depth achieved
in this work cannot be significantly improved.
Our algorithm is applied to simulating three physical models: the Heisenberg
model, the Sachdev-Ye-Kitaev model and a quantum chemistry model in second
quantization. By explicitly calculating the gate complexity for implementing
the oracles, we show that on all these models, the total gate depth of our
algorithm has a dependence in the
parallel setting.Comment: Minor revision. 55 pages, 6 figures, 1 tabl
Unambiguous discrimination of mixed quantum states
In this paper, we consider the problem of unambiguous discrimination between
a set of mixed quantum states. We first divide the density matrix of each mixed
state into two parts by the fact that it comes from ensemble of pure quantum
states. The first part will not contribute anything to the discrimination, the
second part has support space linearly independent to each other. Then the
problem we consider can be reduced to a problem in which the strategy of set
discrimination can be used in designing measurements to discriminate mixed
states unambiguously. We find a necessary and sufficient condition of
unambiguous mixed state discrimination, and also point out that searching the
optimal success probability of unambiguous discrimination is mathematically the
well-known semi-definite programming problem. A upper bound of the optimal
success probability is also presented. Finally, We generalize the concept of
set discrimination to mixed state and point out that the problem of
discriminating it unambiguously is equivalent to that of unambiguously
discriminating mixed states.Comment: 7 page
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