6 research outputs found
Improving Data Locality in Applications using Message Passing
This thesis presents a systematic study of two modes of program execution: synchronous and asynchronous. In synchronous mode, program components are tightly coupled. Traditional procedure call represents the synchronous execution mode. In asynchronous mode, program components execute independently of each other. Asynchronous message passing represents the asynchronous execution mode. The asynchronous mode of execution introduces communication overhead in the execution of program components.
However it improves the temporal locality of data in a program by facilitating temporal and spatial reorganization of program components. Temporal reorganization refers to the batched execution of program components. Spatial reorganization refers to the scheduling of components on different processors in order to avoid the over-subscription of cache memory. Synchronous execution avoids the communication overhead. The goal of this
study is to systematically understand the trade-offs associated with each execution mode and the effect of each mode on the throughput and the resource utilization of applications. The findings of this study help derive application designs for achieving high throughput in current and future multicore hardware
Exponential Modalities and Complementarity (extended abstract)
The exponential modalities of linear logic have been used by various authors
to model infinite-dimensional quantum systems. This paper explains how these
modalities can also give rise to the complementarity principle of quantum
mechanics.
The paper uses a formulation of quantum systems based on dagger-linear logic,
whose categorical semantics lies in mixed unitary categories, and a formulation
of measurement therein. The main result exhibits a complementary system as the
result of measurements on free exponential modalities. Recalling that, in
linear logic, exponential modalities have two distinct but dual components, !
and ?, this shows how these components under measurement become "compacted"
into the usual notion of complementary Frobenius algebras from categorical
quantum mechanics.Comment: In Proceedings ACT 2021, arXiv:2211.01102. A full version of this
paper, containing all proofs, appears at arXiv:2103:0519
Extending Resource Monotones using Kan Extensions
In this paper we generalize the framework proposed by Gour and Tomamichel
regarding extensions of monotones for resource theories. A monotone for a
resource theory assigns a real number to each resource in the theory signifying
the utility or the value of the resource. Gour and Tomamichel studied the
problem of extending monotones using set-theoretical framework when a resource
theory embeds fully and faithfully into the larger theory. One can generalize
the problem of computing monotone extensions to scenarios when there exists a
functorial transformation of one resource theory to another instead of just a
full and faithful inclusion. In this article, we show that (point-wise) Kan
extensions provide a precise categorical framework to describe and compute such
extensions of monotones. To set up monontone extensions using Kan extensions,
we introduce partitioned categories (pCat) as a framework for resource theories
and pCat functors to formalize relationship between resource theories. We
describe monotones as pCat functors into , and describe
extending monotones along any pCat functor using Kan extensions. We show how
our framework works by applying it to extend entanglement monotones for
bipartite pure states to bipartite mixed states, to extend classical
divergences to the quantum setting, and to extend a non-uniformity monotone
from classical probabilistic theory to quantum theory.Comment: Accepted at Applied Category Theory 2022, 19 page
On the robustness of bucket brigade quantum RAM
We study the robustness of the bucket brigade quantum random access memory
model introduced by Giovannetti, Lloyd, and Maccone [Phys. Rev. Lett. 100,
160501 (2008)]. Due to a result of Regev and Schiff [ICALP '08 pp. 773], we
show that for a class of error models the error rate per gate in the bucket
brigade quantum memory has to be of order (where is the
size of the memory) whenever the memory is used as an oracle for the quantum
searching problem. We conjecture that this is the case for any realistic error
model that will be encountered in practice, and that for algorithms with
super-polynomially many oracle queries the error rate must be
super-polynomially small, which further motivates the need for quantum error
correction. By contrast, for algorithms such as matrix inversion [Phys. Rev.
Lett. 103, 150502 (2009)] or quantum machine learning [Phys. Rev. Lett. 113,
130503 (2014)] that only require a polynomial number of queries, the error rate
only needs to be polynomially small and quantum error correction may not be
required. We introduce a circuit model for the quantum bucket brigade
architecture and argue that quantum error correction for the circuit causes the
quantum bucket brigade architecture to lose its primary advantage of a small
number of "active" gates, since all components have to be actively error
corrected.Comment: Replaced with the published version. 13 pages, 9 figure
Dagger Linear Logic and Categorical Quantum Mechanics
This thesis develops the categorical proof theory for the non-compact multiplicative dagger linear logic, and investigates its applications to Categorical Quantum Mechanics
(CQM). The existing frameworks of CQM are categorical proof theories of compact dagger linear logic, and are motivated by the interpretation of quantum systems in the category of finite dimensional Hilbert spaces. This thesis describes a new non-compact framework called Mixed Unitary Categories which can accommodate infinite dimensional systems, and develops models for the framework. To this end, it builds on linearly distributive categories, and *-autonomous categories which are categorical proof theories of (non-compact) multiplicative linear logic. The proof theory of non-compact dagger linear logic is obtained from the basic setting of an LDC by adding a dagger functor satisfying appropriate coherences to give a dagger LDC. From every (isomix) dagger LDC one can extract a canonical "unitary core" which up to equivalence is the traditional CQM framework of dagger monoidal categories. This leads to the framework of Mixed Unitary Categories (MUCs): every MUC contains a (compact) unitary core which is extended by a (non-compact) isomix dagger LDC. Various models of MUCs based on Finiteness Spaces, Chu spaces, Hopf modules, etc., are developed in this thesis. This thesis also generalizes the key algebraic structures of CQM, such as observables, measurement, and complementarity, to MUC framework. Furthermore, using the MUC framework, this thesis establishes a connection between the complementary observables of quantum mechanics and the exponential modalities of linear logic