4 research outputs found
Continuous-time quantum computing
Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware.
Continuous-time quantum computing (CTQC) encompasses continuous-time quantum walk computing (QW), adiabatic quantum computing (AQC), and quantum annealing (QA), as well as other strategies which contain elements of these three.
While much of current quantum computing research focuses on the discrete-time gate model, which has an appealing similarity to the discrete logic of classical computation, the continuous nature of quantum information suggests that continuous-time quantum information processing is worth exploring.
A versatile context for CTQC is the transverse Ising model, and this thesis will explore the application of Ising model CTQC to classical optimization problems.
Classical optimization problems have industrial and scientific significance, including in logistics, scheduling, medicine, cryptography, hydrology and many other areas.
Along with the fact that such problems often have straightforward, natural mappings onto the interactions of readily-available Ising model hardware makes classical optimization a fruitful target for CTQC algorithms.
After introducing and explaining the CTQC framework in detail, in this thesis I will, through a combination of numerical, analytical, and experimental work, examine the performance of various forms of CTQC on a number of different optimization problems, and investigate the underlying physical mechanisms by which they operate.Open Acces
On streaming approximation algorithms for constraint satisfaction problems
In this thesis, we explore streaming algorithms for approximating constraint
satisfaction problems (CSPs). The setup is roughly the following: A computer
has limited memory space, sees a long "stream" of local constraints on a set of
variables, and tries to estimate how many of the constraints may be
simultaneously satisfied. The past ten years have seen a number of works in
this area, and this thesis includes both expository material and novel
contributions. Throughout, we emphasize connections to the broader theories of
CSPs, approximability, and streaming models, and highlight interesting open
problems.
The first part of our thesis is expository: We present aspects of previous
works that completely characterize the approximability of specific CSPs like
Max-Cut and Max-Dicut with -space streaming algorithm (on
-variable instances), while characterizing the approximability of all CSPs
in space in the special case of "composable" (i.e., sketching)
algorithms, and of a particular subclass of CSPs with linear-space streaming
algorithms.
In the second part of the thesis, we present two of our own joint works. We
begin with a work with Madhu Sudan and Santhoshini Velusamy in which we prove
linear-space streaming approximation-resistance for all ordering CSPs (OCSPs),
which are "CSP-like" problems maximizing over sets of permutations. Next, we
present joint work with Joanna Boyland, Michael Hwang, Tarun Prasad, and
Santhoshini Velusamy in which we investigate the -space streaming
approximability of symmetric Boolean CSPs with negations. We give explicit
-space sketching approximability ratios for several families of CSPs,
including Max-AND; develop simpler optimal sketching approximation
algorithms for threshold predicates; and show that previous lower bounds fail
to characterize the -space streaming approximability of Max-AND.Comment: Harvard College senior thesis; 119 pages plus references; abstract
shortened for arXiv; formatted with Dissertate template (feel free to copy!);
exposits papers arXiv:2105.01782 (APPROX 2021) and arXiv:2112.06319 (APPROX
2022