69 research outputs found
Transforming Comparison Model Lower Bounds to the PRAM
This note provides general transformations of lower bounds in Valiant'sparallel comparison decision tree model to lower bounds in the priorityconcurrent-read concurrent-write parallel-random-access-machine model.The proofs rely on standard Ramsey-theoretic arguments that simplifythe structure of the computation by restricting the input domain. Thetransformation of comparison model lower bounds, which are usually easierto obtain, to the parallel-random-access-machine, unifies some knownlower bounds and gives new lower bounds for several problems
Resource optimization for fault-tolerant quantum computing
In this thesis we examine a variety of techniques for reducing the resources
required for fault-tolerant quantum computation. First, we show how to simplify
universal encoded computation by using only transversal gates and standard
error correction procedures, circumventing existing no-go theorems. We then
show how to simplify ancilla preparation, reducing the cost of error correction
by more than a factor of four. Using this optimized ancilla preparation, we
develop improved techniques for proving rigorous lower bounds on the noise
threshold.
Additional overhead can be incurred because quantum algorithms must be
translated into sequences of gates that are actually available in the quantum
computer. In particular, arbitrary single-qubit rotations must be decomposed
into a discrete set of fault-tolerant gates. We find that by using a special
class of non-deterministic circuits, the cost of decomposition can be reduced
by as much as a factor of four over state-of-the-art techniques, which
typically use deterministic circuits.
Finally, we examine global optimization of fault-tolerant quantum circuits
under physical connectivity constraints. We adapt techniques from VLSI in order
to minimize time and space usage for computations in the surface code, and we
develop a software prototype to demonstrate the potential savings.Comment: 231 pages, Ph.D. thesis, University of Waterlo
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
International Congress of Mathematicians: 2022 July 6–14: Proceedings of the ICM 2022
Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022.
Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress.
The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library
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