DISSERTATION DEFENSE

Author : Rabins Wosti
Advisor: Dr. Stephen Fenner
Date: Oct 17th, 2025
Time: 3:00 pm
Place: Room 2265 Innovation Building

Abstract

The accurate computation of advanced quantum algorithms like Shor’s integer factorization, quantum phase estimation (QPE), and the quantum Fourier transform (QFT) requires quantum circuits of considerable size and depth. It is difficult to achieve reliable computation with deep quantum circuits due to the limited coherence times of the current noisy quantum devices. The quantum fanout gate is known to be a powerful primitive for reducing the depth of many quantum circuits (Høyer and Špalek 2003; Gottesman and Isaac L. Chuang 1999). Shallow or constant-depth quantum circuits are desirable for both near-term and fault-tolerant quantum computations as they reduce noise and allow faster execution of quantum algorithms, potentially skirting the effects of short coherence times. In this work, we show new approaches towards implementation of quantum fanout gate. In particular, we show that by analogously time-evolving the quantum systems according to two well-studied Hamiltonians, namely quantum Ising and quantum Heisenberg models, we can implement quantum fanout operator using constant additional layers of digital quantum gates.

Important foundations to the area of quantum encoding were provided by Schumacher who proved the quantum analog of Shannon’s noiseless coding theorem for an independent and identically distributed (i.i.d.) quantum source, (Schumacher 1995). In this work, we show a lossless, variable-length block encoding scheme of quantum information emitted from a completely general stochastic quantum source, and it is encoded into the Fock space. While doing so, we extend the notion of uniquely de- codable (or completely lossless) quantum codes to be used for quantum block data compression. As our main result, for a fixed ml many pure states emitted by a given quantum stochastic source, we derive the optimal lower bound of the average codeword length over a subset of uniquely decodable quantum codes called “special block codes”, which are applied to encode the pure states of m many blocks each of block size l. Additionally, we show that for quantum stationary sources in particular, the optimal lower bound of the average codeword length per symbol computed over a subset of special block codes called “constrained special block codes” equals the von-Neumann entropy rate of the source for an asymptotically long block size.