Date of Award
Fall 2025
Document Type
Open Access Dissertation
Department
Computer Science and Engineering
First Advisor
Stephen Fenner
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 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 analogue time-evolving the quantum systems according to two well-studied Hamiltonians, namely, quantum Ising and quantum Heisenberg models, we can implement the quantum fanout operator using constantly many 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 decodable (or completely lossless) quantum codes to be used for quantum block data compression. As our main result, for a fixed mlmany 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.
Rights
© 2025, Rabins Wosti
Recommended Citation
Wosti, R.(2025). New Approaches on Source Coding for Quantum Stochastic Sources and Implementation of Quantum Fanout Gate. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/8680