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On the Theory of Quantum and Towards Practical Computation

Robert Kudelić

TL;DR

This article surveys the history and current state of quantum computation, tracing milestones from early quantum mechanics to modern hardware and algorithms. It defines foundational terminology, explains gate-based quantum circuits, and discusses how quantum parallelism and interference enable speedups, while addressing decoherence and error correction. A design-pattern lens is applied through Bernstein–Vazirani to illustrate phase-kickback and oracle-based strategies, alongside practical discussions of universal vs non-universal implementations and variational approaches. The work also surveys challenges, computational complexity relationships such as $BQP$ vs $NP$ and the prospects for scalable quantum devices and post-quantum cryptography, concluding with an open outlook for the next decade.

Abstract

Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current outlook on quantum computation that is geared toward computer experts but also to experts from other disciplines as well. It is an article that will bridge the vast gap between classical and quantum computation and open an entering wedge through which one will be able to both bring himself up to speed on quantum computation and, intrinsically, in a straightforward manner, become acquainted with it. We are indeed in luck to be living in an age where computing is being reinvented, and not only seeing history in the making firsthand but, in fact, having the opportunity to be the ones who are reinventing--and that is quite a thought.

On the Theory of Quantum and Towards Practical Computation

TL;DR

This article surveys the history and current state of quantum computation, tracing milestones from early quantum mechanics to modern hardware and algorithms. It defines foundational terminology, explains gate-based quantum circuits, and discusses how quantum parallelism and interference enable speedups, while addressing decoherence and error correction. A design-pattern lens is applied through Bernstein–Vazirani to illustrate phase-kickback and oracle-based strategies, alongside practical discussions of universal vs non-universal implementations and variational approaches. The work also surveys challenges, computational complexity relationships such as vs and the prospects for scalable quantum devices and post-quantum cryptography, concluding with an open outlook for the next decade.

Abstract

Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current outlook on quantum computation that is geared toward computer experts but also to experts from other disciplines as well. It is an article that will bridge the vast gap between classical and quantum computation and open an entering wedge through which one will be able to both bring himself up to speed on quantum computation and, intrinsically, in a straightforward manner, become acquainted with it. We are indeed in luck to be living in an age where computing is being reinvented, and not only seeing history in the making firsthand but, in fact, having the opportunity to be the ones who are reinventing--and that is quite a thought.
Paper Structure (9 sections, 13 equations, 12 figures)

This paper contains 9 sections, 13 equations, 12 figures.

Table of Contents

  1. For Once It All Began
  2. Quantumness of Quantum Computing
  3. Foundational Terminology
  4. Quantum Effects and the Universe we Live in
  5. Computation with Quantum Gates
  6. Bernstein–Vazirani Algorithm Design Pattern
  7. Questions that Puzzle the Mind
  8. Moving Forward
  9. Few Last Words

Figures (12)

  • Figure 1: Quantum Computing Timeline: 1900-1979.
  • Figure 2: Quantum Computing Timeline: 1980-2000.
  • Figure 3: Quantum Computing Timeline: 2001-2015.
  • Figure 4: Quantum Computing Timeline: 2016-2023.
  • Figure 5: Illustrative example of a quantum phenomenon known as superposition. Under, for example, a measurement, superposition would collapse, and one would observe either a white or a black state, or a white or black ball in this instance.
  • ...and 7 more figures