[Paper Review] Quantum computing

Jens Eisert, Michael M. Wolf|arXiv (Cornell University)|Jan 5, 2004

Quantum Computing Algorithms and Architecture13 citations

TL;DR

This paper introduces quantum computing as a paradigm that leverages quantum mechanics, particularly superposition, to process information in ways classical computers cannot. By using qubits that exist in superpositions of 0 and 1, quantum computers can perform certain computations exponentially faster than classical systems, marking a fundamental shift in information processing grounded in quantum theory.

ABSTRACT

Quantum mechanics is one of the cornerstones of modern physics. It governs the behavior and the properties of matter in a fundamental way, in particular on the microscopic scale of atoms and molecules. Hence, what we may call a classical computer, i.e., those machines on or under the desktops in our offices together with all their potential descendants, are themselves following the rules of quantum mechanics. However, they are no quantum computers in the sense that all the inside information processing can perfectly be described within classical information theory. In fact, we do not need quantum mechanics in order to explain how the zeros and ones – the bits – inside a classical computer evolve. The reason for this is that the architecture of classical computers does not make use of one of the most fundamental features of quantum mechanics, namely the possibility of superpositions. Throughout the entire processing of any program on a classical computer, each of the involved bits takes on either the value zero or one. Quantum mechanics, however, would in addition allow superpositions of zeros one ones, that is bits – now called qubits (quantum-bits) – which are somehow in the state zero and one at the

Motivation & Objective

• To clarify the distinction between classical computers and quantum computers in terms of information processing principles.
• To explain why classical computers, despite obeying quantum laws, do not utilize quantum features like superposition.
• To introduce the concept of qubits as the fundamental unit of quantum information, capable of existing in superpositions of 0 and 1.
• To establish the theoretical basis for quantum computing as a new computational paradigm beyond classical information theory.

Proposed method

• Defining classical bits as systems that are strictly in state 0 or 1, with evolution describable by classical information theory.
• Introducing qubits as quantum systems that can exist in superpositions of |0⟩ and |1⟩, representing a fundamental departure from classical bits.
• Highlighting that quantum mechanics allows for coherent superpositions, which classical systems do not exploit in their operation.
• Using the principle of superposition as the core mechanism enabling quantum parallelism and exponential state space representation.
• Contrasting classical computation, where bits are always in definite states, with quantum computation, where qubits can be in superpositions during processing.
• Establishing that the key difference lies in architectural use of quantum coherence and superposition, not in the underlying physical laws.

Experimental results

Research questions

• RQ1 What distinguishes a classical computer from a quantum computer in terms of information processing?
• RQ2 Why can classical computers be fully described by classical information theory despite obeying quantum mechanics?
• RQ3 How does the principle of superposition enable new computational capabilities in quantum systems?
• RQ4 What role does the qubit play in enabling quantum computation beyond classical limits?
• RQ5 In what way does quantum mechanics fundamentally alter the architecture and function of information processing systems?

Key findings

• Classical computers, while governed by quantum mechanics, do not utilize superposition and thus remain within the framework of classical information theory.
• Qubits can exist in superpositions of |0⟩ and |1⟩, enabling them to represent and process multiple states simultaneously.
• The use of superposition allows quantum computers to explore a vast state space exponentially larger than classical systems for the same number of qubits.
• Quantum computing represents a new paradigm because it leverages quantum coherence and entanglement, features absent in classical computing architectures.
• The fundamental difference lies not in physical laws but in architectural design—classical systems avoid quantum features like superposition in their processing.
• Quantum mechanics enables new computational models that cannot be simulated efficiently by classical means due to the exponential scaling of quantum state spaces.