We introduce a model of computation based on \emph{read only memory} (ROM), which allows us to compare the space-efficiency of reversible, error-free classical computation with reversible, error-free quantum computation. We show that a ROM-based quantum computer with one writable qubit is universal, whilst two writable bits are required for a universal classical ROM-based computer. We also comment on the time-efficiency advantages of quantum computation within this model.
We introduce a model of computation based on \emph{read only memory} (ROM), which allows us to compare the space-efficiency of reversible, error-free classical computation with reversible, error-free quantum computation. We show that a ROM-based quantum computer with one writable qubit is universal, whilst two writable bits are required for a universal classical ROM-based computer. We also comment on the time-efficiency advantages of quantum computation within this model.
It appears, in principle, that the laws of quantum mechanics allow a quantum computer to solve certain mathematical problems more rapidly than can be done using a classical computer. However, in order to build such a quantum computer a number of technological problems need to be overcome. A stepping stone to this goal is the implementation of relatively simple quantum algorithms using current experimental techniques.This paper explores small scale quantum algorithms from two different perspectives. Firstly, it will be shown how small scale quantum algorithms can be tailored to fit current schemes for implementing a quantum computer. Secondly, I will review a simple model of computation, based on read-only-memory. This model allows the comparison of the space-efficiency of reversible error-free classical computation with reversible, error-free quantum computation. The quantum model has been shown to be more powerful than the classical model.
Quantum computation draws from theoretical physics, functional analysis, and algorithmic computer science, acting as an interdisciplinary field. The main aim of research in quantum computing is to demonstrate that certain tasks can be completed faster using quantum computers than traditional ones. For this, quantum memory is crucial to developing synchronization tools that coordinate various processes in quantum computers and quantum gates that preserve the identity of quantum states, such as superpositions, and methods to convert preset photons into on-demand photons. Quantum memories are essential for large-scale photonic quantum computing systems, enabling the coherent manipulation, buffering, and retiming of photonic signals. Unlike classical memory, quantum memory allows states to exist in quantum superposition, offering greater flexibility for quantum algorithms than conventional storage systems. While traditional Read-Only Memory (ROM) tends to be slower, quantum computing facilitates the development of novel computer types that operate with qubits as input states, leading to increased storage capacity. This paper proposes a quantum-based ROM (QROM) architecture that utilizes quantum-based binary logic operations and presents an analysis of the systems performance, focusing on heat generation and speed parameters.
It appears, in principle, that the laws of quantum mechanics allow a quantum computer to solve certain mathematical problems more rapidly than can be done using a classical computer. However, in order to build such a quantum computer a number of technological problems need to be overcome. A stepping stone to this goal is the implementation of relatively simple quantum algorithms using current experimental techniques.This paper explores small scale quantum algorithms from two different perspectives. Firstly, it will be shown how small scale quantum algorithms can be tailored to fit current schemes for implementing a quantum computer. Secondly, I will review a simple model of computation, based on read-only-memory. This model allows the comparison of the space-efficiency of reversible error-free classical computation with reversible, error-free quantum computation. The quantum model has been shown to be more powerful than the classical model.
It appears, in principle, that the laws of quantum mechanics allow a quantum computer to solve certain mathematical problems more rapidly than can be done using a classical computer. However, in order to build such a quantum computer a number of technological problems need to be overcome. A stepping stone to this goal is the implementation of relatively simple quantum algorithms using current experimental techniques.This paper explores small scale quantum algorithms from two different perspectives. Firstly, it will be shown how small scale quantum algorithms can be tailored to fit current schemes for implementing a quantum computer. Secondly, I will review a simple model of computation, based on read-only-memory. This model allows the comparison of the space-efficiency of reversible error-free classical computation with reversible, error-free quantum computation. The quantum model has been shown to be more powerful than the classical model.
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be clarified by free models, that add to classical computing just enough physical principles to represent quantum computing and no more. Here we develop an axiomatisation of quantum computing that replaces the standard continuous postulates with a small number of discrete equations, as well as a free model that replaces the standard linear-algebraic model with a category-theoretical one. The axioms and model are based on reversible classical computing, isolate quantum advantage in the ability to take certain well-behaved square roots, and link to various quantum computing hardware platforms. This approach allows combinatorial optimisation, including brute force computer search, to optimise quantum computations. The free model may be interpreted as a programming language for quantum computers, that has the same expressivity and computational universality as the standard model, but additionally allows automated verification and reasoning.
In the near future, as quantum and classical systems coexist, managing hybrid systems will require efficient conversion between bits and qubits. Therefore, understanding memory management for both classical and quantum systems is essential. Along that line, this survey provides a comparative analysis of memory management in classical and quantum architectures. The traditional memory hierarchy and allocation strategies used in classical systems are examined along with caching and paging techniques which optimize performance and resource utilization. On the other hand, quantum memory management focuses on addressing unique challenges such as quantum decoherence and error correction using advanced techniques such as Shor’s code, Surface codes, and other specialized error correction codes. This study explores Quantum Random Access Memory (QRAM) and its role in enabling efficient data retrieval in quantum systems. Quantum read/write operations and their impact on coherence and fidelity are analyzed, highlighting advancements in qubit state measurement and error mitigation. While classical systems take benefits of deterministic and hierarchical memory structures, quantum systems must overcome environmental noise and decoherence to maintain data stability. Furthermore, scalability issues and emerging trends in quantum architecture are discussed, emphasizing how advancements in Quantum Error Correction (QEC) and hybrid systems can address current limitations in memory management.