Quantum register
In quantum computing, a quantum register is a system comprising multiple qubits.[1] It is the quantum analog of the classical processor register. Quantum computers perform calculations by manipulating qubits within a quantum register.[2]
Definition
An size quantum register is a quantum system comprising qubits.
The Hilbert space, , in which the data is stored in a quantum register is given by where is the tensor product.[3]
The number of dimensions of the Hilbert spaces depend on what kind of quantum systems the register is composed of. Qubits are 2-dimensional complex spaces, while qutrits are 3-dimensional, et.c. For a register composed of n number of d-level quantum systems we have the Hilbert space
Quantum vs. classical register
First, there's a conceptual difference between the quantum and classical register. An size classical register refers to an array of flip flops. An size quantum register is merely a collection of qubits.
Moreover, while an size classical register is able to store a single value of the possibilities spanned by classical pure bits, a quantum register is able to store all possibilities spanned by quantum pure qubits at the same time.
For example, consider a 2-bit-wide register. A classical register is able to store only one of the possible values represented by 2 bits - accordingly.
If we consider 2 pure qubits in superpositions and , using the quantum register definition it follows that it is capable of storing all the possible values spanned by two qubits simultaneously.
References
- ^ Ekert, Artur; Hayden, Patrick; Inamori, Hitoshi (2008). "Basic concepts in quantum computation". arXiv:quant-ph/0011013.
- ^ Ömer, Bernhard (2000-01-20). Quantum Programming in QCL (PDF) (Thesis). p. 52. Retrieved 2021-05-24.
- ^ Major, Günther W., V.N. Gheorghe, F.G. (2009). Charged particle traps II : applications. Berlin: Springer. p. 220. ISBN 978-3540922605.
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Further reading
- Arora, Sanjeev; Barak, Boaz (2016). Computational Complexity: A Modern Approach. Cambridge University Press. pp. 201–236. ISBN 978-0-521-42426-4.