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A Quantum Circuit Design for Grover ’ s Algorithm
| Content Provider | Semantic Scholar |
|---|---|
| Author | Diao, Zijian Zubairya, M. Suhail Chenb, Goong |
| Copyright Year | 2002 |
| Abstract | Quantum computing utilizes unique quantum features such as quantum coherence and quantum entanglement to solve some problems much faster than on classical Turing machines. The most dramatic example of the power of quantum computing is Shor’s algorithm for factoring a large integer [1]. This algorighm is substantially faster than any known classical algorithms of subexponential complexity. Another major example is the search of an object in unsorted data containing N elements. Classically it would require, on the average, O (N) searches. However, Grover showed that, by employing quantum superposition and quantum entanglement, the search can be carried out with only O ( N) steps [2–4]. Grover’s algorithm thus represents a polynomial advantage over classical counterparts. In recent years, Grover’s algorithm has been realized in NMR [5], optical systems [6], and a proposal has been made for its implementation in cavity QED systems [7]. All these studies are, however, restricted to N = 4 for which only one step is required to recover the target state with probability 1. An extension to higher values of N would be rather complicated [8]. The first step towards realizing the search algorithm for arbitrary N is to construct a circuit diagram in terms of quantum logic gates. It is the objective of this paper to devise such a circuit consisting of basic quantum logic gates. Due to the coherent nature of quantum mechanics, quantum computing algorithms are based on unitary transformations. The one-bit unitary gate and two-bit quantum phase gate suffice as the basic building blocks for quantum algorithms. The design circuit elements are based on the following gates that are representable in matrix forms as |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://people.ohio.edu/diao/papers/qcg.pdf |
| Alternate Webpage(s) | http://www.ohio.edu/people/diao/papers/qcg.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Body cavities Circuit design Circuit diagram Coherence (physics) Computation (action) Integer (number) Integer factorization Kolmogorov complexity Logic gate Optical System Polynomial QED (text editor) Quantum algorithm Quantum circuit Quantum computing Quantum entanglement Quantum gate Quantum logic Quantum mechanics Quantum superposition Search algorithm Shor's algorithm Turing machine cell transformation |
| Content Type | Text |
| Resource Type | Article |
