dorsal/arxiv
View SchemaAn intuitive Hamiltonian for quantum search
| Authors | Stephen A. Fenner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0004091 |
| URL | https://arxiv.org/abs/quant-ph/0004091 |
Abstract
We present new intuition behind Grover's quantum search algorithm by means of a Hamiltonian. Given a black-box Boolean function f mapping strings of length n into {0,1} such that f(w) = 1 for exactly one string w, L. K. Grover describes a quantum algorithm that finds w in O(2^{n/2}) time. Farhi & Gutmann show that w can also be found in the same amount time by letting the quantum system evolve according to a simple Hamiltonian depending only on f. Their system evolves along a path far from that taken by Grover's original algorithm, however. The current paper presents an equally simple Hamiltonian matching Grover's algorithm step for step. The new Hamiltonian is similar in appearance from that of Farhi & Gutmann, but has some important differences, and provides new intuition for Grover's algorithm itself. This intuition both contrasts with and supplements other explanations of Grover's algorithm as a rotation in two dimensions, and suggests that the Hamiltonian-based approach to quantum algorithms can provide a useful heuristic for discovering new quantum algorithms.
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"abstract": "We present new intuition behind Grover\u0027s quantum search algorithm by means of\na Hamiltonian. Given a black-box Boolean function f mapping strings of length n\ninto {0,1} such that f(w) = 1 for exactly one string w, L. K. Grover describes\na quantum algorithm that finds w in O(2^{n/2}) time. Farhi \u0026 Gutmann show that\nw can also be found in the same amount time by letting the quantum system\nevolve according to a simple Hamiltonian depending only on f. Their system\nevolves along a path far from that taken by Grover\u0027s original algorithm,\nhowever. The current paper presents an equally simple Hamiltonian matching\nGrover\u0027s algorithm step for step. The new Hamiltonian is similar in appearance\nfrom that of Farhi \u0026 Gutmann, but has some important differences, and provides\nnew intuition for Grover\u0027s algorithm itself. This intuition both contrasts with\nand supplements other explanations of Grover\u0027s algorithm as a rotation in two\ndimensions, and suggests that the Hamiltonian-based approach to quantum\nalgorithms can provide a useful heuristic for discovering new quantum\nalgorithms.",
"arxiv_id": "quant-ph/0004091",
"authors": [
"Stephen A. Fenner"
],
"categories": [
"quant-ph"
],
"title": "An intuitive Hamiltonian for quantum search",
"url": "https://arxiv.org/abs/quant-ph/0004091"
},
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