dorsal/arxiv
View SchemaQuantum Algorithms with Fixed Points: The Case of Database Search
| Authors | Lov K. Grover, Apoorva Patel, Tathagat Tulsi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603132 |
| URL | https://arxiv.org/abs/quant-ph/0603132 |
Abstract
The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which get around this limitation. The first replaces selective inversions in the algorithm by selective phase shifts of $\frac{\pi}{3}$. The second controls the selective inversion operations using two ancilla qubits, and irreversible measurement operations on the ancilla qubits drive the starting state towards the target state. Using $q$ oracle queries, these variations reduce the probability of finding a non-target state from $\epsilon$ to $\epsilon^{2q+1}$, which is asymptotically optimal. Similar ideas can lead to robust quantum algorithms, and provide conceptually new schemes for error correction.
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"abstract": "The standard quantum search algorithm lacks a feature, enjoyed by many\nclassical algorithms, of having a fixed-point, i.e. a monotonic convergence\ntowards the solution. Here we present two variations of the quantum search\nalgorithm, which get around this limitation. The first replaces selective\ninversions in the algorithm by selective phase shifts of $\\frac{\\pi}{3}$. The\nsecond controls the selective inversion operations using two ancilla qubits,\nand irreversible measurement operations on the ancilla qubits drive the\nstarting state towards the target state. Using $q$ oracle queries, these\nvariations reduce the probability of finding a non-target state from $\\epsilon$\nto $\\epsilon^{2q+1}$, which is asymptotically optimal. Similar ideas can lead\nto robust quantum algorithms, and provide conceptually new schemes for error\ncorrection.",
"arxiv_id": "quant-ph/0603132",
"authors": [
"Lov K. Grover",
"Apoorva Patel",
"Tathagat Tulsi"
],
"categories": [
"quant-ph"
],
"title": "Quantum Algorithms with Fixed Points: The Case of Database Search",
"url": "https://arxiv.org/abs/quant-ph/0603132"
},
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