# Complete 3-Qubit Grover Search on a Programmable Quantum Computer

## TL;DR

This paper demonstrates a complete 3-qubit Grover search on a scalable trapped ion quantum computer, outperforming classical methods and implementing advanced multi-qubit gates with high fidelity.

## Contribution

It presents the first full 3-qubit Grover search on a scalable quantum platform, including all possible oracles and two state-marking methods, with implementation of a Toffoli-4 gate.

## Key findings

- Quantum solutions outperform classical counterparts.
- Successful implementation of a Toffoli-4 gate with 70.5% fidelity.
- All 8 single-result and 28 two-result oracles executed successfully.

## Abstract

Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state-marking scheme required to perform a classical search. All quantum solutions are shown to outperform their classical counterparts. We also report the first implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5% and 89.6%, respectively.

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Source: https://tomesphere.com/paper/1703.10535