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Complete 3-Qubit Grover Search on a Programmable Quantum Computer
C. Figgatt, D. Maslov, K. A. Landsman, N. M. Linke, S. Debnath, C. Monroe
TL;DR
Implementing three-qubit Grover search requires circuits that support multiple possible oracles. The paper presents modular optimized circuits for Boolean and phase oracles and reports an average Toffoli-3 success probability of 82.1(2)%, indicating faithful operation for arbitrary input states.
Problem
The work addresses implementing Grover search circuits for multiple possible oracles in a three-qubit setting.
Method
The authors use modular Grover circuits with independently optimized initialization and amplification stages for Boolean and phase oracles.
Results
82.1(2)% average success probability was measured for the Toffoli-3 gate, indicating faithful operation for arbitrary input states.
Takeaways & Limitations
The characterized Toffoli-3 gate faithfully operates on arbitrary input states within the reported verification procedure.
Abstract
from arXiv · showhide
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.
Supplementary Materials
The supplementary materials detail the native-gate circuit constructions for Grover search and characterize the Toffoli-3 gate using limited tomography. The Toffoli-3 verification achieved an average success probability of 82.1(2)%.
- Grover Circuit Implementations: Grover-search circuits use native R(θ, φ) and XX(χ) gates, with initialization and amplification stages optimized independently to minimize gate times.Boolean-oracle circuits include an ancilla, while phase-oracle circuits omit it.
- Composite Gate Implementations: CNOT and controlled-Z composites each require one XX gate and several single-qubit rotations, while Toffoli-3 and CCZ circuits implement the three-qubit operations.The gate constructions account for experimentally determined signs of XX-gate parameters for each ion pair.
- Composite Gate Implementations: The Toffoli-4 circuit implements a four-qubit interaction with three control qubits and one target qubit, and additionally requires an ancilla qubit.Its construction uses XX(χ), Rx(θ), Ry(θ), and R(θ, φ) gates.