[Paper Review] Demonstration of Optimal Fixed-Point Quantum Search Algorithm in IBM Quantum Computer

Kamal Gurnani, Bikash K. Behera+1 more|arXiv (Cornell University)|Dec 29, 2017

Quantum Computing Algorithms and Architecture34 references3 citations

TL;DR

This paper demonstrates the implementation of the Optimal Fixed-Point Quantum Search (OFPQS) algorithm on a five-qubit IBM quantum computer, leveraging state vector rotation in Hilbert space to precisely locate target states. By performing one and two iterations and validating results via quantum state tomography, the study confirms high-fidelity state preparation and accurate convergence to the target, showcasing the algorithm's precision in a real quantum hardware setting.

ABSTRACT

Quantum search algorithm can be described as the rotation of state vectors in a Hilbert space. The state vectors uniformly rotate by iterative sequences until they hit the target position. To optimize the algorithm, it is necessary to have the precise knowledge about some parameters like the number of target positions. Here we demonstrate the implementation of optimal fixed-point quantum search (OFPQS) algorithm in a five-qubit quantum computer developed by IBM Corporation. We perform the OFPQS algorithm for one and two-iterations and confirm the accuracy of our results by state tomography process.

Motivation & Objective

• To implement the Optimal Fixed-Point Quantum Search (OFPQS) algorithm on a real quantum processor.
• To validate the accuracy of the OFPQS algorithm using quantum state tomography in a noisy intermediate-scale quantum (NISQ) device.
• To investigate the performance of OFPQS with one and two iterations on a five-qubit IBM quantum computer.
• To confirm that precise knowledge of target count enables optimal convergence in fixed-point search.

Proposed method

• The OFPQS algorithm is implemented on a five-qubit IBM quantum processor using iterative state vector rotations in Hilbert space.
• The algorithm is executed for one and two iterations to evaluate convergence behavior and fidelity.
• Quantum state tomography is applied to reconstruct the final quantum state and verify the accuracy of the search outcome.
• The method relies on precise control of rotation angles derived from the known number of target states to achieve fixed-point convergence.
• The implementation uses standard quantum gates and circuit optimization techniques suitable for NISQ-era hardware.
• The fidelity of the final state is assessed by comparing the reconstructed density matrix with the ideal target state.

Experimental results

Research questions

• RQ1 Can the OFPQS algorithm be successfully implemented on a real five-qubit quantum processor?
• RQ2 How does the algorithm perform with one and two iterations in terms of state fidelity and convergence?
• RQ3 To what extent does quantum state tomography confirm the correctness of the OFPQS output on noisy hardware?
• RQ4 Does the fixed-point convergence property hold in a real quantum computing environment with decoherence and gate errors?
• RQ5 Can precise knowledge of the number of target states enable optimal performance in a physical quantum device?

Key findings

• The OFPQS algorithm was successfully implemented on a five-qubit IBM quantum computer using iterative state rotations.
• The algorithm achieved high-fidelity state preparation after one and two iterations, as confirmed by quantum state tomography.
• The reconstructed quantum states showed strong overlap with the ideal target states, indicating accurate convergence.
• The results demonstrated that fixed-point convergence is attainable in a real NISQ device with proper parameter tuning.
• The study confirmed that precise knowledge of the number of target states enables optimal performance in the search process.
• The implementation validated the theoretical framework of OFPQS in a physical quantum hardware setting, despite noise and decoherence effects.