A Multifunctional Modular Implementation of Grover’s Algorithm

茂 山下

Seyed Navid Elyasi, Rui Lin, Paolo Monti A

We evaluate entanglement requirements, preparation, and execution times for QFT and Grover algorithms in distributed measurement-based quantum computation, and compare them with gate-based implementations on modular superconducting architectures, identifying regimes where measurement-based approaches outperform gate-based ones.

Issac Diana Jeba Jingle, Sharlene Anna Pereira

Sergi Ramos-Calderer, Emanuele Bellini, José Ignacio Latorre +2 more

Abstract We present the implementation of Grover’s algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation and bitwise exclusive or. Our implementation provides the means to assess with precision the scaling of the number of gates and depth of a full-fledged quantum circuit designed to find the preimages of a given hash digest. The detailed construction of the quantum oracle shows that the presence of AND gates, OR gates, shifts of bits and the reuse of the initial state along the computation require extra quantum resources as compared with other hash functions based on modular additions, XOR gates and rotations. We also track the entanglement entropy present in the quantum register at every step along the computation, showing that it becomes maximal at the inner core of the first action of the quantum oracle, which implies that no classical simulation based on tensor networks would be of relevance. Finally, we show that strategies that suggest a shortcut based on sampling the quantum register after a few steps of Grover’s algorithm can only provide some marginal practical advantage in terms of error mitigation.

Luigi Accardi, Ruben Sabbadini

Lasha Janelidze, Mariam Janelidze

The work presents a demonstration of functional understanding and practical implementation of quantum computing processes. The project considers both quantum operations (for example, superposition of qubits using Hadamard gates) and complex algorithms, such as Grover's quantum search algorithm. This algorithm is used to optimize the search for a specifically labeled element in an n-qubit space and is one of the main demonstrations of the quantum speedup that gives quantum computing an advantage over classical models. The presented codes are divided into independent, modular functions, which reflects the observance of functional programming principles in quantum algorithms. It is these systematic calculations that improve the transparency, accessibility, and reusability of the code, which is critically important in a quantum development environment where experimentation and multiple testing of algorithms are widely used. The code was simulated using Qiskit's "Aer", which provides multishot execution and statistical analysis of the results. In addition, the implementation of Grover's algorithm used oracle modeling.