Optimizing the walk coin in the quantum random walk search algorithm through machine learning
arXiv:2105.08020
Abstract
This paper examines the stability of the quantum random walk search algorithm, when the walk coin is constructed by generalized Householder reflection and additional phase shift, against inaccuracies in the phases used to construct the coin. The optimization of the algorithm is done by numerical methods - Monte Carlo, neural networks, and supervised machine learning. The results of numerical simulations show that, with such a construction of the Householder reflection, the algorithm is more stable to inaccuracies in the specific values of these phases, as long as it is possible to control the phase difference between the phase shift and the phase involved in the Householder reflection. This paper explicitly shows as an example, how achieving a properly designed phase difference would make quantum random walk search on a hypercube more stable for coin register consisting of one, two, and three qubits.
arXiv comment35 pages, 15 figures, 2 tables, Fixed a typo in Eq.(35)
References in corpus (23)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Quantum Computation with Quantum Dots
- The Physical Implementation of Quantum Computation
- Quantum Amplitude Amplification and Estimation
- Quantum Computation and Decision Trees
- A Quantum Random Walk Search Algorithm
- Stimulated Raman adiabatic passage in physics, chemistry and beyond
- Spatial search by quantum walk
- Implementing the quantum random walk
- A random walk approach to quantum algorithms
- Optimized quantum random-walk search algorithms
- Quantum Random Walks Hit Exponentially Faster
- Quantum algorithm for non-homogeneous linear partial differential equations
- Geometric phase gates based on stimulated Raman adiabatic passage in tripod systems
- Time-efficient implementation of quantum search with qudits
- Quantum Computing: An Overview Across the System Stack
- Quantum search algorithms on a regular lattice
- Neural-network-designed pulse sequences for robust control of singlet-triplet qubits
- Strategy for quantum algorithm design assisted by machine learning
- Search on a Fractal Lattice using a Quantum Random Walk
- Finding paths in tree graphs with a quantum walk
- The quantum query complexity of read-many formulas
- Quantum Search in an Ordered List via Adaptive Learning