Quantum circuit implementation of the Hamiltonian versions of Grover's algorithm
arXiv:quant-ph/0302138 · doi:10.1103/PhysRevA.68.062311
Abstract
We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely related algorithms in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This make it possible to implement the last two algorithms by Hamiltonian evolution on a conventional quantum circuit, while keeping the quadratic speedup of Grover's original algorithm.
5 pages, 3 figures
References in corpus (2)
Cited by in corpus (22)
- On the relationship between continuous- and discrete-time quantum walk
- Noise resistance of adiabatic quantum computation using random matrix theory
- Simulating Quantum Dynamics On A Quantum Computer
- Improved Error-Scaling for Adiabatic Quantum State Transfer
- Quantum walk-based portfolio optimisation
- Hamiltonian Oracles
- On the optimality of spatial search by continuous-time quantum walk
- Improved Error Bounds for the Adiabatic Approximation
- Adiabatic quantum search algorithm for structured problems
- Finding a marked node on any graph by continuous-time quantum walk
- Approximating Fractional Time Quantum Evolution
- Irreconcilable Difference Between Quantum Walks and Adiabatic Quantum Computing
- Non-Adiabatic Quantum Dynamics of Grover's Adiabatic Search Algorithm
- Quantum computers can search rapidly by using almost any selective transformations
- Optimization of probabilistic quantum search algorithm with a priori information
- A framework for optimal quantum spatial search using alternating phase-walks
- Grover search algorithm
- Invariance of success probability in Grover's quantum search under local noise with memory
- The Dynamics of Entanglement in the Adiabatic Search and Deutsch Algorithms
- Is Quantum Search Practical?
- Optimisation of Quantum Hamiltonian Evolution: From Two Projection Operators to Local Hamiltonians
- More On Grover's Algorithm