Entangled Quantum States Generated by Shor's Factoring Algorithm
arXiv:quant-ph/0510042 · doi:10.1103/PhysRevA.72.062308
Abstract
The intermediate quantum states of multiple qubits, generated during the operation of Shor's factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian measure. It is found that the entanglement is generated during the pre-processing stage of the algorithm and remains nearly constant during the quantum Fourier transform stage. The entanglement is found to be correlated with the speedup achieved by the quantum algorithm compared to classical algorithms.
7 pages, 4 figures submitted to Phys. Rev. A
References in corpus (13)
- Separability Criterion for Density Matrices
- Quantum Mechanics helps in searching for a needle in a haystack
- Efficient classical simulation of slightly entangled quantum computations
- Quantifying Entanglement
- Entanglement Measures and Purification Procedures
- On the volume of the set of mixed entangled states
- On the role of entanglement in quantum computational speed-up
- Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
- Quantum Algorithms and the Fourier Transform
- An entanglement monotone derived from Grover's algorithm
- Geometric Strategy for the Optimal Quantum Search
- Characterization of pure quantum states of multiple qubits using the Groverian entanglement measure
- Analysis of Grover's quantum search algorithm as a dynamical system
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- ZKCM: a C++ library for multiprecision matrix computation with applications in quantum information
- Mermin Polynomials for Entanglement Evaluation in Grover's algorithm and Quantum Fourier Transform
- Necessity of Superposition of Macroscopically Distinct States for Quantum Computational Speedup
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- On Shor's Factoring Algorithm with More Registers and the Problem to Certify Quantum Computers
- Entanglement and its Role in Shor's Algorithm
- Superposition of Macroscopically Distinct States in Adiabatic Quantum Computation
- Geometric Measure of Entanglement and Schmidt Decomposition of Multipartite Systems
- Quantum Algorithms in Cybernetics
- Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift