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Block-encoding A way to represent large matrices on a quantum computer efficiently
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Classroom Contents
High-Dimensional Linear Algebra in Quantum Algorithms - From Quantum Walks to Matrix Inversion
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- 1 High-dimensional linear algebra in quantum algorith from quantum walks to matrix inversion
- 2 High-level explanation of quadratic speed-ups Quantum fast-forwarding (Apers & Sarlette 2018) We can implement a unitary V such that
- 3 Szegedy quantum walk based search Suppose we have some unknown marked vertices MCV. Quadratically faster hitting Hitting time: expected time to hit a marked verlax Starting from the stationary distr.…
- 4 k-distinctness Are there k distinct elements mapped to the same image?
- 5 Block-encoding A way to represent large matrices on a quantum computer efficiently
- 6 Quantum Singular Value Transformation (QSVT) Main theorem about OSVT (G, Su, Low, Wiebe 2018)
- 7 Amplitude amplification and estimation Fixed-point amplitude ampl. (Yoder, Low, Chuang 2014) Amplitude amplification problem: Given U such that
- 8 Detecting a bias in a quantum sampler Suppose we are given such that
- 9 Speeding up Monte Carlo methods Montanaro 2015 Sampling algorithm Suppose we have a sampling algorithm sampling from a random variable X.
- 10 Direct implementation of the pseudoinverse (HHL)
- 11 Application for Boolean equations - Chen & Gao 201
- 12 Continuous optimization Convex optimization
