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Optimal Scaling Quantum Linear Systems Solver via Discrete Adiabatic Theorem
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- 1 Intro
- 2 Why do we care?
- 3 Quantum linear systems problem
- 4 Complexity scaling
- 5 Continuous adiabatic algorithm
- 6 Adiabatic approach to QLSP
- 7 Non-symmetric case
- 8 Adiabatic walk
- 9 Norm of differences
- 10 Multistep gap
- 11 Discrete adiabatic theorem
- 12 Summation by parts formula
- 13 Contour integrals for bounds
- 14 Multiple eigenvalues problem
- 15 Numerical testing for constant factor
- 16 Filtering solution
- 17 LCU with two qubits
- 18 Putting it all together
- 19 Lower bound
- 20 Conclusions
