Optimal Scaling Quantum Linear Systems Solver via Discrete Adiabatic Theorem

Optimal Scaling Quantum Linear Systems Solver via Discrete Adiabatic Theorem

Institute for Pure & Applied Mathematics (IPAM) via YouTube Direct link

Putting it all together

18 of 20

18 of 20

Putting it all together

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Optimal Scaling Quantum Linear Systems Solver via Discrete Adiabatic Theorem

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

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