Quantum Brainstorm

Notes about previous and future quantum brainstorm sessions.

FUTURE

https://arxiv.org/pdf/2310.12726.pdf

Swap test : phase problem (Lila)

24 October 2023

Chiara - QCELS:

Early fault tolerant phase estimation algorithm:

• split up the phase estimation into separate Hadamard tests, only one ancilla qubit required for each test
• Heisenberg limit (1/eps rather than 1/eps^2) scaling retained
• T_max is much lower than in conventional QPE => early Fault tolerant
• only requires a squares overlap with the GS of 0.5

Paper 1: https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.4.020331

Paper 2 (about one month later, they realised their analysis wasn't optimal - you only need a squared overlap with the GS of 0.5, rather than 0.71): https://arxiv.org/abs/2303.05714

Nice talk from IPAM 2023: https://www.youtube.com/watch?v=j-MaQtgzksY