Quantum Brainstorm: Difference between revisions
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* Parameter shift rule: can use the same circuit to evaluate cost function + gradient in cost function, highly parallelisable |
* Parameter shift rule: can use the same circuit to evaluate cost function + gradient in cost function, highly parallelisable |
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* Parameter shift rule holds true even under noisy conditions due to trace linearity (https://johannesjakobmeyer.com/blog/004-noisy-parameter-shift/) |
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* Ansatze for local cost functions do not exhibit barren plateaus (eg https://arxiv.org/pdf/2102.01828.pdf) |
* Ansatze for local cost functions do not exhibit barren plateaus (eg https://arxiv.org/pdf/2102.01828.pdf) |
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* MSE loss function computed classically from quantum measurements |
* MSE loss function computed classically from quantum measurements |
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* Quantum state preparation (loading classical data into a quantum state) is possibly the largest bottleneck? Can do this with qGANs (problem: large number of samples) |
* Quantum state preparation (loading classical data into a quantum state) is possibly the largest bottleneck? Can do this with qGANs (problem: large number of samples) |
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===Other things=== |
===Other things=== |
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Revision as of 08:26, 9 November 2023
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
7 November 2023
Choy Boy - QML, classification:
- Parameter shift rule: can use the same circuit to evaluate cost function + gradient in cost function, highly parallelisable
- Parameter shift rule holds true even under noisy conditions due to trace linearity (https://johannesjakobmeyer.com/blog/004-noisy-parameter-shift/)
- Ansatze for local cost functions do not exhibit barren plateaus (eg https://arxiv.org/pdf/2102.01828.pdf)
- MSE loss function computed classically from quantum measurements
- Quantum state preparation (loading classical data into a quantum state) is possibly the largest bottleneck? Can do this with qGANs (problem: large number of samples)
Other things
Appendix B in: https://journals.aps.org/pra/pdf/10.1103/PhysRevA.98.062324
- Looks at the effect of applying a small perturbation to one of the angles in the Ansatz (depolarising error) - due to the unitarity of the gates, the perturbation gets washed out (fidelity susceptibility is independent of the layer index in which the perturbation occurs)
- Figure 7 shows the distribution of gradients for the MMD loss function: distribution is shown to be independent of the layer; also, variance decays exponentially with the number of shots taken
Can switch loss function to get a slightly different landscape: https://www.mdpi.com/1099-4300/23/10/1281
Recent paper that compares global vs local cost functions for binary and multi-class classification: for binary classification global cost function seems to perform better, while multiclass classification local cost function seems to perform better: https://iopscience.iop.org/article/10.1088/2632-2153/acb12f/pdf
Barren plateaus
Would be nice to have an explanation of exactly what a barren plateau is... gradient and variance in gradient decays exponentially to zero with system size? Unique to quantum circuits...
- More expressive means more likely to exhibit barren plateaus: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.010313