Quantum Brainstorm: Difference between revisions
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==FUTURE== |
==FUTURE== |
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https://arxiv.org/pdf/2310.12726.pdf |
https://arxiv.org/pdf/2310.12726.pdf |
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Swap test : phase problem (Lila) |
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==24 October 2023== |
==24 October 2023== |
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===Choy Boy - QML, classification:=== |
===Choy Boy - QML, classification:=== |
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* For a variational quantum supervised classifier, data is first loaded (most commonly using rotation encoding via rotation gates), and an ansatz is used to minimise the cost function associated with the data's labels |
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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 ( |
* 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) |
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| ⚫ | |||
* Hypothesis that local minima could give rise to better classification rates than the global minimum under certain scenarios, in a similar vein to QAOA where certain graphs at finite number of ansatz layers have local minima with a higher probability of finding the correct max-cut solution than the global minimum |
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===Other things=== |
===Other things=== |
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* 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) |
* 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) |
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* 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 |
* 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 |
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| ⚫ | |||
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 |
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===Barren plateaus=== |
===Barren plateaus=== |
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Latest revision as of 12:12, 5 March 2024
Notes about previous and future quantum brainstorm sessions.
FUTURE
https://arxiv.org/pdf/2310.12726.pdf
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:
- For a variational quantum supervised classifier, data is first loaded (most commonly using rotation encoding via rotation gates), and an ansatz is used to minimise the cost function associated with the data's labels
- 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)
- Hypothesis that local minima could give rise to better classification rates than the global minimum under certain scenarios, in a similar vein to QAOA where certain graphs at finite number of ansatz layers have local minima with a higher probability of finding the correct max-cut solution than the global minimum
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