From 5f1bad5eacf5ba19378975e113e87a8e5dcb3173 Mon Sep 17 00:00:00 2001
From: Mohammed Boky <57175861+Mboky@users.noreply.github.com>
Date: Tue, 5 Dec 2023 14:18:16 +0100
Subject: [PATCH] Fix non convergence in example of usage (#13)
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Hi,

The current example of usage does not converge in the amount of
iterations specified

```python
import netket as nk
import netket_fidelity as nkf

# Create the Hilbert space and the variational states |ψ⟩ and |ϕ⟩
hi = nk.hilbert.Spin(0.5, 4)
sampler = nk.sampler.MetropolisLocal(hilbert=hi, n_chains_per_rank=16)
model = nk.models.RBM(alpha=1, param_dtype=complex, use_visible_bias=False)
phi = nk.vqs.MCState(sampler=sampler, model=model, n_samples=100)
psi = nk.vqs.MCState(sampler=sampler, model=model, n_samples=100)

# Transformation U
U = nkf.operator.Hadamard(hi, 0)

# Create the driver
optimizer = nk.optimizer.Sgd(learning_rate=0.01)
te =  nkf.driver.InfidelityOptimizer(phi, optimizer, U=U, U_dagger=U, variational_state=psi, is_unitary=True, cv_coeff=-1/2)

# Run the driver
te.run(n_iter=100)
```

This keeps yielding an infidelity around 0.5. Either adding more
iterations or changing to the Adam optimizer fixes this.
With Adam and the same number of iterations, infidelity is consistently
smaller than 0.001

Co-authored-by: Mohammed Boky <mohammedboky@gmail.com>
---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index c0add77..0ee7fba 100644
--- a/README.md
+++ b/README.md
@@ -61,7 +61,7 @@ psi = nk.vqs.MCState(sampler=sampler, model=model, n_samples=100)
 U = nkf.operator.Hadamard(hi, 0)
 
 # Create the driver
-optimizer = nk.optimizer.Sgd(learning_rate=0.01)
+optimizer = nk.optimizer.Adam(learning_rate=0.01)
 te =  nkf.driver.InfidelityOptimizer(phi, optimizer, U=U, U_dagger=U, variational_state=psi, is_unitary=True, cv_coeff=-1/2)
 
 # Run the driver