Variational Principle in Quantum Physics

Which equation we need to solve to find the ground state of a quantum system with a Hamiltonian H

• Hamilton-Jacobi equations

• Shrodinger equation

• Wave equation

The complexity of diagonalizing a Hamiltonian of a quantum many-body system with size N is:

• Linear in N

• Quadratic in N

• Exponential in N

• Logarithmic in N

The variational energy is always

• bigger or equal to the ground state energy

• lower or equal to the ground state energy

• equal to the ground state enegy

How should we design the wavefunction ansatz for our variational calculations?

• It should be physically informed to have a good overlap with the ground state. We can also choose it to be expressive enough.

• it should be a Tensor Network

• Whatever we choose is good enough.

• it should be a neural network

To analytically find the optimal parameters that minimizes the variational energy:

• We set the second derivatives of the variational energy to zero

• We set the first derivatives of the variational energy to zero

• We set the variational energy to zero

• We do a set of random guesses

For gradient descent to succeed at minimizing the variational energy, we update the parameters to

• the same direction of the gradients of the variational energy

• the opposite direction of the gradients of the variational energy

• the opposite direction of the gradients of the variational energy for some and the same direction for others

• random directions by flipping a coin

What is the principle we could use to check convergence

• Zero energy principle

• Updating the parameters as much as we can

• Zero variance principle

• None of the previous answers