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WorksheetsVariational Principle in Quantum Physics
Total questions: 7
Worksheet time: 3mins
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
