Quantum evolutiom
A sum of constraints and objective hamiltonians
Need to choose proper values A_1, A_2, B.
Alternatively turn to QUBO and then to 2-local Ising model
non unique!
New qubits!
J_{ij} != 0 iff s_i and s_j are connected - more qubits needed!
A sum of constraints and objective hamiltonians
Need to choose proper values A_1, A_2, B.
Always commuting!
Always commuting!
Extra qubit needed but CNOT-s commutes!
Note that not all qubits may be connected for QC as well - but we can SWAP
Depending on classical algorithm we use we may need:
The more derivatives we know - usually the better the algorithm works
We need to estimate the energy of the state given Hamiltonian
Measurement
0100100...10
Hamiltonian
The mean of energies E_i is expectedly the correct energy
We may need to estimate the gradient
First way: calculate from the definition of gradient based on
Problem:
One can choose a different linear combination of energies for different thetas, however then the time complexity grows
Energy estimation techniques
Hence we can estimate energy for each P_i independently.
2. Since all P_i commute, we can estimate energy based on bit-strings coming out from measurement.
Levels of simulation truth
1. Calculate |phi> and then classicaly calculate <phi|H|phi>
"fast", but completely unphysical
2. Calculate |phi>, then make measurements and estimate energy
perfect but super slow
3. Calculate (noisy) |phi>, then make (noisy) measurement and estimate energy
slow, physical, but not NISQ-y
depth