size of initial Hamiltonian
Hello!
Can you suggest any academic papers or textbooks which prove that D-Wave system can handle arbitrary Hamiltonians (of any size, not only 2^{n}, where n is the number of qubits)? I am interested in computing energy gap given initial and problem Hamiltonian. Now, my problem Hamiltonian is of size 24*24 and now I am wondering how can I prepare initial Hamiltonian of same size 24*24. In "getting start " file they mention that initial Hamiltonian can be obtained by Pauli matrices which means its size of order 2^{n}? Hence I am a little bit confused with the size of initial Hamiltonian....
Thank you!
Comments
Hello,
Can you please give some clarification on your question. I'm not completely sure what you are asking.
Is 2^{n} talking about the solution space of the problem?
Are you asking about the option to represent n discrete values (e.g. {1,2,3,4,5} == 5^{n}) instead of n binary variables (e.g. {0,1} == 2^{n})?
Are you able to provide an example problem Hamiltonian to illustrate your question?
24*24 sounds like a square matrix, representing a fully connected QUBO problem or something similar.
Are you asking about problems that are not binary optimization problems?
In the initial Hamiltonian, all qubits are in superposition and is the state in which the QPU starts. You can see that A(s), the initial Hamiltonian, starts out high and then goes to zero by the end of the annealing process, while B(s), the final Hamiltonian, increases throughout the annealing process.
https://docs.dwavesys.com/docs/latest/c_gs_2.html#the-hamiltonian-and-the-eigenspectrum
The Annealing Implementation and Controls documentation might also be helpful:
https://docs.dwavesys.com/docs/latest/c_qpu_annealing.html
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