I am a graduate student in the Department of Computer Engineering, and I am currently doing research on superconducting quantum computers. In particular, I am focusing on quantum annealing machines and working on building a simulation environment for quantum annealing machines.

In order to simulate the quantum mechanical behavior of quantum annealing machines, we need to know the Hamiltonian of superconducting quantum circuits, so I investigated the Hamiltonian of real machines by reading the following paper from D-Wave.

From these references, we have been able to grasp the structure of the quantum annealing machine. However, because the paper introduces a Hamiltonian in the descent, In particular, the equations for the rf-SQUID (made by compound Josephson junction or compound-compound Josephson junction) that makes up the qubit are difficult to understand.

What knowledge do I need to understand the Hamiltonian of this qubit? And I would like you to suggest a suitable textbook/paper. I have studied computer science, basic quantum mechanics, statistical mechanics, and quantum information.

Also, if possible, I would like to know if there is a tool that can simulate a superconducting quantum circuit taking into account the applied flux bias.

  • $\begingroup$ Does scQubit do the job of the tool you are looking for? $\endgroup$
    – FDGod
    Commented Nov 21, 2023 at 9:14
  • $\begingroup$ I know that tool can simulate the original circuit including the external magnetic flux, but can it also take into account the mutual inductance between the qubit and the coupler? $\endgroup$
    – Aki
    Commented Nov 22, 2023 at 11:01
  • $\begingroup$ Does WRSpice do the job of the tool you are looking for? $\endgroup$
    – FDGod
    Commented Dec 5, 2023 at 22:15
  • $\begingroup$ I didn't know there is a SPICE tool that could also handle Josephson Junction. I would like to investigate how to use this tool. Thank you very much. $\endgroup$
    – Aki
    Commented Dec 7, 2023 at 8:16


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