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I'm still unsure on the difference between adiabatic quantum computing (AQC) and quantum annealing (QA). Please critique these interpretations:

  • AQC: Define a Hamiltonian with an easy-to-prepare ground state $H_0$ and a problem Hamiltonian $H_1$. The experimentalist can affect the environment such that at $H(0)=H_0$ and $H(1) = H_1$ where $H(t)$ is a function of time. If we prepare the system in the ground state of $H(0)=H_0$ and slowly "turn on" $H_1$ (i.e. letting $t$ go from $0$ to $1$), the final state of the system is the ground state of $H(1)=H_1$.

  • QA: For a restricted class of Hamiltonians (i.e. Ising models?), prepare the ground state of $H_0$. Then slowly turn on $H_1$ and let natural fluctuations move the state around the Hilbert space. Try to find the state with an energy that's low enough for your purposes.

I'm extremely unsure about my interpretation of QA and would appreciate some clarity. Other posts on this site have helped a bit but I'm not 100% there yet.

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