4.1 Adiabatic quantum computing
In Chapter 1, Foundations of Quantum Computing, we focused mainly on quantum circuits but we briefly mentioned that there were other equivalent quantum computing models. One of them is adiabatic quantum computing, introduced in 2000 by Farhi, Goldstone, Gutmann, and Sipser in a widely influential paper [36].
When using quantum circuits, we apply operations (our beloved quantum gates) through discrete, sequential steps. However, adiabatic quantum computing relies on the use of continuous transformations. Namely, we will use a Hamiltonian that will vary with time and that will be the driving force to change the state of our qubits according to the time-dependent Schrödinger equation:
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As you may remember, in Chapter 1, Foundations of Quantum Computing, we talked about the time-independent Schrödinger equation. In that case, the Hamiltonian — which you can think of as a mathematical object that can describe the...
