Models of quantum computation
We will cover several different models of quantum computation
- Quantum circuit model
- Topological quantum computing
- Quantum walk
- Quantum adiabatic/annealing computations
- Measurement based quantum computation (MBQC)
These models proved to be universal quantum computing. Although they are equivalent to the quantum Turing machine. This equivalence need not hold exactly for practical quantum computers, since the overhead of simulation may be different for different algorithms. For example, the topological quantum computing are good at AJL algorithm since AJL algorithm was derived by considering the knot as the trace closure of a braid, which are similar to braiding of anyons in topological quantum computing.
Quantum circuit model is a quantum analogy of the classical circuit. In the circuit model of quantum computation, we prepare an initial state as input, apply a sequence of quantum gates to computing, and finally do some measurement to obtain the result.
While In Measurement based quantum computation (MBQC), there is no need to apply any multi-qubit operations. we prepare a entangled state of qubits, make single-qubit measurements in suitably chosen bases.