How can I find a Clifford+T approximation of an arbitrary one qubit gate in Qiskit?

Question

I know the Solovay-Kitaev algorithm can achieve this. Is there an implementation of this or any other algorithm for the same task in Qiskit? Or perhaps some other library that interfaces well with Qiskit?

Answer 1

On the Qiskit front, a Solovay-Kitaev algorithm implementation is on its way https://github.com/Qiskit/qiskit-terra/pull/5657.

If you want to use or have a look to this LNoorl:feature/sk-pass branch (remember is a WIP), you can install it like this:

pip install git+https://github.com/LNoorl/qiskit-terra.git@feature/sk-pass

Here is a usage example:

from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import TGate, HGate, TdgGate
from qiskit.transpiler.passes import SolovayKitaevDecomposition

circuit = QuantumCircuit(1)
circuit.rx(0.7, 0)

print('Orginal circuit:')
print(circuit)

basis_gates = [TGate(), TdgGate(), HGate()]
skd = SolovayKitaevDecomposition(recursion_degree=2, basis_gates=basis_gates, depth=5)

discretized = skd(circuit)

print('Discretized circuit:')
print(discretized)

Orginal circuit:
     ┌─────────┐
q_0: ┤ RX(0.7) ├
     └─────────┘
Discretized circuit:
global phase: -π/8
     ┌───┐┌───┐┌───┐┌─────┐┌───┐┌───┐┌───┐┌───┐┌───┐┌─────┐┌───┐┌───┐┌───┐»
q_0: ┤ H ├┤ T ├┤ H ├┤ TDG ├┤ H ├┤ T ├┤ H ├┤ T ├┤ H ├┤ TDG ├┤ H ├┤ T ├┤ H ├»
     └───┘└───┘└───┘└─────┘└───┘└───┘└───┘└───┘└───┘└─────┘└───┘└───┘└───┘»
«     ┌─────┐┌───┐┌─────┐┌─────┐┌───┐┌───┐┌───┐┌───┐┌───┐┌───┐┌───┐┌───┐┌─────┐»
«q_0: ┤ TDG ├┤ H ├┤ TDG ├┤ TDG ├┤ H ├┤ T ├┤ H ├┤ T ├┤ T ├┤ H ├┤ T ├┤ H ├┤ TDG ├»
«     └─────┘└───┘└─────┘└─────┘└───┘└───┘└───┘└───┘└───┘└───┘└───┘└───┘└─────┘»
«     ┌─────┐┌───┐┌─────┐┌───┐┌───┐┌───┐┌───┐┌───┐┌───┐┌───┐┌─────┐┌───┐┌─────┐»
«q_0: ┤ TDG ├┤ H ├┤ TDG ├┤ H ├┤ T ├┤ H ├┤ T ├┤ H ├┤ T ├┤ H ├┤ TDG ├┤ H ├┤ TDG ├»
«     └─────┘└───┘└─────┘└───┘└───┘└───┘└───┘└───┘└───┘└───┘└─────┘└───┘└─────┘»
«     ┌─────┐┌───┐┌─────┐┌───┐┌───┐┌───┐┌───┐┌───┐┌───┐┌─────┐
«q_0: ┤ TDG ├┤ H ├┤ TDG ├┤ H ├┤ T ├┤ T ├┤ H ├┤ T ├┤ H ├┤ TDG ├
«     └─────┘└───┘└─────┘└───┘└───┘└───┘└───┘└───┘└───┘└─────┘
```