An example with logical qubits
When you use a logical backend, you get error-corrected qubits with all-to-all connectivity and a universal gate set.
Logical backends are less noisy than physical backends, but they still feature noise. You may tune the backend's noise characteristics using parameters distance, kappa_1, kappa_2 and average_nb_photons (read Supported instructions for more details about these parameters and how to set them).
For the time being, logical backends are all emulators, but creating a QPU able to run in logical mode is Alice & Bob's main goal.
Here's an example using a logical backend, showing how continuous gates are decomposed into discrete gates.
We start by getting one of the two logical backends (EMU:15Q:LOGICAL_EARLY).
from qiskit_alice_bob_provider import AliceBobLocalProvider
from qiskit import QuantumCircuit, transpile
import numpy as np
ab = AliceBobLocalProvider()
backend = ab.get_backend('EMU:15Q:LOGICAL_EARLY')
We then apply a rx gate, which is not supported by physical backends as it is not bias-preserving, and which is not a native logical operation either.
circ = QuantumCircuit(1,1)
circ.rx(np.pi / 8.0, 0)
circ.measure(0,0)
So, when we transpile the result to our logical backend:
circ = transpile(circ, backend)
print(circ)
We get the following circuit using only native logical gates:
┌───────────────┐┌─────┐┌───┐┌───┐┌───┐┌─────┐┌───┐┌─────┐┌───┐┌───┐┌───┐»
q ┤ Initialize(0) ├┤ Tdg ├┤ H ├┤ T ├┤ H ├┤ Tdg ├┤ H ├┤ Tdg ├┤ H ├┤ T ├┤ T ├»
└───────────────┘└─────┘└───┘└───┘└───┘└─────┘└───┘└─────┘└───┘└───┘└───┘»
c: 1/═════════════════════════════════════════════════════════════════════════»
»
« ┌───┐┌───┐┌───┐┌─────┐┌───┐┌─────┐┌───┐┌───┐┌───┐┌─────┐┌───┐┌───┐┌───┐»
« q ┤ T ├┤ T ├┤ H ├┤ Tdg ├┤ H ├┤ Tdg ├┤ H ├┤ T ├┤ H ├┤ Tdg ├┤ H ├┤ T ├┤ H ├»
« └───┘└───┘└───┘└─────┘└───┘└─────┘└───┘└───┘└───┘└─────┘└───┘└───┘└───┘»
«c: 1/═══════════════════════════════════════════════════════════════════════»
« »
« ┌─────┐┌───┐┌─────┐┌───┐┌─────┐┌───┐┌───┐┌───┐┌───┐┌───┐┌───┐┌───┐┌─────┐»
« q ┤ Tdg ├┤ H ├┤ Tdg ├┤ H ├┤ Tdg ├┤ H ├┤ T ├┤ H ├┤ T ├┤ T ├┤ T ├┤ H ├┤ Tdg ├»
« └─────┘└───┘└─────┘└───┘└─────┘└───┘└───┘└───┘└───┘└───┘└───┘└───┘└─────┘»
«c: 1/═════════════════════════════════════════════════════════════════════════»
« »
« ┌───┐┌───┐┌───┐┌───┐┌───┐┌─────┐┌─────┐┌─────┐┌───┐┌─────┐┌───┐┌───┐┌───┐»
« q ┤ H ├┤ T ├┤ H ├┤ T ├┤ H ├┤ Tdg ├┤ Tdg ├┤ Tdg ├┤ H ├┤ Tdg ├┤ H ├┤ T ├┤ H ├»
« └───┘└───┘└───┘└───┘└───┘└─────┘└─────┘└─────┘└───┘└─────┘└───┘└───┘└───┘»
«c: 1/═════════════════════════════════════════════════════════════════════════»
« »
« ┌───┐┌───┐┌───┐┌───┐┌─────┐┌───┐┌─────┐┌─┐
« q ┤ T ├┤ H ├┤ T ├┤ H ├┤ Tdg ├┤ H ├┤ Tdg ├┤M├
« └───┘└───┘└───┘└───┘└─────┘└───┘└─────┘└╥┘
«c: 1/════════════════════════════════════════╩═
« 0
This circuit may then be executed like any Qiskit circuit:
job = backend.run(circ, shots=1_000)
print(job.result().get_counts())
💡 Note: backend.run() transpiles your circuit if you didn't do it manually, but transpiling yourself enables you to examine the circuit which is actually executed.
Use logical backends to run quantum algorithms.
Don't hesitate to play with the distance, kappa_1, kappa_2 and average_nb_photons settings to change the noise characteristics of your backend and study how this affects your results (read Supported instructions for more details about these parameters and how to set them).
⚠️ Warning: As you'll notice above, the native gate set of our logical backends include a T gate, which is not planned to be a native logical gate in our target architecture.
Our current target logical gate set is Clifford + Toffoli, which has been proved to be universal: https://arxiv.org/pdf/quant-ph/0205115.pdf https://arxiv.org/pdf/quant-ph/0301040.pdf
We are working on a compilation engine which will target Clifford + Toffoli, but our shortcut with the T gate lets you experiment with the logical mode earlier.