GHZ

This repo contains some tests on creating GHZ states using Qiskit.

For this project, the idea was to explore some different techniques to create big GHZ states.

The techniques I used were:

• circuit knitting
• topology mapping
• circuit transpilation (using Qiskit PassManager and Sampler)

In total, 4 circuits were built mixing some of these techniques.

Circuits

5 qubits GHZ - notebook

This one was the first test done with circuit knitting, using the cutqc module from circuit knitting toolbox package.

Here the circuit was cut in 2 separated parts, measured and them joined together.

cuts	exported data
subcircuit 0	cuts
subcircuit 1	probabilities
	reconstructed probabilities

16 qubits GHZ - notebook

The second is a 16 qubits circuit, following the topology of IBM's Guadalupe backend. After mapping each qubit connection, the resulting distribution after simulating was:

This one, was also cut using cutqc giving the following results:

cuts	exported data
subcircuit 0	cuts
subcircuit 1	probabilities
subcircuit 2	reconstructed probabilities

28 qubits GHZ - notebook

The 28 qubits version was based on IBM's Cambridge backend, however this one wasn't executed due to hardware issues. Nevertheless, some cuts were done.

cuts	exported data
subcircuit 0	cuts
subcircuit 1	probabilities
subcircuit 2
subcircuit 3

127 qubits GHZ - notebook

The biggest one, is based on IBM's Osaka backend. This one, was transpiled and executed on real hardware, the outcomes were the following:

These results seem really wrong, once the expected was nearly 50% of probability for $|00000...0\rangle$ and 50% for $|11111...1\rangle$. However, due the amount of errors for cx gates, it's probably the accurate result for a real device.

This effect can be seem in a local test executed with 20 qubits.

Even that the extreme states are with high probability, it tends to deviate at each qubit addition.