Qiskit - Parallelization of a quantum circuit

Question

I have the following circuit, which is the implementation of a quantum oracle for a fuzzy inference engine:

As you can see this is composed of blocks, between barriers, which can be considered independent. Since the depth of the transpiled circuit is prohibitive (more than 1000), I am trying to reduce it at the expense of the width by executing the blocks in parallel, I mean leveraging the available 127 qubits available on IBM real backend. Do you know if there's a way in Qiskit to automatically do it?

EDIT: I managed to decompose my circuit in subcircuits and assemble them in parallel as in the following image. For doing that I defined a new quantum circuit and used the function quantum_circuit.append(subcircuit) specifying the correct qubits to use for each subcircuit. Sadly I found out that the result from this new circuit is even worse than the one from the original one. Is it because of the width?

Answer 1

A simple and effective way to reduce the depth of this circuit is to use ancilla qubits.

First add ancilla register and add it to your circuit:

anc = QuantumRegister(2, 'anc')
circ = QuantumCircuit(theta, omega, anc, current, cr)

then, change the mode of every multi-controlled NOT gate to be 'v-chain' and pass the ancilla qubits. For example,

circ.mcx(theta[:] + omega[:], current[2], ancilla_qubits=anc, mode='v-chain')

When I transpiled the original circuit against FakeTorino I got

Depth: 1690, 2Q Depth: 558

and when I transpiled the circuit with ancillas I got

Depth: 882, 2Q Depth: 223

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Note that: if the input state to omega register is actually the vector state $\left[{\begin{array}{*{20}{c}}1 & 0 & 0 & 0\end{array}}\right]$, you can replace the multi-controlled NOTs with Toffoli gates which will reduce the circuit depth dramatically.