Automatic cuts

QCut comes with functionality for automatically finding good cut locations that can place both wire and gate cuts. The number of partitions, the size of the partitions, and the type of cuts can be specified.

Under the hood QCut uses pymetis to find good cut locations based on the circuit’s graph representation.

from qiskit import QuantumCircuit
from qiskit.quantum_info import SparsePauliOp
import QCut as ck
from QCut import find_cuts, CutOptions

circuit = QuantumCircuit(6)
for qubit in range(6):
    circuit.h(qubit)
for control, target in [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5)]:
    circuit.rzz(0.8, control, target)
for qubit in range(6):
    circuit.rx(0.6, qubit)

observables = SparsePauliOp(["IIIIZZ", "IIIZZI", "IZZIII", "ZZIIII"])

options = CutOptions(
   finder_num_partitions=2,
   finder_cut_mode="both",
)

cut_circuit = find_cuts(circuit, options=options)

print(cut_circuit.cut_locations)
print([subcircuit.num_qubits for subcircuit in cut_circuit.subcircuits])

estimated_expectation_values = ck.run_cut_circuit(cut_circuit, observables)

Nothing here says where to cut. The finder settles on the single rzz in the middle of the chain, splitting the six qubits into two halves of three for 12 experiment circuits. Cutting a wire there instead would cost \(\gamma = 4\) against roughly 2.4 for that gate, which is the sort of choice finder_cut_mode="both" exists to make; restricting it to "wire" or "gate" forces one kind.

finder_num_partitions asks for a number of pieces, and finder_max_qubits asks instead for a size limit per piece, either as one number for all of them or as a list with one entry per partition. At least one of the two has to be given.

How cuts are costed

METIS minimises the sum of the weights of the edges it cuts, but the sampling overhead of a set of cuts is the product of their \(\gamma\) values. Taking the logarithm turns one into the other, so each edge is weighted by \(\log\gamma\) rather than by \(\gamma\), and the partitioner then optimises the cost that actually matters.

A wire cut weighs \(\log 4\), and a gate cut weighs the logarithm of its own \(\gamma\), so an rzz with a small angle is correctly treated as nearly free. A cut whose \(\gamma\) is exactly 1 costs no shots at all, but it still adds circuits, so its weight floors at one rather than zero.

One thing the weights cannot express is that parallel rotation gates get cheaper when cut together, since that is a property of a set of edges rather than of any one edge. Choosing between candidate partitions ————————————–

METIS minimises the weighted edge cut. With log gamma weights that is exactly the true cost of a plan, right up until two cuts share a decomposition. A joint rotation bundle or a communicating block of wires costs less than the product of its parts, and METIS cannot know that. It also returns only the partitioning that scored best by its own measure, discarding the rest.

So the finder asks for one partitioning per seed, builds each one out in full, and costs the finished plans with plan_cost(), which does see the bundles. The cheapest wins. CutOptions.finder_candidates (default 5) sets how many to try, and because the seeds are consecutive a larger set contains the smaller one, so raising it cannot give a worse answer.

Meeting a qubit budget

A budget has to be asked for rather than repaired for. The graph METIS partitions has one node per wire segment, so several nodes belong to one qubit and balancing node counts says nothing about how many qubits a partition ends up holding. Each of a qubit’s nodes therefore carries an equal share of one qubit’s worth, which makes a partition’s weight its qubit count, and max_qubits becomes the share each partition may hold. A straddling qubit counts in both, which is what a wire cut costs anyway.

The weighting only applies when there is a budget. With none, an unbalanced split is often cheaper, so forcing balance would make that case worse.

find_cuts still applies joint cutting to whatever cuts it settles on, it just does not actively steer the partitioner towards cut sets that would bundle well.