Circuit cutting

Cut a gate, run the halves, recombine: the sampling overhead and when it pays off.

Advanced14 min read3 sections · 2 questions+45

By the end you will be able to

01Explain a gate cut as a quasi-probability decomposition.
02Compute the sampling overhead for k cuts.
03Work out what a cut of a small circuit costs and returns.

A two-qubit gate that straddles two groups of qubits can be replaced by a weighted sum of products of single-qubit operations on each side. Each term is a circuit you can run on a smaller device; the weights can be negative, which is why it is a quasi-probability decomposition. Expectation values of the original circuit are recovered exactly, on average, from the sub-circuit results.

CNOT = i \sum c_{i} A_{i} \otimes B_{i}, γ = i \sum ∣ c_{i} ∣ = 3, shots \propto γ^{2 k} = 9^{k}

One cut costs 9× the shots for the same variance; two cuts 81×; three 729×. Cutting is for a few cuts on circuits that otherwise would not fit at all.

Worked solution

Cut a GHZ in half

A four-qubit GHZ circuit (H on q0, then CNOTs q0→q1, q1→q2, q2→q3) must run on devices of two qubits. We want ⟨ZZII⟩ and ⟨IIZZ⟩.

1Split the qubits into {q0, q1} and {q2, q3}. Only the CNOT q1→q2 crosses the split, so one gate cut is enough.
2The cut CNOT becomes a weighted sum of local operations on each half, with γ = 3. Every term is a pair of two-qubit circuits.
3Shots for the same precision grow by γ² = 9 for one cut.
4In a GHZ state neighbouring qubits always agree, so the exact values are ⟨ZZII⟩ = ⟨IIZZ⟩ = 1. The weighted halves reproduce these on average.

Answer: One cut, 9× the shots, and both expectation values come back as 1 (up to shot noise). QubitLab explains cutting but does not run it on the shared server; qiskit-addon-cutting does it on your own machine.

Knowledge check

2 questions · one try each counts

Question 1

With three gate cuts, roughly how many more shots are needed for the same precision?

Question 2

What does cutting give you back?

You are reading without signing in. Sign in or continue as guest to take quizzes and climb the ranks.

LearnQC 302Cutting and Quantum MLLesson 1 of 7