Low overhead circuit cutting with operator backpropagation

TL;DR

The paper tackles the scalability limits of circuit cutting caused by exponential overheads, by integrating operator backpropagation (OBP) with circuit cutting and optimizing the backpropagation parameter via simulated annealing. The authors demonstrate substantial reductions in circuit executions—about $3x$ for VQE and $10x$ for Hamiltonian simulation—while maintaining or improving accuracy, and show consistent gains across additional Benchpress circuits and various observables. A key contribution is the SA-based method to select the optimal max_qwc_group, which minimizes classical overhead and avoids pathological increases in overhead from naive OBP usage. Overall, the approach broadens the practical applicability of circuit cutting to deeper and wider quantum circuits on near-term hardware, with a largely generalizable procedure for parameter optimization.

Abstract

Current quantum computers suffer from noise due to lack of error correction. Several techniques to mitigate the effect of noise have been studied, in particular to extract the expectation value of observables. One such technique, circuit cutting, partitions large circuits into smaller, less noisy subcircuits, but the exponential increase in the number of circuit executions limits its scalability. Another method, operator backpropagation (OBP) reduces circuit depth by classically simulating parts of it, yet often escalates the number of circuit executions by some factor due to additional non-commuting terms in the updated observable. This paper introduces an optimized approach for minimizing noise in quantum circuits using operator backpropagation (OBP) combined with circuit cutting. We demonstrate that the strategic use of OBP with circuit cutting can mitigate the execution overhead. By employing simulated annealing, our proposed method identifies the optimal backpropagation parameter for specific circuits and observables, maximizing resource reduction in cutting. Results show a 3x and 10x decrease in resource requirements for Variational Quantum Eigensolver and Hamiltonian simulation circuits respectively, while maintaining or even enhancing accuracy. This approach also yields similar savings for other circuits from the Benchpress database and various observable weights, providing an efficient method to lower circuit cutting overhead without compromising performance.

Figures (9)

• Figure 1: (a) A 3-qubit circuit with gates $U$ and $V$, and interaction on the middle qubit (green triangles), rewritten as two 2-qubit circuits with a virtual break between them. (b) Cutting a 2-qubit gate $U_{AB}$ into multiple instances of single-qubit gates $F_i^{A}$ and $F_i^{B}$. The coefficients $a_i$ form a quasi-probability distribution, i.e., $\sum_i a_i = 1$, but it is not necessary that $0 \leq a_i \leq 1$$\forall$$i$.
• Figure 2: A circuit unitary $U$, virtually divided into $U = U_CU_Q$ with $O$ as the observable whose expectation value is to be calculated. After backpropagation $U_CU_Q$ becomes $U_Q$ having lower depth and updated observable as $O_{new} = U_C^{\dagger}OU_C$
• Figure 3: The number of cuts required for a 3-qubit circuit for disjoint partitioning vs that required when OBP is used before cutting.
• Figure 4: A 6-qubit EfficientSU2 circuit
• Figure 5: A comparative analysis of quantum resource overhead in a 6-qubit VQE for the original (uncut) circuit, vs vanilla circuit cutting (cut) and improving circuit cutting with OBP (Cut+OBP). The values inside the bars indicate the number of quantum circuit executions required for each case.