Joint Cutting for Hybrid Schrödinger-Feynman Simulation of Quantum Circuits

TL;DR

The paper tackles the exponential memory/time barrier in classical quantum circuit simulation by enhancing Hybrid Schrödinger-Feynman (HSF) simulation with a joint cuttingStrategy. By grouping gates into blocks and applying Schmidt decomposition collectively, the authors reduce the number of paths $n_p$ that must be explored, improving efficiency over standard HSF and Schrödinger-style methods for suitable circuits. They provide theoretical bounds, discuss preprocessing overhead, and demonstrate significant empirical speedups on QAOA Max-Cut instances, illustrating that joint cutting extends the practical reach of HSF to structured circuits. The work offers practical guidance for implementing joint cuts and contributes to circuit cutting literature, with code available for reuse.

Abstract

Despite the continuous advancements in size and robustness of real quantum devices, reliable large-scale quantum computers are not yet available. Hence, classical simulation of quantum algorithms remains crucial for testing new methods and estimating quantum advantage. Pushing classical simulation methods to their limit is essential, particularly due to their inherent exponential complexity. Besides the established Schrödinger-style full statevector simulation, so-called Hybrid Schrödinger-Feynman (HSF) approaches have shown promise to make simulations more efficient. HSF simulation employs the idea of "cutting" the circuit into smaller parts, reducing their execution times. This, however, comes at the cost of an exponential overhead in the number of cuts. Inspired by the domain of Quantum Circuit Cutting, we propose an HSF simulation method based on the idea of "joint cutting" to significantly reduce the aforementioned overhead. This means that, prior to the cutting procedure, gates are collected into "blocks" and all gates in a block are jointly cut instead of individually. We investigate how the proposed refinement can help decrease simulation times and highlight the remaining challenges. Experimental evaluations show that "joint cutting" can outperform the standard HSF simulation by up to a factor $\approx 4000\times$ and the Schrödinger-style simulation by a factor $\approx 200\times$ for suitable instances. The implementation is available at https://github.com/cda-tum/mqt-qsim-joint-cutting.

Figures (6)

• Figure 1: Quantum circuit (a) and the corresponding gates (b) for a Bell state preparation.
• Figure 2: Bipartite representation of the CNOT gate. The orange, dotted line indicates the "cut".
• Figure 3: (a) An exemplary circuit of which different depths $d$ are considered. For $d=2$ only the two leftmost gates are included and so on. The dotted, orange line indicates the location of the cut. (b) For different depths $d$, the number of paths $n_p$ increases more rapidly with standard cutting compared to joint cuts, which saturate. The steeper slope from $d=3$ to $d=4$ for standard cutting is due to the SWAP gate's Schmidt rank $r=4$, whereas the others have $r=2$.
• Figure 4: Illustration of reshaping the matrix of $A$ and performing an SVD.
• Figure 5: A "cascade" of CNOT gates.

Theorems & Definitions (4)

• Example 1
• Example 2
• Example 3
• Example 4