Cutting Quantum Circuits Beyond Qubits

TL;DR

This work addresses the scalability bottlenecks of quantum computing by extending circuit cutting to heterogeneous registers composed of mixed-dimensional qudits. It introduces a decomposition framework based on generalized Gell-Mann matrices to express non-local interactions, enabling high-dimensional gates (e.g., CX) to be implemented as a sum of local operations across disconnected hardware fragments. The approach achieves exact state reconstruction with TVD $0$ in both homogeneous and heterogeneous cuts and demonstrates substantial memory savings (from $128$ MB to $64$ KB per subcircuit) in an 8-qudit stress test, underpinning a practical path toward distributed quantum computing. Future directions include optimizing the decomposition basis to reduce sampling overhead and enabling multiple simultaneous cuts to further enhance scalability.

Abstract

We extend quantum circuit cutting to heterogeneous registers comprising mixed-dimensional qudits. By decomposing non-local interactions into tensor products of local generalised Gell-Mann matrices, we enable the simulation and execution of high-dimensional circuits on disconnected hardware fragments. We validate this framework on qubit--qutrit ($2$--$3$) interfaces, achieving exact state reconstruction with a Total Variation Distance of 0 within single-precision floating-point tolerance. Furthermore, we demonstrate the memory advantage in an 8-particle, dimension-8 system, reducing memory usage from 128 MB to 64 KB per circuit.

Figures (2)

• Figure 1: sQED circuit with a horizontal cut between qudits of dimension 2 and 3.
• Figure 2: The scaling of TVD and simulation time with increasing system size for different truncation thresholds shows us that even when we truncate coefficients up to $10^{-2}$, while we can maintain a low TVD, there is not much time saved. However, for higher truncation thresholds, we can see a significant reduction in simulation time at the cost of increased TVD.