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arXiv:2601.02064

Cutting Quantum Circuits Beyond Qubits

Manav Seksaria, Anil Prabhakar

quant-phcs.DCSubmitted Jan 5, 2026• Announced Jan 6, 2026• 0 citations• Revised Jan 29, 2026 (v2)
v1 · Jan 5, 2026v2 · Jan 29, 2026
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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.

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Near-term hardware is constrained by high error rates, small qubit counts, and relatively low output fidelity, making the execution of large, high performance quantum circuits difficult. Circuit partitioning (or circuit cutting) has emerged as a promising approach to circumvent these limitations by decomposing circuits into smaller subcircuits at two-qubit interaction points. However, it remains unclear which classes of circuits benefit the most from partitioning and under what hardware conditions it is most effective. In this work, we evaluate the suitability of quantum circuits for partitioning from three perspectives: improving fidelity, enabling distributed execution, and scaling to larger circuit sizes. Specifically, we compare uncut circuit execution against two circuit partitioning approaches: Qiskit's automatic cut finding technique and a custom performance optimized circuit cutting method. We also measure these across GHZ, QFT, brickwork, and random quantum circuits ranging from 4 to 14 qubits, using mean absolute error of expectation values and overall output fidelity. Our results show that partitioning benefits larger, highly interconnected circuits, with our custom method reducing error by up to 55\% and improve fidelity for GHZ circuits, but degrading performance for brickwork circuits at larger scales.

quant-pharXiv:2604.22664•Apr 27, 2026•0 citations
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 (222--333) 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.
Circuit cutting partitions a large quantum circuit into smaller subcircuits that can be executed independently and recombined by classical post-processing. In classical state-vector simulation with full-state reconstruction, the runtime is governed by a trade-off between reduced subcircuit size and the overheads of exponentially many subcircuits and full-state reconstruction. For equal partitioning, we derive threshold conditions on the number of cuts below which cutting reduces the wall-clock time. State-vector experiments validate the predicted speedup boundary up to 24 qubits, and a runtime breakdown up to 30 qubits identifies crossovers at q≈18q \approx 18q≈18 and q≈22q \approx 22q≈22 where merging overtakes first preprocessing and then subcircuit simulation. As a practical guideline, we show that under a 10-minute wall-clock budget, two-way cutting extends the maximum feasible qubit count by 4 to 6 qubits relative to simulation without cutting.
Quantum computing has the potential to accelerate various fields by solving specific problems significantly faster than classical computers. Solving more complex problems generally requires a larger number of qubits. However, current quantum devices are constrained by limited qubit counts and environmental noise. Quantum circuit cutting bridges the gap between the theoretical requirements of large quantum circuits and the practical limitations of current quantum hardware by decomposing large circuits into smaller subcircuits. Tang et al. introduced CutQC, a framework that reduces the number of generated subcircuits and reconstructs the complete quantum state with limited memory consumption. Despite these advances, CutQC faces performance bottlenecks in classical postprocessing, leading to long execution times. To address this limitation, we propose QCutSim, an efficient simulation-based framework guided by insights from the postprocessing stage. It improves performance through optimized simulation and reconstruction strategies, along with computational optimizations such as vectorization and parallelization. QCutSim demonstrates that even consumer-grade systems can efficiently simulate 100-qubit circuits and achieves a speedup of up to 5.1x compared to prior work on the same hardware. In the worst-case scenario of reconstructing dense solution circuits, QCutSim achieves a speedup of 6 to 8 orders of magnitude.
Quantum computers are becoming a reality thanks to the accomplishments made in recent years. The quantum computers available today offer hundreds of qubits but are still limited in the number of operations they can perform before errors accumulate and the quantum state decays. In regard to the error accumulation, non-local operations such as CX or CZ are main contributors. One promising solution to reduce the number of required non-local operations is to make a more efficient use of the quantum hardware by exploiting the inherent high-dimensional capabilities of quantum systems. In a process called circuit compression, non-local operations between qubits are mapped to local operations in qudits, i.e., higher-dimensional systems. In this work, we present a strategy for enabling quantum circuit compression with the aim of mapping clusters of qubits in a given circuit to the mixed-dimensional qudits of the target hardware. Further, we discuss the principles of circuit compression as well as the physical structure of qubits and qudits, before introducing a new representation that captures the essence of quantum operations, affecting the different logical levels in the quantum states in nodes and edges of a graph. Based on this, we propose an automated approach for mapping qubit circuits of arbitrary gate sets to mixed-dimensional quantum systems, lowering the number of non-local operations. Empirical evaluations confirm the effectiveness of the proposed approach reducing the number of non-local operations by up to 50% for almost half of the cases. Finally, the corresponding source code is available freely at github.com/cda-tdum/qudit-compression.
In the NISQ era, limited qubit resources make it difficult to execute large quantum circuits directly on real hardware. Quantum circuit cutting mitigates this limitation by decomposing a large circuit into smaller subcircuits, but it shifts substantial overhead to classical post-processing. As circuit size, complexity, and cut count increase, reconstruction becomes a major computational and storage bottleneck. This paper presents a CPU+DCU heterogeneous parallel framework for circuit-cutting post-processing reconstruction. Instead of constructing a dense 2n2^n2n-dimensional probability vector or returning only high-probability states, the framework reconstructs the nonzero-probability states in the original output distribution from subcircuit measurement results. It combines heterogeneous CPU+DCU execution with a high/low-word integer representation for global basis-state indices beyond 64 bits and a three-level cooperative storage mechanism spanning device memory, host memory, and out-of-core storage. Experiments on the Songshan supercomputer show that the framework maintains high reconstruction fidelity while achieving up to 259×259\times259× speedup over an optimized serial baseline on linear-cluster states and up to 4×4\times4× speedup over a homogeneous CPU-parallel method on random circuits. The framework can also complete reconstruction tasks at the hundred-qubit scale. These results demonstrate that HPC-oriented heterogeneous reconstruction can effectively alleviate the classical post-processing bottleneck and improve reconstruction scalability.
Decomposing unitary operations into native gates is an essential step for implementing quantum algorithms. For qubit-based devices, where native gates are typically single- and two-qubit operations, a range of decomposition techniques have been developed. In particular, efficient algorithms exist for decomposing exponentials of Pauli strings while taking hardware topology in account. Motivated by the growing interest in qutrit-based quantum computing, we develop analogous decomposition methods for qutrit systems. Specifically, we introduce an algorithm that decomposes the exponential of an arbitrary tensor product of Weyl-Heisenberg operators (plus their Hermitian conjugation) into single- and two-qutrit gates. We further extend this approach to unitaries generated by Gell-Mann string (i.e., a tensor product of Gell-Mann matrices). Since both Gell-Mann matrices and Weyl-Heisenberg operators form (together with identity) complete operator bases of qutrit operators, we can use this result also to decompose any multi-qutrit gate that is diagonal up to single-qutrit rotations. As a practical application, we use our method to decompose the layers of the quantum approximate optimization algorithm for qutrit-based implementations of the graph k-coloring problem. For values of kkk well-suited to qutrit architectures (e.g., k=3k=3k=3 or in general k=3nk=3^nk=3n), our approach yields significantly shallower circuits compared to qubit-based implementations, an advantage that grows with problem size, while also requiring a smaller total Hilbert space dimension. Finally, we also address the routing challenge in qutrit architectures that arises due to the limited connectivity of the devices. In particular, we generalize the Steiner-Gauss method, originally developed to reduce CNOT counts in qubit circuit, to optimize gate routing in qutrit-based systems.
Near-term hardware is constrained by high error rates, small qubit counts, and relatively low output fidelity, making the execution of large, high performance quantum circuits difficult. Circuit partitioning (or circuit cutting) has emerged as a promising approach to circumvent these limitations by decomposing circuits into smaller subcircuits at two-qubit interaction points. However, it remains unclear which classes of circuits benefit the most from partitioning and under what hardware conditions it is most effective. In this work, we evaluate the suitability of quantum circuits for partitioning from three perspectives: improving fidelity, enabling distributed execution, and scaling to larger circuit sizes. Specifically, we compare uncut circuit execution against two circuit partitioning approaches: Qiskit's automatic cut finding technique and a custom performance optimized circuit cutting method. We also measure these across GHZ, QFT, brickwork, and random quantum circuits ranging from 4 to 14 qubits, using mean absolute error of expectation values and overall output fidelity. Our results show that partitioning benefits larger, highly interconnected circuits, with our custom method reducing error by up to 55\% and improve fidelity for GHZ circuits, but degrading performance for brickwork circuits at larger scales.