[Paper] Cutting Quantum Circuits Beyond Qubits

Source: arXiv - 2601.02064v1

Overview

The paper “Cutting Quantum Circuits Beyond Qubits” expands the concept of quantum circuit cutting—splitting large quantum programs into smaller pieces that can run on limited hardware—to heterogeneous quantum registers that mix qubits (2‑level systems) with higher‑dimensional qudits (e.g., qutrits, 3‑level systems). By doing so, the authors show that complex, high‑dimensional quantum algorithms can be simulated or executed on fragmented, low‑memory devices without sacrificing exactness.

Key Contributions

• Generalized cutting framework for mixed‑dimensional registers (qubits + qudits) using tensor products of generalized Gell‑Mann matrices.
• Exact state reconstruction for qubit–qutrit interfaces, achieving a Total Variation Distance (TVD) of 0 within single‑precision floating‑point tolerance.
• Memory‑efficiency demonstration on an 8‑particle, dimension‑8 system, cutting required memory from ~128 MB down to ~64 KB per sub‑circuit.
• Practical validation on both simulated and (where possible) hardware‑connected fragments, confirming that the method works beyond idealized qubit‑only settings.

Methodology

1. Circuit Decomposition – The authors express any non‑local gate acting on heterogeneous registers as a sum of tensor products of local generalized Gell‑Mann operators (the natural basis for d‑level systems).
2. Cutting Procedure – Each term in the decomposition corresponds to a fragment that can be executed independently on a hardware piece that only supports a subset of the full register.
3. Classical Post‑Processing – After running all fragments, the results are combined using a weighted linear combination (the same weights that appear in the decomposition) to reconstruct the global quantum state.
4. Error Analysis – Because the decomposition is exact, the only numerical error stems from finite‑precision arithmetic; the authors verify that single‑precision floating‑point arithmetic yields TVD = 0 for the tested cases.

The approach mirrors classical “divide‑and‑conquer” but respects quantum linearity by expanding gates into a complete operator basis that works for any dimension.

Results & Findings

• Qubit–Qutrit Interface: For circuits that entangle a qubit with a qutrit, the cutting method reproduced the exact output state (TVD = 0) when the fragments were simulated with single‑precision floats.
• Memory Savings: In an 8‑particle system where each particle lives in an 8‑dimensional Hilbert space (total dimension (8^8)), naive simulation would need ~128 MB of memory per full circuit. Cutting the circuit into 8 fragments reduced the per‑fragment memory footprint to ~64 KB, a >2000× reduction.
• Scalability: The authors show that the number of fragments grows linearly with the number of non‑local gates, while the memory per fragment stays bounded by the dimension of the local registers, making the technique viable for larger heterogeneous systems.

Practical Implications

• Hardware‑Fragmented Quantum Clouds: Cloud providers that expose only small qubit or qutrit devices can now jointly run larger heterogeneous algorithms by stitching together results, expanding the effective device size without new physical hardware.
• Hybrid Quantum‑Classical Workflows: Developers can offload high‑dimensional sub‑routines (e.g., qutrit‑based error‑correction or encoding) to specialized simulators while keeping the rest on native qubit hardware, optimizing cost and runtime.
• Memory‑Constrained Simulators: Classical simulation tools (e.g., Qiskit Aer, Cirq) can adopt this cutting technique to simulate larger systems on modest machines, enabling rapid prototyping of high‑dimensional algorithms.
• Algorithm Design: Algorithm engineers may deliberately introduce higher‑dimensional qudits to exploit their richer gate sets, knowing that circuit cutting can mitigate the hardware connectivity constraints.

Limitations & Future Work

• Fragment Overhead: The number of fragments grows with each non‑local gate, potentially leading to a combinatorial explosion of runs for deep circuits.
• Noise Sensitivity: The current study focuses on exact (noise‑free) simulations; extending the method to noisy intermediate‑scale quantum (NISQ) devices will require robust error mitigation strategies.
• Generalization to Arbitrary Dimensions: While the paper demonstrates qubit–qutrit cuts, scaling to even higher dimensions (e.g., ququart, qudit‑d > 5) may encounter practical challenges in operator decomposition and classical post‑processing cost.

Future research directions include adaptive cutting strategies that minimize fragment count, integration with error‑mitigation pipelines, and experimental validation on heterogeneous quantum hardware platforms.

Authors

• Manav Seksaria
• Anil Prabhakar

Paper Information

• arXiv ID: 2601.02064v1
• Categories: quant-ph, cs.DC
• Published: January 5, 2026
• PDF: Download PDF