DistributedEstimator: Distributed Training of Quantum Neural Networks via Circuit Cutting

Prabhjot Singh; Adel N. Toosi; Rajkumar Buyya

cs.DCFeb 18, 2026

DistributedEstimator: Distributed Training of Quantum Neural Networks via Circuit Cutting

Authors: Prabhjot Singh, Adel N. Toosi, Rajkumar Buyya

Organizations: Quantum Cloud Computing and Distributed Systems (qCLOUDS) Lab, School of Computing and Information Systems, The University of Melbourne, Melbourne, VIC, 3010, Australia

Abstract

Circuit cutting decomposes a large quantum circuit into smaller subcircuits executed independently; expectation values are recovered by classically combining subcircuit outcomes. Prior work characterises cutting overhead via subcircuit counts and sampling complexity, but its end-to-end impact on iterative, estimator-driven training pipelines remains under-measured from a systems perspective. We propose DistributedEstimator, a cut-aware estimator execution pipeline that treats circuit cutting as a staged distributed workload, instrumenting each query across four phases: partitioning, subexperiment generation, parallel execution, and classical reconstruction. Using logged runtime traces and learning outcomes on two binary classification workloads (Iris and MNIST), we quantify cutting overheads, scaling limits, and sensitivity to injected stragglers, and assess whether accuracy and robustness are preserved under matched training budgets. Reconstruction dominates per-query time -- a median of 53% and 95th percentile of 58% at three cuts -- bounding achievable speed-up under parallelism. Despite this, test accuracy is fully preserved on Iris and maintained without systematic degradation on MNIST across all cut configurations. Robustness under Gaussian noise and FGSM perturbations is similarly preserved, with several configurations matching or improving on the uncut baseline. Exponential growth of subexperiment counts ( ${O}(9^c)$ for CNOT-based decomposition) is a fundamental barrier limiting practical experimentation to small qubit counts. These results establish that practical scaling for learning workloads requires reducing and overlapping reconstruction, scheduling policies for barrier-dominated critical paths, and computationally efficient reconstruction strategies for larger qubit counts.

Figures & tables

Figure 1: Independent subcircuits generated by cutting a circuit. The dashed line indicates the cut location; the resulting fragments (left and right subcircuits) can be executed independently on smaller devices. Each cut exponentially increases the number of subexperiments and reconstruction terms.

Work	Approach	Overhead	Training	Hardware	Bottleneck
		analysis	integration	evaluation	identification
Peng et al. [ 31 ]	T	A	$\times$	$\times$	$\times$
Tang et al. (CutQC) [ 43 ]	TF	A+E	$\times$	✓	$\times$
Piveteau & Sutter [ 33 ]	T	A	$\times$	$\times$	$\times$
Lowe et al. [ 24 ]	T	A	$\times$	$\times$	$\times$
Harrow & Lowe [ 14 ]	T	A	$\times$	$\times$	$\times$

Table 1: Comparison with key related work on circuit cutting. Approach : theoretical analysis (T), end-to-end toolflow (TF), or systems profiling (SP). Overhead analysis : asymptotic bounds (A), empirical measurement (E), or both. Training integration : whether cutting is embedded in an iterative variational training loop. Hardware evaluation : whether results on a real QPU are reported. Bottleneck identification : whether specific pipeline stages are measured and identified as scaling limiters.

Figure 2:

Figure 3:

Qubits	Parts	Cuts	$K$	$T_{\mathrm{part}}$ (ms)	$T_{\mathrm{gen}}$ (ms)
4	2	1	12	1.3	2.7
8	2	1	12	1.5	4.1
12	2	1	12	2.1	5.7
16	2	1	12	2.4	7.3
12	3	2	108	2.1	33.1
12	4	3	864	2.4	218.7

Table 2:

Panel of Figure 4 — Figure 4: Training time increases substantially with cut count due to subexperiment expansion and reconstruction overhead.

Panel of Figure 5 — Figure 5: Bars report speed-up at 16 workers relative to 1 worker for matched pairs. Speed-up near or below 1 indicates reconstruction overhead dominates.

#cuts	$n$	median $T_{\mathrm{rec}}/T_{\mathrm{total}}$	p95 $T_{\mathrm{rec}}/T_{\mathrm{total}}$
1	41	0.430	0.474
2	28	0.489	0.533
3	5	0.530	0.580

Table 3: RQ2: Reconstruction share (

T_{\mathrm{rec}}/T_{\mathrm{total}}

) from estimator-call summaries under clean execution ( straggler_delay_s

=0.0

). The monotonic increase with cut count confirms that reconstruction progressively dominates per-query time.

Panel of Figure 6 — Figure 6: Bars report slowdown at $p=0.2$ relative to $p=0.0$ . Reconstruction-dominated configurations show lower sensitivity to execution-side stragglers.

Panel of Figure 7 — Figure 7: On Iris, accuracy is invariant across cut settings. On MNIST, accuracy is not systematically degraded by cutting.

Panel of Figure 8 — Figure 8: Bars report mean accuracy over non-zero perturbation magnitudes (Gaussian and FGSM). Robustness is not systematically degraded by cutting.

Config	$K$	$T_{\mathrm{exec}}^{\mathrm{wall}}$ (s)	$t_{\mathrm{run}}$ (s)	$T_{\mathrm{rec}}$ (s)	QPU Acc.
No cut (AAAA)	10	10.73	0.00	0.028	100%
1 cut (AABB)	120	52.52	9.27	0.195	100%
2 cuts (AABC)	1080	458.84	367.45	1.676	100%

Table 4: Real-hardware validation on ibm_kingston (IBM Heron r2, 156 qubits), Iris binary task, 4 qubits, 1024 shots, train-on-simulator/evaluate-on-hardware.

K

is the number of executed subexperiment circuits per evaluation round;

T_{\mathrm{exec}}^{\mathrm{wall}}

includes queueing and chunked submission,

t_{\mathrm{run}}

is on-device execution time,

T_{\mathrm{rec}}

is classical reconstruction. Accuracy and robustness are identical on simulator and QPU.

Quantum Machine Learning

Quantum machine learning uses quantum circuits and quantum data to build learning algorithms and study their computational and statistical limits.

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How Much Reconstruction Does Quantum Machine Learning Need? Late Fusion of Independently Trained Quantum Subcircuits

Prabhjot Singh, Adel N. Toosi, Rajkumar Buyya

Quantum Cloud Computing and Distributed Systems (qCLOUDS) Lab, School of Computing and Information Systems, The University of Melbourne, Melbourne, VIC, 3010, Australia

Late Fusion Quantum Machine Learning Hybrid Quantum-Classical ML Quantum Neural Networks

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Circuit cutting lets a large quantum neural network (QNN) run as independent subcircuits on small devices, but rebuilding its outputs by reconstruction carries a classical sampling overhead exponential in the number of cuts - the dominant runtime cost in prior work. We ask whether, for machine-learning tasks, this step is necessary, and replace it with late fusion: each subcircuit is trained and measured independently, and a small classical head combines their outputs - a linear-cost, decision-level combination borrowed from multimodal learning. To characterize the trade-off we introduce a quantumness dial

Q

, a tunable reconstruction budget interpolating from pure fusion to full reconstruction, and a cut-entanglement diagnostic that indicates how much reconstruction a task needs (Spearman

ρ=0.59

over

104

runs). Across synthetic and standard datasets, independently trained late fusion matches full reconstruction accuracy within

0.04

at every point of the controlled sweep and on every classical benchmark, at exponentially lower cost; it is also markedly more robust to shot and device noise. Controlled entangled-data experiments locate the boundary where fusion must fail. We do not claim advantage over classical machine learning - consistent with recent benchmarking, quantum offers no accuracy edge on these datasets. Late fusion is thus an efficient, noise-robust, self-characterizing alternative to reconstruction for circuit-cutting QML.

Abstract

Quantum Machine Learning

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