Distributed Quantum Circuit Optimisation: Evaluating Global and Local encodings

Majid Haghparast; Maria Gragera Garces

arxiv: 2605.02727 · v2 · submitted 2026-05-04 · 🪐 quant-ph · cs.DC

Distributed Quantum Circuit Optimisation: Evaluating Global and Local encodings

Maria Gragera Garces , Majid Haghparast This is my paper

Pith reviewed 2026-05-12 03:07 UTC · model grok-4.3

classification 🪐 quant-ph cs.DC

keywords distributed quantum computingquantum circuit optimizationcircuit partitioningtelegatecompilation overheadglobal vs local optimizationhybrid optimization

0 comments

The pith

Circuit optimisation does not uniformly benefit distributed quantum execution, with global, local, and hybrid strategies trading off computational, communication, and compilation costs differently.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper compares three ways to optimise quantum circuits before or after they are split across multiple processors in a distributed architecture. Global optimisation is applied to the full circuit first, local optimisation is applied only to the parts on each processor, and a hybrid combines both. Using telegate-based partitioning on a large set of quantum algorithms, the work measures resulting gate counts, circuit depth, non-local gates that require communication, and the time to compile. Global optimisation cuts overall resources and preprocessing time most effectively. Local optimisation unexpectedly lowers communication needs without being designed for it. The hybrid reduces both resource types but takes far longer to prepare.

Core claim

Using a large benchmark suite of quantum algorithms and telegate-based partitioning, the study shows that global circuit optimisation minimises computational resources like gate counts and circuit depth while achieving the lowest compilation overhead. Local optimisation, applied after partitioning, can reduce communication cost by lowering induced non-local gates even without being explicitly communication-aware. The hybrid strategy reduces both computational and communication overheads but incurs significantly higher compilation time.

What carries the argument

Comparison of global optimisation (full circuit before partition), local optimisation (per-partition after), and hybrid strategies, evaluated via telegate-based partitioning that counts non-local gates as communication cost.

If this is right

Global optimisation produces the smallest total gate counts, shallowest depth, and fastest compilation for distributed workloads.
Local optimisation can decrease the number of non-local gates that must cross processors even though it ignores communication during its passes.
Hybrid optimisation simultaneously lowers both computational resources and communication overhead.
No single strategy improves every measured cost at once; each choice creates a distinct trade-off profile.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This suggests distributed quantum compilers could benefit from optimisation passes that explicitly track and minimise non-local operations rather than applying local tweaks after the fact.
The hybrid approach's high compilation time points to a possible bottleneck for scaling to larger algorithms where preprocessing must stay fast.
Results indicate that benchmarks focused only on gate count may miss communication savings available from simple local optimisation.

Load-bearing premise

The large benchmark suite of quantum algorithms and telegate-based partitioning provide a representative approximation of computational, communication, and classical preprocessing costs in real distributed quantum architectures.

What would settle it

Running the same optimised distributed circuits on actual multi-processor quantum hardware and measuring real execution time, communication latency, and error rates against the paper's approximated gate counts and overheads would test whether the reported benefits hold.

Figures

Figures reproduced from arXiv: 2605.02727 by Majid Haghparast, Maria Gragera Garces.

**Figure 1.** Figure 1: Computational resource comparison across optimi view at source ↗

**Figure 2.** Figure 2: Mean inter-QPU communication cost under different view at source ↗

read the original abstract

As distributed quantum architectures begin to emerge, understanding the interaction between quantum circuit optimisation and circuit partitioning becomes increasingly important. In this work, we study how circuit optimisation influences distributed quantum workloads under system-level trade-offs. We compare three compilation strategies (global optimisation, local optimisation, and a hybrid approach) across a large benchmark suite of quantum algorithms. Using telegate-based partitioning, we evaluate the resulting distributed circuits in terms of gate counts, circuit depth, the number of induced non-local gates, and compilation overhead, thereby approximating computational, communication, and classical preprocessing costs. Our results show that circuit optimisation does not uniformly benefit distributed execution. Global optimisation minimises computational resources and achieves the lowest compilation overhead. Local optimisation can reduce communication cost even though it is not explicitly communication-aware. The hybrid strategy can simultaneously reduce both computational and communication overhead, but at the expense of significantly increased compilation time.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper compares global, local, and hybrid circuit optimizations for telegate-partitioned distributed quantum systems and reports non-uniform benefits across resources, communication, and compilation time, but the abstract alone makes those results impossible to verify.

read the letter

The one or two things to take away from this paper are that optimization strategies for quantum circuits do not all help distributed execution in the same way, and that a hybrid global-local approach can balance computational and communication costs but at the price of much longer compilation times. They reach this by testing global optimization, local optimization, and the hybrid on a large benchmark suite of quantum algorithms, using telegate-based partitioning to split the circuits across multiple devices. What the paper does is apply these known optimization techniques to the specific setting of distributed quantum computing and measure the outcomes in terms of total gates, circuit depth, how many non-local gates get created, and the time spent compiling. This gives a practical view of the trade-offs between reducing computation, lowering communication needs, and the classical overhead of doing the optimization itself. The finding that local optimization can still cut communication costs even without being communication-aware is a useful observation. The work is new in the sense that it provides this side-by-side comparison under telegate partitioning, which is a realistic way to handle distributed systems where qubits can't move freely between processors. It credits the idea that you have to consider the full system costs rather than optimizing in isolation. The main soft spot is that we only have the abstract. There are no details on the exact optimization algorithms used, how the partitioning is done, what the benchmark circuits are, or any numbers from the experiments. Without raw data, error bars, or the code, it's impossible to judge whether the benchmark suite really represents real distributed quantum workloads or if the metrics accurately capture communication and preprocessing costs. The claims sound reasonable on the surface, but they can't be checked for accuracy or reproducibility right now. This paper is for people working on quantum circuit compilers and those planning for near-term distributed quantum hardware. A reader who wants to understand the practical implications of optimization choices in multi-processor quantum systems would find the high-level results interesting, even if they can't dig into the evidence yet. I would bring this to a reading group only after the full paper is available with the experimental setup and data. It probably deserves peer review in its full form because the questions it asks are relevant to an emerging area, and empirical comparisons like this can guide future work if the methodology is sound. Right now, with just the abstract, it would be better to wait for more details before investing referee time.

Referee Report

2 major / 1 minor

Summary. The manuscript examines the effects of quantum circuit optimization on distributed quantum execution under telegate-based partitioning. It compares three strategies—global optimization, local optimization, and a hybrid approach—across a large benchmark suite of quantum algorithms. The evaluation uses metrics of gate counts, circuit depth, induced non-local gates, and compilation overhead to approximate computational, communication, and classical preprocessing costs. The central claim is that optimization does not uniformly benefit distributed circuits: global optimization minimizes computational resources and compilation overhead, local optimization reduces communication cost despite not being communication-aware, and the hybrid strategy reduces both computational and communication overhead at the expense of significantly higher compilation time.

Significance. If the reported empirical trade-offs are reproducible and the benchmark suite is representative, the work would offer useful guidance on selecting optimization strategies for emerging distributed quantum architectures, clarifying that global, local, and hybrid approaches produce distinct impacts on resource and overhead metrics. However, the absence of any methodology, data, or implementation details in the provided manuscript makes it impossible to assess whether these distinctions are correctly measured or generalizable.

major comments (2)

Abstract: the manuscript asserts specific comparative outcomes ('Global optimisation minimises computational resources...', 'Local optimisation can reduce communication cost...', 'The hybrid strategy can simultaneously reduce both...') but supplies no methodology, benchmark list, optimization implementations, partitioning algorithm, metric definitions, raw data, error bars, or statistical analysis, so the claims cannot be verified or reproduced from the text.
Abstract: the evaluation is said to approximate 'computational, communication, and classical preprocessing costs' via gate counts, depth, non-local gates, and overhead, yet no concrete definitions, formulas, or measurement procedures are given, leaving open whether the reported non-uniform benefits follow from the chosen metrics or from unstated assumptions about the telegate model.

minor comments (1)

The title refers to 'encodings' while the abstract discusses 'optimisation' and 'compilation strategies'; a brief clarification of how the two concepts relate would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their review and for highlighting the need for greater clarity on methodology and metrics. We address each major comment below. The full manuscript contains the benchmark details, implementations, and metric definitions referenced in the abstract; we are prepared to revise the abstract for improved self-containment where feasible.

read point-by-point responses

Referee: Abstract: the manuscript asserts specific comparative outcomes ('Global optimisation minimises computational resources...', 'Local optimisation can reduce communication cost...', 'The hybrid strategy can simultaneously reduce both...') but supplies no methodology, benchmark list, optimization implementations, partitioning algorithm, metric definitions, raw data, error bars, or statistical analysis, so the claims cannot be verified or reproduced from the text.

Authors: The abstract summarises the principal empirical outcomes of the study. The complete manuscript specifies the benchmark suite, the three optimisation strategies and their implementations, the telegate-based partitioning procedure, all metric definitions, and the full set of results including any statistical considerations. We can revise the abstract to include a short clause directing readers to the relevant sections for full reproducibility. revision: partial
Referee: Abstract: the evaluation is said to approximate 'computational, communication, and classical preprocessing costs' via gate counts, depth, non-local gates, and overhead, yet no concrete definitions, formulas, or measurement procedures are given, leaving open whether the reported non-uniform benefits follow from the chosen metrics or from unstated assumptions about the telegate model.

Authors: The main text defines each proxy metric explicitly: gate count and depth for computational cost, number of induced non-local gates for communication cost under the telegate model (where non-local operations are realised via remote gates), and measured compilation time for classical preprocessing overhead. These choices follow directly from the telegate execution model described in the paper. We will add a brief clarifying sentence to the abstract if length permits. revision: partial

Circularity Check

0 steps flagged

Empirical benchmark evaluation exhibits no circularity

full rationale

The paper's central claims consist of direct empirical observations from comparing global, local, and hybrid optimization strategies across a benchmark suite under telegate-based partitioning, using measured metrics of gate counts, depth, non-local gates, and overhead. No equations, derivations, fitted parameters, predictions, or self-citations are present in the available text that would reduce any result to its inputs by construction. The evaluation is self-contained against external benchmarks and does not invoke uniqueness theorems, ansatzes, or renamings that loop back to prior assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that telegate partitioning and the chosen metrics validly approximate real distributed quantum costs, plus the representativeness of the benchmark suite; no free parameters or invented entities are evident from the abstract.

axioms (1)

domain assumption Telegate-based partitioning is a valid model for distributed quantum computation costs.
Invoked to evaluate non-local gates and communication overhead in the distributed setting.

pith-pipeline@v0.9.0 · 5419 in / 1339 out tokens · 82352 ms · 2026-05-12T03:07:12.009110+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Our results show that circuit optimisation does not uniformly benefit distributed execution. Global optimisation minimises computational resources and achieves the lowest compilation overhead. Local optimisation can reduce communication cost even though it is not explicitly communication-aware.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Using telegate-based partitioning, we evaluate the resulting distributed circuits in terms of gate counts, circuit depth, the number of induced non-local gates, and compilation overhead

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages

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A. Barencoet al., “Elementary gates for quantum computation,”Phys- ical review A, 1995

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Cognac: Circuit optimization via gradients and noise- aware compilation,

F. V oichicket al., “Cognac: Circuit optimization via gradients and noise- aware compilation,”arXiv preprint:2311.02769, 2023

work page arXiv 2023

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Automated optimization of large quantum circuits with continuous parameters,

Y . Namet al., “Automated optimization of large quantum circuits with continuous parameters,”npj Quantum Information

work page

[4] [4]

Optimising quantum circuits is generally hard,

J. van de Wetering and M. Amy, “Optimising quantum circuits is generally hard,”arXiv preprint:2310.05958, 2023

work page arXiv 2023

[5] [5]

Exact quantum circuit optimization is co-nqp- hard,

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work page arXiv 2025

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F. Zilket al., “Breaking down quantum compilation: Profiling and identifying costly passes,” in2025 IEEE ISVLSI

work page

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Reducing the compilation time of quantum circuits using pre-compilation on the gate level,

N. Quetschlichet al., “Reducing the compilation time of quantum circuits using pre-compilation on the gate level,” inQCE, 2023

work page 2023

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Optimized compiler for distributed quantum comput- ing,

D. Cuomoet al., “Optimized compiler for distributed quantum comput- ing,”ACM Transactions on Quantum Computing, 2023

work page 2023

[9] [9]

Efficient gate reordering for distributed quantum compiling in data centers,

R. Mengoniet al., “Efficient gate reordering for distributed quantum compiling in data centers,” inQCE, 2025

work page 2025

[10] [10]

Distributed quantum error mitigation: Global and local zne encodings,

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work page 2026

[11] [11]

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Automated distribution of quantum circuits via hypergraph partitioning,

P. Andres-Martinez and C. Heunen, “Automated distribution of quantum circuits via hypergraph partitioning,”Physical Review A

work page

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Review of distributed quantum computing: From single qpu to high performance quantum computing,

D. Barralet al., “Review of distributed quantum computing: From single qpu to high performance quantum computing,”Computer Science Review, 2025

work page 2025

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Simulating large quantum circuits on a small quantum computer,

T. Penget al., “Simulating large quantum circuits on a small quantum computer,”Physical review letters, 2020

work page 2020

[15] [15]

Circuit knitting facing exponential sampling-overhead scaling bounded by entanglement cost,

M. Jinget al., “Circuit knitting facing exponential sampling-overhead scaling bounded by entanglement cost,”Physical Review A

work page

[16] [16]

Approximate quantum circuit reconstruction,

D. Chenet al., “Approximate quantum circuit reconstruction,”QCE, 2022

work page 2022

[17] [17]

A lazy resynthesis approach for simultaneous t gate and two-qubit gate optimization of quantum circuits,

M.-T. Lauet al., “A lazy resynthesis approach for simultaneous t gate and two-qubit gate optimization of quantum circuits,”arXiv preprint:2508.04092, 2025

work page arXiv 2025

[18] [18]

Towards optimal topology aware quantum circuit synthesis,

M. G. Daviset al., “Towards optimal topology aware quantum circuit synthesis,” inQCE, 2020

work page 2020

[19] [19]

Optimized compilation for distributed quantum computing,

M. Bandiniet al., “Optimized compilation for distributed quantum computing,”arXiv preprint:2602.24062, 2026

work page arXiv 2026

[20] [20]

Autocomm: A framework for enabling efficient commu- nication in distributed quantum programs

A. Wuet al., “Autocomm: A framework for enabling efficient commu- nication in distributed quantum programs.” IEEE, 2022

work page 2022

[21] [21]

Distributing circuits over heterogeneous, modular quantum computing network architectures,

P. Andres-Martinezet al., “Distributing circuits over heterogeneous, modular quantum computing network architectures,”Quantum Science and Technology, 2024

work page 2024

[22] [22]

A modular quantum compilation framework for distributed quantum computing,

D. Ferrariet al., “A modular quantum compilation framework for distributed quantum computing,”IEEE TQE, 2023

work page 2023

[23] [23]

Mqt bench: Benchmarking software and design automation tools for quantum computing,

N. Quetschlichet al., “Mqt bench: Benchmarking software and design automation tools for quantum computing,”Quantum, 2023

work page 2023

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Open source software in quantum computing,

M. Fingerhuthet al., “Open source software in quantum computing,” PloS one, 2018

work page 2018

[25] [25]

On the distortion of partitioning performance by random quantum circuits,

M. Gragera Garces, “On the distortion of partitioning performance by random quantum circuits,” inDisQIC, ICDCS, 2026

work page 2026

[26] [26]

High-quality hypergraph partitioning,

S. Schlaget al., “High-quality hypergraph partitioning,”ACM Journal of Experimental Algorithmics, 2023

work page 2023

[27] [27]

Set transpiler optimization level,

IBM Corporation, “Set transpiler optimization level,” quantum.cloud.ibm.com/docs/en/guides/set-optimization, feb 2025

work page 2025

[28] [28]

Entanglement-efficient distribution of quantum circuits over large-scale quantum networks,

F. Burtet al., “Entanglement-efficient distribution of quantum circuits over large-scale quantum networks,” inQCE, 2025

work page 2025

[29] [29]

Non-identity-check is qma complete,

D. Janzinget al., “Non-identity-check is qma complete,”International Journal of Quantum Information, 2005

work page 2005

[30] [30]

tket: a retargetable compiler for nisq devices,

S. Sivarajahet al., “tket: a retargetable compiler for nisq devices,” Quantum Science & Technology, 2021

work page 2021