arxiv: 2605.09580 · v2 · submitted 2026-05-10 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

Estimating The Energy Consumption of Quantum Computing from A Full System Aspect

Di Wu, Kwanming Yu, Ozgur Ozan Kilic, Siyuan Niu

Authors on Pith no claims yet

Pith reviewed 2026-05-13 06:48 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum computing energyNISQfault tolerant quantum computingquantum error mitigationquantum error correctionsystem energy modelhigh performance computing

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The pith

A full-system energy model shows NISQ costs dominated by error mitigation sampling and FTQC costs by physical qubit overhead.

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

This paper introduces a first-order full-system energy model for quantum computing that distinguishes costs shared across regimes from those specific to NISQ error mitigation or FTQC error correction. It applies the model to Heisenberg time-evolution simulations and a VQE workload to quantify energy use. A reader would care if quantum computing's energy demands turn out to limit its scalability as much as its technical challenges do. The results indicate that different strategies are needed to reduce energy in near-term versus fault-tolerant systems.

Core claim

The paper presents a first-order, full-system energy model for quantum computing in an HPC context. The model separates costs common to NISQ and FTQC, such as system maintenance and classical processing, from regime-specific ones such as error mitigation for NISQ and error correction for FTQC. Instantiations on 96- and 100-qubit Heisenberg time-evolution simulations and a VQE workload show that NISQ energy is dominated by the QEM sampling multiplier, while FTQC cost shifts to physical-qubit overhead set by the code distance and magic states.

What carries the argument

The first-order full-system energy model that separates common HPC costs from NISQ-specific quantum error mitigation sampling multipliers and FTQC-specific physical qubit overheads determined by code distance and magic states.

If this is right

NISQ workloads incur energy costs that scale with the number of samples required for error mitigation.
FTQC energy use is set primarily by the ratio of physical to logical qubits needed for the chosen error-correcting code.
System maintenance and classical processing contribute to energy use in both regimes but are not the dominant factors.
Energy-efficient quantum advantage depends on reducing the sampling multiplier in NISQ and the qubit overhead in FTQC.

Where Pith is reading between the lines

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

Hardware designers could use similar models to optimize power consumption alongside performance.
Algorithm developers might incorporate energy estimates when choosing between NISQ and FTQC approaches for a given problem.
Future quantum advantage demonstrations may need to report energy usage in addition to runtime to assess practicality.

Load-bearing premise

The first-order model and its parameter choices accurately capture real energy costs for the chosen workloads without requiring hardware-specific measurements or additional validation data beyond the described instantiations.

What would settle it

A comparison between the model's energy predictions for the Heisenberg simulations and direct measurements of electrical power consumption during actual runs of those simulations.

read the original abstract

Quantum computing promises disruptive capabilities, yet its energy footprint has received far less attention than its asymptotic speedups. We present a first-order, full-system energy model for quantum computing in an high performance computing (HPC) context. The model separates costs common to NISQ and FTQC, such as system maintenance and classical processing, from regime-specific ones such as error mitigation for NISQ and error correction for FTQC. We instantiate the model on 96- and 100-qubit Heisenberg time-evolution simulations on IBM Eagle r3 and a representative VQE workload, and sketch the FTQC energy pipeline. We find that NISQ energy is dominated by the QEM sampling multiplier, while FTQC cost shifts to physical-qubit overhead set by the code distance and magic states. Our model provides actionable insights into the energy consumption of both NISQ and FTQC workloads, and paves the way toward energy-efficient quantum advantage.

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

The paper offers a first-order full-system energy model that separates common and regime-specific costs, but its dominance claims rest on unvalidated parameter values rather than hardware measurements.

read the letter

The main takeaway is that this paper sets out a first-order energy model for quantum systems running in HPC environments. It splits costs that apply across NISQ and FTQC, such as maintenance and classical processing, from the parts that differ by regime: error mitigation sampling overhead for NISQ and physical-qubit scaling plus magic-state costs for FTQC. The authors apply the model to a 96-qubit Heisenberg simulation on IBM Eagle r3, a VQE workload, and a rough FTQC sketch, concluding that the QEM multiplier drives most NISQ energy while code distance dominates FTQC energy. That separation and the concrete workload examples are the new pieces. The structure gives a workable way to organize energy accounting instead of just counting gates or runtime, which is useful as systems grow and power budgets become real constraints. The paper does a reasonable job keeping the model simple enough to be actionable while still covering the main terms. The soft spots sit in the inputs. The headline results depend on specific numbers chosen for the QEM sampling multiplier, per-shot energy, and baseline power terms. The text does not show direct wall-plug measurements from the IBM hardware or any sensitivity checks on those values. If the assumed multiplier is higher than what actually occurs or if maintenance power is larger than modeled, the reported dominance can reverse without changing the model itself. The stress-test note about unvalidated parameters matches what is visible. This work is aimed at quantum algorithm developers and HPC planners who need a starting framework for energy estimates. A reader looking for practical guidance on where energy costs concentrate would get value from the breakdown even if the numbers require checking. It deserves peer review because the topic is timely and the model structure is straightforward, though reviewers should be asked to examine the parameter sources and any validation data. I would send it out rather than desk reject.

Referee Report

2 major / 2 minor

Summary. The paper introduces a first-order full-system energy model for quantum computing in an HPC setting. It separates shared costs (system maintenance, classical processing) from NISQ-specific costs (quantum error mitigation sampling overhead) and FTQC-specific costs (physical-qubit overhead from code distance and magic-state distillation). The model is instantiated on 96- and 100-qubit Heisenberg time-evolution workloads on IBM Eagle r3 and a representative VQE circuit; the authors conclude that NISQ energy consumption is dominated by the QEM sampling multiplier while FTQC energy is dominated by the physical-qubit overhead set by code distance and magic states.

Significance. If the parameter choices prove representative, the model supplies a useful decomposition that identifies concrete targets for energy reduction—lowering QEM overhead in NISQ devices and optimizing code distance/magic-state costs in FTQC—thereby guiding hardware and algorithm co-design toward energy-efficient quantum advantage. The work is among the first to treat the full system (cryogenics, classical control, and error-handling overhead) rather than isolated gate or qubit energy.

major comments (2)

[§3.2] §3.2 (Model Instantiation for IBM Eagle r3): The headline claim that NISQ energy is dominated by the QEM sampling multiplier rests on a specific numerical choice for that multiplier together with baseline power terms; the manuscript supplies no direct comparison against measured wall-plug energy or power data for the 96-qubit Heisenberg workload, so the reported dominance is not yet shown to be robust to plausible variations in those parameters.
[§4.1] §4.1 (FTQC energy pipeline): The sketch of FTQC costs assumes particular code distances and magic-state overheads without an explicit derivation linking these quantities to the error budget or logical-qubit requirements of the target workload; the resulting dominance statement therefore depends on unstated assumptions about the underlying error model.

minor comments (2)

[Figure 2] Figure 2: axis labels and units for the energy breakdown are not fully legible at print size; please enlarge or add a supplementary table of numerical values.
[Introduction] The manuscript cites prior energy-estimation studies only in passing; a short related-work subsection would help readers place the first-order model relative to existing qubit-level or gate-level estimates.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the scope and limitations of our first-order model. We address each major comment below and will incorporate revisions to improve transparency and robustness.

read point-by-point responses

Referee: [§3.2] §3.2 (Model Instantiation for IBM Eagle r3): The headline claim that NISQ energy is dominated by the QEM sampling multiplier rests on a specific numerical choice for that multiplier together with baseline power terms; the manuscript supplies no direct comparison against measured wall-plug energy or power data for the 96-qubit Heisenberg workload, so the reported dominance is not yet shown to be robust to plausible variations in those parameters.

Authors: We agree that direct wall-plug measurements would provide stronger validation, but such data for the specific 96-qubit Heisenberg workload on IBM Eagle r3 are not publicly available. Our model uses literature-derived estimates for the QEM multiplier and power terms as a first-order approximation. To address robustness, we will add a sensitivity analysis in the revised §3.2, varying the QEM overhead and baseline powers over plausible ranges (e.g., factor of 2) to confirm that the dominance conclusion holds under reasonable parameter variations. revision: yes
Referee: [§4.1] §4.1 (FTQC energy pipeline): The sketch of FTQC costs assumes particular code distances and magic-state overheads without an explicit derivation linking these quantities to the error budget or logical-qubit requirements of the target workload; the resulting dominance statement therefore depends on unstated assumptions about the underlying error model.

Authors: We accept that the FTQC sketch would be strengthened by explicit linkage to the workload's error requirements. The chosen code distances and magic-state overheads follow standard surface-code assumptions for achieving logical error rates suitable for the Heisenberg simulation (targeting ~10^{-10} per logical gate). In the revision, we will expand §4.1 to include a brief derivation of the required code distance from the physical error rate, circuit depth, and target logical error budget, with references to standard error models in the literature. revision: yes

Circularity Check

1 steps flagged

Dominance of QEM multiplier and code-distance overhead reduces to chosen parameter values in the instantiated model

specific steps

fitted input called prediction [Abstract and model instantiation section]
"We instantiate the model on 96- and 100-qubit Heisenberg time-evolution simulations on IBM Eagle r3 and a representative VQE workload... We find that NISQ energy is dominated by the QEM sampling multiplier, while FTQC cost shifts to physical-qubit overhead set by the code distance and magic states."

The model defines total energy as base costs multiplied by the QEM sampling factor (or by physical-qubit overhead for FTQC). Inserting the chosen numerical values for those factors necessarily produces the reported dominance; the result is therefore the input parameters renamed as a finding, with no separate empirical check against hardware measurements.

full rationale

The paper constructs a first-order energy model, then instantiates it on specific workloads (96-qubit Heisenberg on IBM Eagle r3, VQE) using chosen numerical values for QEM sampling overhead, per-shot energy, maintenance power, and code distance. The headline finding that NISQ energy is dominated by the QEM multiplier follows directly from multiplying the base energy by that overhead factor; the FTQC shift to physical-qubit overhead follows from the distance and magic-state terms in the same equations. No external measured wall-plug data or independent validation is supplied to test whether the chosen parameters are representative, so the reported dominance is a direct consequence of the model's inputs rather than an independent derivation. This matches the fitted-input-called-prediction pattern at the level of the central claims.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Review is abstract-only; free parameters such as the QEM sampling multiplier and code distance are implied by the findings but not quantified or derived in the provided text. No explicit axioms or invented entities are stated.

free parameters (2)

QEM sampling multiplier
Described as the dominant NISQ energy factor; value must be chosen or fitted to produce the reported dominance.
code distance
Sets the physical-qubit overhead for FTQC; value is workload-dependent and not independently derived in the abstract.

axioms (1)

domain assumption A first-order model can usefully separate common HPC costs from regime-specific quantum costs.
Central premise of the full-system approach stated in the abstract.

pith-pipeline@v0.9.0 · 5462 in / 1395 out tokens · 84425 ms · 2026-05-13T06:48:03.205539+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
We present a first-order, full-system energy model... E_tot = E_sys + E_cls + E_exec_NISQ or E_exec_FTQC (Eq. 5). NISQ energy is dominated by the QEM sampling multiplier... FTQC cost shifts to physical-qubit overhead set by the code distance and magic states.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
Instantiate the model on 96- and 100-qubit Heisenberg... with specific parameter choices... no direct comparison against measured wall-plug power

Reference graph

Works this paper leans on

42 extracted references · 42 canonical work pages · 2 internal anchors

[1]

Quantum error correction below the surface code threshold

2025. Quantum error correction below the surface code threshold. Nature638, 8052 (2025), 920–926

work page 2025
[2]

2012.PUE: A Com- prehensive Examination of the Metric

Victor Avelar, Dan Azevedo, and Alan French. 2012.PUE: A Com- prehensive Examination of the Metric. Technical Report. The Green Grid

work page 2012
[3]

Sergey Bravyi and Jeongwan Haah. 2012. Magic-state distillation with low overhead.Physical Review A—Atomic, Molecular, and Optical Physics86, 5 (2012), 052329. Conference acronym ’XX, June 03–05, 2018, Woodstock, NY Niu et al

work page 2012
[4]

ZhenyuCai,RyanBabbush,SimonCBenjamin,SuguruEndo,WilliamJ Huggins, Ying Li, Jarrod R McClean, and Thomas E O’Brien. 2023. Quantum error mitigation.Reviews of Modern Physics95, 4 (2023), 045005

work page 2023
[5]

Shane A Caldwell, Moein Khazraee, Elena Agostini, Tom Lassiter, Corey Simpson, Omri Kahalon, Mrudula Kanuri, Jin-Sung Kim, Sam Stanwyck, Muyuan Li, et al. 2025. Platform Architecture for Tight Coupling of High-Performance Computing with Quantum Processors. arXiv preprint arXiv:2510.25213(2025)

work page arXiv 2025
[6]

S. Chen. 2023. Are Quantum Computers Really Energy Efficient? Nature Computational Science3 (2023), 457–460

work page 2023
[7]

Zi-Han Chen, Ming-Cheng Chen, Chao-Yang Lu, and Jian-Wei Pan

work page
[8]

Transversal logical Clifford gates on the rotated surface code with reconfigurable neutral atom arrays.Physical Review Letters136, 13 (2026), 130601

work page 2026
[9]

Seokwon Choi, Talal Ahmed Chowdhury, and Kwangmin Yu

work page
[10]

arXiv:2506.20125 [quant-ph]https://arxiv.org/abs/2506.20125

Quantum Utility-Scale Error Mitigation for Quantum Quench Dynamics in Heisenberg Spin Chains.arXiv e-prints(2025). arXiv:2506.20125 [quant-ph]https://arxiv.org/abs/2506.20125

work page arXiv 2025
[11]

Talal Ahmed Chowdhury, Kwangmin Yu, Mahmud Ashraf Shamim, M. L. Kabir, and Raza Sabbir Sufian. 2024. Enhancing quantum utility: Simulating large-scale quantum spin chains on superconducting quantum computers.Physical Review Research6, 3, Article 033107 (July 2024), 033107 pages

work page 2024
[12]

Mehiar Dabbagh, Bechir Hamdaoui, Mohsen Guizani, and Ammar Rayes. 2014. Energy-Efficient Cloud Resource Management. InIEEE INFOCOM Workshops

work page 2014
[13]

Howard David, Eugene Gorbatov, Ulf Hanebutte, Rahul Khanna, and Christian Le. 2010. RAPL: Memory Power Estimation and Capping. In Proceedings of the ACM/IEEE International Symposium on Low Power Electronics and Design

work page 2010
[14]

Nicolas Delfosse and Naomi H Nickerson. 2021. Almost-linear time decoding algorithm for topological codes.Quantum5 (2021), 595

work page 2021
[15]

Available: https://doi.org/10.1103/PhysRevX.8.031027

Suguru Endo, Simon C. Benjamin, and Ying Li. 2018. Practical Quan- tumErrorMitigationforNear-FutureApplications.PhysicalReviewX8, 3,Article031027(July2018),031027pages. arXiv:1712.09271[quant- ph] doi:10.1103/PhysRevX.8.031027

work page doi:10.1103/physrevx.8.031027 2018
[16]

Rolando P Hong Enriquez, Rosa M Badia, Barbara Chapman, Kirk Bresniker, Aditya Dhakal, Eitan Fractenberg, Gourav Rattihalli, Ninad Hogade, Pedro Bruel, Alok Mishra, et al. 2023. Estimating energy- efficiency in quantum optimization algorithms. InCray User Group Conference Proceedings

work page 2023
[17]

Austin G Fowler, Matteo Mariantoni, John M Martinis, and Andrew N Cleland. 2012. Surface codes: Towards practical large-scale quantum computation.Physical Review A—Atomic, Molecular, and Optical Physics86, 3 (2012), 032324

work page 2012
[18]

Joydip Ghosh, Austin G Fowler, and Michael R Geller. 2012. Surface code with decoherence: An analysis of three superconducting architec- tures.Physical Review A—Atomic, Molecular, and Optical Physics86, 6 (2012), 062318

work page 2012
[19]

Craig Gidney and Martin Ekerå. 2021. How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits.Quantum5 (2021), 433

work page 2021
[20]

Craig Gidney, Noah Shutty, and Cody Jones. 2024. Magic state cul- tivation: growing T states as cheap as CNOT gates.arXiv preprint arXiv:2409.17595(2024)

work page internal anchor Pith review Pith/arXiv arXiv 2024
[21]

HarperRGrimsley,SophiaEEconomou,EdwinBarnes,andNicholasJ Mayhall. 2019. An adaptive variational algorithm for exact molecular simulations on a quantum computer.Nature communications10, 1 (2019), 3007

work page 2019
[22]

Daniel Jaschke and Simone Montangero. 2023. Is quantum comput- ing green? An estimate for an energy-efficiency quantum advantage. Quantum Science and Technology8, 2 (2023), 025001

work page 2023
[23]

Córcoles, Antonio Mez- zacapo, Jerry M

Abhinav Kandala, Kristan Temme, Antonio D. Córcoles, Antonio Mez- zacapo, Jerry M. Chow, and Jay M. Gambetta. 2019. Error mitigation extends the computational reach of a noisy quantum processor.Nature 567, 7749 (March 2019), 491–495. arXiv:1805.04492

work page arXiv 2019
[24]

Wood, Theodore J

Youngseok Kim, Christopher J. Wood, Theodore J. Yoder, Seth T. Merkel, Jay M. Gambetta, Kristan Temme, and Abhinav Kandala

work page
[25]

2023), 752–759

Scalable error mitigation for noisy quantum circuits produces competitive expectation values.Nature Physics19, 5 (Feb. 2023), 752–759

work page 2023
[26]

Daniel Litinski. 2019. Magic state distillation: Not as costly as you think.Quantum3 (2019), 205

work page 2019
[27]

Energy use in quantum data centers: Scaling the impact of computer architecture, qubit performance, size, and thermal parameters.IEEE Transactions on Sustainable Computing (2022)

Michael James Martin et al.2022. Energy use in quantum data centers: Scaling the impact of computer architecture, qubit performance, size, and thermal parameters.IEEE Transactions on Sustainable Computing (2022)

work page 2022
[28]

Ac/dc: Automated compilation for dynamic circuits.arXiv preprint arXiv:2412.07969(2024)

Siyuan Niu, Efekan Kokcu, Anupam Mitra, Aaron Szasz, Akel Hashim, JustinKalloor,WibeAlbertdeJong,CostinIancu,andEdYounis.2024. Ac/dc: Automated compilation for dynamic circuits.arXiv preprint arXiv:2412.07969(2024)

work page arXiv 2024
[29]

White, Simon Burton, and Earl Campbell

Joschka Roffe, David R. White, Simon Burton, and Earl Campbell

work page
[30]

Decoding across the quantum low-density parity-check code landscape.Physical Review Research2, 4 (Dec 2020)

work page 2020
[31]

Francisco JR Ruiz, Tuomas Laakkonen, Johannes Bausch, Matej Balog, Mohammadamin Barekatain, Francisco JH Heras, Alexander Novikov, NathanFitzpatrick,BernardinoRomera-Paredes,JohnVanDeWetering, et al. 2025. Quantum circuit optimization with alphatensor.Nature Machine Intelligence7, 3 (2025), 374–385

work page 2025
[32]

Referencearchitectureofaquantum-centric supercomputer.arXiv preprint arXiv:2603.10970(2026)

Seetharami Seelam, Jerry M Chow, Antonio Córcoles, Sarah Sheldon, TusharMittal,AbhinavKandala,SeanDague,IanHincks,HiroshiHorii, BlakeJohnson,etal .2026. Referencearchitectureofaquantum-centric supercomputer.arXiv preprint arXiv:2603.10970(2026)

work page arXiv 2026
[33]

Sumeet Shirgure, Efekan Kökcü, Anupam Mitra, Wibe Albert de Jong, Costin Iancu, and Siyuan Niu. 2026. Characterizing and Benchmarking Dynamic Quantum Circuits.arXiv preprint arXiv:2604.03360(2026)

work page internal anchor Pith review Pith/arXiv arXiv 2026
[34]

Sagar Silva Pratapsi, Patrick H Huber, Patrick Barthel, Sougato Bose, Christof Wunderlich, and Yasser Omar. 2023. Classical half-adder using trapped-ion quantum bits: Toward energy-efficient computation. Applied Physics Letters123, 15 (2023)

work page 2023
[35]

Bolanos, Arabella Schelpe, Tianyi Hao, Philip Seitz, Gian Gia- como Guerreschi, Ángela Elisa Álvarez Pérez, Reinhard Stahn, Jerome Lenssen, Brendan Reid, and Austin Fowler

Adrien Suau, Yiming Zhang, Purva Thakre, Yilun Zhao, Kabir Dubey, Jose A. Bolanos, Arabella Schelpe, Tianyi Hao, Philip Seitz, Gian Gia- como Guerreschi, Ángela Elisa Álvarez Pérez, Reinhard Stahn, Jerome Lenssen, Brendan Reid, and Austin Fowler. 2026. tqec: A Python package for topological quantum error correction.Journal of Open Source Software11, 120 (...

work page doi:10.21105/joss.09142 2026
[36]

Gambetta

Kristan Temme, Sergey Bravyi, and Jay M. Gambetta. 2017. Error Mitigation for Short-Depth Quantum Circuits.Physical Review Letters 119, 18, Article 180509 (Nov. 2017), 180509 pages

work page 2017
[37]

Barbara M Terhal. 2015. Quantum error correction for quantum memories.Reviews of Modern Physics87, 2 (2015), 307–346

work page 2015
[38]

2014.A Power Measurement Methodology for Large- Scale, High-Performance Computing

The Green Grid. 2014.A Power Measurement Methodology for Large- Scale, High-Performance Computing. Technical Report

work page 2014
[39]

Yue Wu, Namitha Liyanage, and Lin Zhong. 2025. Micro blossom: Accelerated minimum-weight perfect matching decoding for quantum error correction. InProceedings of the 30th ACM International Con- ference on Architectural Support for Programming Languages and Operating Systems, Volume 2. 639–654. doi:10.1145/3676641.3716005

work page doi:10.1145/3676641.3716005 2025
[40]

LotteryBP:UnlockingQuantumErrorDecodingatScale

Yanzhang Zhu, Chen-Yu Peng, Yun Hao Chen, Yeong-Luh Ueng, and DiWu.2026. LotteryBP:UnlockingQuantumErrorDecodingatScale. arXiv(2026)

work page 2026
[41]

Hang Zou, Martin Rahm, Anton Frisk Kockum, and Simon Olsson

work page
[42]

Generative flow-based warm start of the variational quantum eigensolver.npj Quantum Information(2025)

work page 2025