Energetic quantum advantage of trapped-ion quantum computation under fault-tolerant, realistic-architecture accounting

Góis, Pezzutto, and Omar (arXiv:2404.11572) estimated the full energy cost of a quantum Fourier transform (QFT) implemented with microwave-driven trapped ions and argued that an energetic quantum advantage over classical supercomputers could appear at smaller input sizes than a computational-time advantage — but only under idealized assumptions: perfect pulses, noise-free entangling gates, all-to-all connectivity within a single trap, no quantum error correction (QEC), and constant per-trap baseline power. The open problem is whether this energetic-advantage threshold survives realistic fault-tolerant and scalable accounting — the energetic overhead of QEC in a trapped-ion QFT, the energy cost of multi-trap architectures with ion shuttling, and the energy cost of cryogenic operation — along with related directions the source raises: noise-coupled models relating energy consumption to algorithmic fidelity, measured (rather than assumed) component energy scaling across trap architectures, and energy-optimization pathways.

Background

The quantum Fourier transform (QFT) is the linear map taking a computational basis state of $n$ qubits to an equal-weight superposition with phases $e^{2\pi ijk/N}$, $N=2^n$; it is the quantum analogue of the discrete Fourier transform and a subroutine of phase estimation and factoring algorithms. In Góis, Pezzutto, and Omar (arXiv:2404.11572, v1 titled "Towards Energetic Quantum Advantage in Trapped-Ion Quantum Computation"), the QFT was analyzed for a trapped-ion processor: qubits are stored in hyperfine states of $^{171}$Yb$^+$ ions confined in a Paul trap (an oscillating-electric-field ion trap), with single- and two-qubit gates driven by microwave pulses in a static magnetic-field gradient, following the microwave-driven trapped-ion spin system demonstrated by Piltz et al. (Science Advances 2, e1600093 (2016)); an earlier trapped-ion logic-gate energy estimate by the same collaboration is Pratapsi et al. (Applied Physics Letters 123, 154003 (2023)). The energy accounting covers every stage of a computation — Doppler cooling and sideband cooling of the ions (laser cooling stages that first cool the ion motion broadly and then near the motional ground state), state preparation, the gate sequence, readout — plus a baseline power drawn continuously by the trap radio-frequency supply (about 10 W) and re-pumping laser, independent of the computation. Because ambient magnetic-field noise limits the qubit coherence time to roughly 200 $\mu$s, dynamical decoupling (DD), i.e. periodic $\pi$ pulses that refocus low-frequency noise, is applied (60 $\pi$ pulses per qubit in the analyzed 3-qubit experiment). The QFT gate count grows as $n^2$, and extrapolating the measured component energies gives a total energy $E_{\mathrm{QC}}(n)$ that is compared with the energy a state-of-the-art classical supercomputer needs to run the fast Fourier transform (FFT) on $N=2^n$ inputs. The headline claim is that the crossover to an energetic quantum advantage occurs at a smaller input size than the crossover for a time advantage. The extrapolation, however, rests on simplifying assumptions the authors themselves flag: perfect pulses, noise-free entangling gates, all-to-all connectivity inside one trap (a single trap holds at most about 40 ions), no quantum error correction (QEC, the encoding of logical qubits into many physical qubits with repeated syndrome-extraction cycles to detect and correct errors), baseline treated as constant per trap, and a room-temperature (non-cryogenic) setup. Three gaps are emphasized in the source: scaling beyond one trap requires QEC and shuttling ions between traps to interaction regions, with many additional operations each carrying energy cost; future trapped-ion setups will most likely need a cryogenic environment whose energetic cost is "most likely higher than any other cost considered so far"; and the paper's own noise model (dephasing from magnetic-field fluctuations plus depolarization from imperfect DD pulses and readout) is not yet coupled to the DD pulse budgets or QEC overhead that fidelity targets would demand. The authors state that an error-correcting implementation of the QFT with trapped ions is beyond the scope of their work and that a proper answer to whether the energetic advantage survives error correction "can only be obtained by studying real case studies". Related frameworks exist but do not answer this question: Jaschke and Montangero (Quantum Science and Technology 8, 025001 (2023); preprint arXiv:2205.12092) defined a "green" advantage threshold depending on gate quality and entanglement; Fellous-Asiani et al. (PRX Quantum 4, 040319 (2023)) built a full-stack resource-efficiency framework including QEC overhead for generic platforms; Stevens and Deffner (arXiv:2605.04329) showed a universal energy-error tradeoff for encoding logical states in repetition, perfect, and Steane codes; Tu et al. (arXiv:2502.11239) and Niu et al. (arXiv:2605.09580) estimated fault-tolerant energy costs for superconducting devices; Carrasco-Codina et al. (arXiv:2605.15090) benchmark current cross-platform energy efficiency; and Alves et al. (arXiv:2601.03141) performed the sibling analysis for Rydberg atoms.

Problem Statement

Determine whether, and at what input size, the energetic quantum advantage of trapped-ion quantum computation survives the transition from the idealized Noisy Intermediate-Scale Quantum (NISQ)-regime analysis of Góis, Pezzutto, and Omar to realistic fault-tolerant, scalable architectures. The single overarching objective is a defensible re-evaluation of the energetic crossover between trapped-ion QFT computation and classical FFT computation on supercomputers, in which each previously idealized ingredient that the crossover accounting requires is either measured or explicitly modeled with uncertainty. Realistic accounting should address the considerations identified in the source: (i) incorporate quantum error correction into the QFT implementation — logical-qubit counts, syndrome-extraction cycles, and ancilla overhead — and recompute the quantum energy scaling $E_{\mathrm{QC}}(n)$ and the crossover against the classical baseline; (ii) account for multi-trap architectures, including ion shuttling to interaction regions or mediated inter-trap gates, with the operation counts and per-operation energies these require; and (iii) include the energetic cost of cryogenic operation and determine whether and how it shifts the crossover, given that it is expected to dominate all other costs. The source further identifies directions that could refine such an accounting but does not make them prerequisites for answering the crossover question: (iv) coupling the noise model (dephasing, coherent gate errors, depolarization) to the required dynamical-decoupling pulse budgets and error-correction overhead, so that energy consumption can be reported against algorithmic fidelity rather than in a noise-free idealization; (v) refining the assumed component constants (trap power, laser and control-electronics scaling, baseline per trap) with measured scaling laws, or explicitly modeled scaling laws with quantified uncertainty, possibly across different ion-trap architectures; and (vi) identifying the key control parameters and design choices (trap electronics, cooling protocols, DD schedules, architecture) that govern the energetic costs, i.e. optimization pathways towards an energetic quantum advantage under realistic constraints. A complete answer states, with quantified uncertainty, where the energetic advantage threshold lies — or that it disappears — relative to the idealized prediction.

References

1. Francisca Góis, Marco Pezzutto, Yasser Omar, "Energetics of Trapped-Ion Quantum Computation" (v1 titled "Towards Energetic Quantum Advantage in Trapped-Ion Quantum Computation"), arXiv:2404.11572 (2024; v2 2026), doi:10.48550/arXiv.2404.11572, https://arxiv.org/abs/2404.11572
2. Christian Piltz, Theeraphot Sriarunothai, Svetoslav S. Ivanov, Sabine Wölk, Christof Wunderlich, "Versatile microwave-driven trapped ion spin system for quantum information processing", Science Advances 2, e1600093 (2016), doi:10.1126/sciadv.1600093, https://doi.org/10.1126/sciadv.1600093 (the experimental system analyzed in the source work)
3. Sagar Silva Pratapsi, Patrick H. Huber, Patrick Barthel, Sougato Bose, Christof Wunderlich, Yasser Omar, "Classical half-adder using trapped-ion quantum bits: Toward energy-efficient computation", Applied Physics Letters 123, 154003 (2023), doi:10.1063/5.0176719, https://doi.org/10.1063/5.0176719 (preprint arXiv:2210.10470, titled "Classical Half-Adder using Trapped-ion Quantum Bits: Towards Energy-efficient Computation", https://arxiv.org/abs/2210.10470)
4. Daniel Jaschke, Simone Montangero, "Is quantum computing green? An estimate for an energy-efficiency quantum advantage", Quantum Science and Technology 8, 025001 (2023), doi:10.1088/2058-9565/acae3e, https://doi.org/10.1088/2058-9565/acae3e (preprint arXiv:2205.12092, https://arxiv.org/abs/2205.12092)
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8. Óscar Alves, Marco Pezzutto, Yasser Omar, "Energetics of Rydberg-atom Quantum Computing", arXiv:2601.03141 (2026), doi:10.48550/arXiv.2601.03141, https://arxiv.org/abs/2601.03141
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