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arxiv: 2511.16855 · v2 · submitted 2025-11-20 · 🪐 quant-ph

Orthogonal frequency-division multiplexing for simultaneous gate operations on multiple qubits via a shared control line

Haruki Mitarai , Yukihiro Tadokoro , Hiroya Tanaka This is my paper

Pith reviewed 2026-05-17 19:57 UTC · model grok-4.3

classification 🪐 quant-ph
keywords frequency division multiplexingquantum gatesqubit controlmicrowave pulsesgate fidelityorthogonal signalsscaling quantum processors
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The pith

Orthogonal frequency-division multiplexing allows high-fidelity simultaneous gate operations on multiple qubits using a single shared control line.

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

This paper analyzes simultaneous gate operations on multiple qubits using microwaves sent through one cable in a frequency-division multiplexing scheme. By using rectangular control pulses, it shows that choosing drive frequencies to make the signals orthogonal or quasi-orthogonal reduces interference between qubits. Theoretical and numerical results indicate that this approach maintains high gate fidelity. The work also offers practical guidelines for choosing pulse length, the number of signals, and rotation angles to achieve precise operations. A reader would care because this method could help scale quantum processors by cutting down on the number of control lines and the associated cryogenic thermal loads.

Core claim

Through theoretical and numerical analyses, orthogonal and quasi-orthogonal microwave signals in a frequency-division multiplexing scheme using rectangular pulses suppress interference in simultaneously driven qubits, thereby ensuring high gate fidelity for multi-qubit operations via a shared control line.

What carries the argument

Orthogonal frequency-division multiplexing (FDM) with rectangular microwave pulses, where appropriate frequency spacing makes signals orthogonal to minimize crosstalk and interference.

If this is right

  • Simultaneous driving of multiple qubits becomes feasible without significant fidelity loss due to interference.
  • Design rules for pulse duration, multiplexing count, and rotation angle ensure accurate qubit rotations.
  • Reduced number of control lines mitigates thermal load issues in large-scale quantum processors.
  • Scalable FDM-based microwave control suitable for processors with many qubits.

Where Pith is reading between the lines

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

  • Implementing this on superconducting qubit hardware could validate the reduction in control lines needed.
  • Similar multiplexing strategies might extend to other control modalities in different quantum systems.
  • The approach assumes ideal rectangular pulses, so real-world filtering effects would need separate study.

Load-bearing premise

That interference from non-orthogonal frequency components is the primary error source and that rectangular pulses can be generated and transmitted without extra phase noise or line-induced crosstalk.

What would settle it

Measuring the gate error rates for two or more qubits driven simultaneously with orthogonal versus closely spaced non-orthogonal frequencies and comparing to the predicted fidelity.

Figures

Figures reproduced from arXiv: 2511.16855 by Haruki Mitarai, Hiroya Tanaka, Yukihiro Tadokoro.

Figure 1
Figure 1. Figure 1: FIG. 1. Conceptual illustration of a model comprising [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Illustration of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Absolute values of the spectra of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (b). The same parameters as those used in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Rotation angles [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Infidelity 1 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (b) shows F (Uideal, U) as a function of N for τ = τ0. An increase in N leads to higher fidelity. The effect of increasing N becomes more pronounced as k0 in￾creases. This observed fidelity enhancement is achieved by the deliberate incorporation of suitably chosen off￾resonant frequency components into the control pulse. This finding challenges the conventional view that off￾resonant microwave components a… view at source ↗
read the original abstract

The increasing number of qubits in quantum processors necessitates a corresponding increase in the number of control lines between the processor, which is typically operated at cryogenic temperatures, and external electronics. Scaling poses significant challenges in terms of the thermal loads, forming a major bottleneck in the realization of large-scale quantum computers. In this study, we analyze simultaneous gate operations on multiple qubits using microwaves transmitted via a single cable in a frequency-division multiplexing (FDM) scheme. By employing rectangular control microwave pulses, we reveal the contribution of drive frequency spacing to gate fidelity. Through theoretical and numerical analyses, we demonstrate that orthogonal and quasi-orthogonal microwave signals suppress interference in simultaneously driven qubits, thereby ensuring high gate fidelity. Additionally, we provide design guidelines for key parameters, including pulse length, number of multiplexed microwave signals, and rotation angle, to achieve precise qubit operations. Our findings enable a scalable FDM-based microwave control scheme suitable for quantum processors with a large number of qubits.

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.

Referee Report

2 major / 2 minor

Summary. The paper analyzes simultaneous single-qubit gates on multiple qubits driven by rectangular microwave pulses transmitted over a shared control line in a frequency-division multiplexing scheme. Analytic integration of the drive Hamiltonian shows that frequency spacings satisfying the orthogonality condition Δf = n/T (n integer, T pulse duration) cause cross terms to integrate to zero; numerical solution of the time-dependent Schrödinger equation then yields high gate fidelities for up to several qubits. Design guidelines are given for pulse length, multiplexing count, and rotation angle.

Significance. If the ideal-pulse results survive realistic hardware imperfections, the scheme would directly address the control-line bottleneck in scaling superconducting processors. The parameter-free orthogonality derivation and the accompanying numerical fidelity estimates constitute clear technical strengths.

major comments (2)
  1. [§3.2, Eq. (8)] §3.2, Eq. (8): the analytic demonstration that the integrated cross-drive term vanishes relies on perfect rectangular envelopes; any finite rise time or dispersion on the shared line introduces sidebands that violate the orthogonality integral, rendering the derived fidelity an upper bound rather than an achievable value.
  2. [§4, Numerical Results] §4, Numerical Results: the reported fidelities (e.g., >99.9 % for four qubits) are obtained under ideal square pulses with no inclusion of amplifier nonlinearity, phase noise, or qubit-frequency drift; these omissions are load-bearing for the claim that the method “ensures high gate fidelity” in a practical large-scale processor.
minor comments (2)
  1. [Abstract] Abstract: the phrase “high gate fidelity” is used without a quantitative threshold or explicit list of error sources considered.
  2. [Figures] Figure captions: units and normalization of the fidelity metric should be stated explicitly (average gate fidelity vs. process fidelity).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight key practical limitations of our ideal-pulse analysis. We address each major comment below and will revise the manuscript accordingly to clarify assumptions and strengthen the discussion of real-world applicability.

read point-by-point responses

  1. Referee: [§3.2, Eq. (8)] §3.2, Eq. (8): the analytic demonstration that the integrated cross-drive term vanishes relies on perfect rectangular envelopes; any finite rise time or dispersion on the shared line introduces sidebands that violate the orthogonality integral, rendering the derived fidelity an upper bound rather than an achievable value.

    Authors: We agree that the derivation of Eq. (8) assumes ideal rectangular envelopes with instantaneous rise and fall times. Any finite rise time or dispersion on the shared control line will generate sidebands that prevent the cross terms from integrating exactly to zero, so the reported fidelities constitute an upper bound for the ideal case. In the revised manuscript we will explicitly state this assumption in §3.2, add a short paragraph in the discussion section on the sensitivity to non-ideal envelopes, and note that pulse-shaping methods could be used to restore approximate orthogonality. We will also qualify the abstract and conclusions to reflect that the orthogonality condition provides a design target rather than a guaranteed result under realistic hardware conditions. revision: yes

  2. Referee: [§4, Numerical Results] §4, Numerical Results: the reported fidelities (e.g., >99.9 % for four qubits) are obtained under ideal square pulses with no inclusion of amplifier nonlinearity, phase noise, or qubit-frequency drift; these omissions are load-bearing for the claim that the method “ensures high gate fidelity” in a practical large-scale processor.

    Authors: We acknowledge that all numerical results in §4 are obtained with perfect square pulses and omit amplifier nonlinearity, phase noise, and qubit-frequency drift. These omissions mean the high-fidelity claims apply strictly to the ideal model and do not yet demonstrate performance in a practical processor. In the revision we will insert explicit caveats at the beginning of §4, revise the abstract and §5 to avoid implying immediate applicability to large-scale hardware, and add a brief forward-looking paragraph on how the orthogonality principle might be combined with calibration or error-mitigation techniques to address these effects. The core technical contribution—analytic identification of the orthogonality condition—remains valid as a starting point for such extensions. revision: yes

Circularity Check

0 steps flagged

Derivation uses standard drive equations and Fourier orthogonality without self-referential reductions

full rationale

The paper's central derivation computes time-integrated drive terms for rectangular microwave pulses at frequencies spaced by integer multiples of 1/T. This follows directly from the standard qubit Hamiltonian in the rotating frame and the integral property of orthogonal sinusoids; the vanishing cross terms are a mathematical identity independent of the target fidelity values. Numerical Schrödinger-equation simulations serve only as confirmation and introduce no fitted parameters that are later renamed as predictions. No self-citations are invoked to establish uniqueness of the orthogonal scheme, and the rectangular-pulse assumption is stated explicitly rather than smuggled in via prior work. The result is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis assumes standard quantum control Hamiltonians and rotating-wave approximation; no new entities are postulated and no free parameters are fitted to data.

axioms (2)
  • domain assumption Rotating-wave approximation remains valid for the chosen drive frequencies and pulse durations
    Invoked implicitly when treating rectangular microwave pulses as resonant drives on individual qubits.
  • domain assumption Qubits are two-level systems with no leakage to higher states during the drive
    Standard assumption in gate-fidelity calculations for superconducting or spin qubits.

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