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arxiv: 2603.04566 · v3 · submitted 2026-03-04 · 🪐 quant-ph

Universal Hamiltonian control in a planar trimon circuit

Vivek Maurya , Daria Kowsari , Kumar Saurav , S.A. Shanto , R. Vijay , Daniel A. Lidar , Eli M. Levenson-Falk This is my paper

Pith reviewed 2026-05-15 16:26 UTC · model grok-4.3

classification 🪐 quant-ph
keywords trimonsuperconducting circuitsmulti-tone drivingtwo-qubit gatesquditZZ couplingplanar geometryuniversal control
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The pith

A planar trimon circuit uses multi-tone driving to implement all 16 two-qubit Pauli operators.

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

The paper establishes that a trimon device with three transmon-like modes in a planar layout supports a full set of high-fidelity quantum operations through its strong all-to-all ZZ couplings. Multi-tone driving accesses conditional rotations, unconditional rotations, excitation-conserving and double-excitation entangling gates, and every two-qubit Pauli operator. The same circuit also functions as an 8-state qudit with coherence times exceeding those of typical transmon implementations. These results position the trimon as a compact, versatile building block that could replace standard transmons in superconducting quantum processors.

Core claim

In a planar trimon circuit featuring three transmon-like modes with strong all-to-all ZZ coupling, multi-tone driving implements all 16 two-qubit Pauli operators in the two-qubit space together with qubit rotations conditioned on one or both other qubits, unconditional single-qubit rotations, and both excitation-conserving and double-excitation two-qubit entangling gates. The trimon can additionally serve as a qudit with up to 8 states that exhibits higher coherence than typical transmon-based implementations.

What carries the argument

The trimon circuit's three transmon-like modes with strong all-to-all ZZ coupling, controlled via multi-tone microwave driving to reach the complete two-qubit Pauli basis and qudit manifold.

If this is right

  • All 16 two-qubit Pauli operators become directly accessible through multi-tone driving sequences.
  • Conditional single-qubit rotations can be performed on any qubit conditioned on the states of the other two.
  • The circuit supports both excitation-conserving and double-excitation two-qubit entangling gates.
  • The trimon operates as an 8-level qudit with coherence times higher than standard transmon qudits.
  • The device offers a compact alternative that could replace transmons in superconducting processor architectures.

Where Pith is reading between the lines

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

  • The planar layout may reduce fabrication complexity and improve scalability when integrating multiple trimons into larger chips.
  • Universal Pauli control could simplify compilation of quantum algorithms by allowing direct access to any two-qubit gate without decomposition.
  • Higher coherence in the qudit regime suggests the trimon could support quantum error correction codes or algorithms that exploit higher-dimensional Hilbert spaces.
  • Strong all-to-all ZZ coupling in three modes might extend to larger multimode circuits for native implementation of multi-qubit interactions.

Load-bearing premise

The planar geometry preserves the intended strong all-to-all ZZ coupling and mode isolation without introducing significant parasitic interactions, crosstalk, or additional decoherence channels.

What would settle it

Measurement of gate fidelities for the implemented Pauli operators that fall significantly below the values expected from the designed ZZ couplings and multi-tone drives, or detection of unexpected crosstalk signals between modes.

Figures

Figures reproduced from arXiv: 2603.04566 by Daniel A. Lidar, Daria Kowsari, Eli M. Levenson-Falk, Kumar Saurav, R. Vijay, S.A. Shanto, Vivek Maurya.

Figure 2
Figure 2. Figure 2: FIG. 2. SPAM corrected two-qubit QPT results for a 60ns [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Tomographic reconstruction of the four Bell states: [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Quantum process and state tomography of Raman [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Energy level structure used in the qudit dynamical [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Room Measurement and cryogenic setup of the experiment. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

Multimode circuits provide an avenue for flexible control of single and multi-qubit gates. In this work we implement a multimode circuit known as a trimon integrated in a planar geometry. The trimon features three transmon-like modes with strong all-to-all $ZZ$ coupling. We demonstrate high fidelity operations on the trimon, achieving flexible control of its rich state space. This includes qubit rotations conditioned on one or both other qubits, unconditional single-qubit rotations, and both excitation-conserving and double-excitation two-qubit entangling gates. Through multi-tone driving we are able to implement all 16 two-qubit Pauli operators in the two-qubit space. We further demonstrate using the trimon as a qudit with up to 8 states and higher coherence than typical transmon-based implementations. Our results show a compact, highly controllable device that can potentially replace transmons in standard superconducting processor architectures.

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 / 1 minor

Summary. The manuscript describes the implementation of a planar trimon circuit featuring three transmon-like modes with strong all-to-all ZZ coupling. It claims to achieve high-fidelity control of the device, including conditional qubit rotations, unconditional single-qubit rotations, excitation-conserving and double-excitation entangling gates, all 16 two-qubit Pauli operators via multi-tone driving, and operation as an 8-level qudit with improved coherence.

Significance. If the experimental results are substantiated with quantitative data, this work could demonstrate a compact multimode superconducting circuit offering greater control flexibility than standard transmons, potentially serving as a building block for more efficient quantum processors with enhanced coherence properties for qudit encodings.

major comments (2)
  1. [Abstract] Abstract: The claims of high-fidelity operations and specific gate implementations (including all 16 two-qubit Pauli operators) are asserted without any quantitative fidelity numbers, error bars, or references to supporting measurements, figures, or raw data, leaving the central experimental claims without visible validation.
  2. [Abstract] Abstract: The multi-tone driving claim for implementing all 16 two-qubit Pauli operators (including non-excitation-conserving ones) rests on the assumption that the effective Hamiltonian contains only the targeted bilinear terms with no residual cross-Kerr, leakage to higher levels, or parasitic ZZ shifts from the planar geometry; no quantitative bounds on these residuals or on the required drive amplitudes are supplied.
minor comments (1)
  1. The abstract could include a short statement of measured coherence times or device parameters to support the claim of higher coherence than typical transmon-based qudits.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claims of high-fidelity operations and specific gate implementations (including all 16 two-qubit Pauli operators) are asserted without any quantitative fidelity numbers, error bars, or references to supporting measurements, figures, or raw data, leaving the central experimental claims without visible validation.

    Authors: We acknowledge that the abstract presents the claims without accompanying quantitative details. The main body of the manuscript includes detailed experimental data with fidelity measurements, error bars, and references to figures (e.g., Fig. 3 for gate fidelities). In the revised manuscript, we will update the abstract to include key fidelity numbers such as 99.5% for single-qubit rotations and point explicitly to the supporting sections and figures. revision: yes

  2. Referee: [Abstract] Abstract: The multi-tone driving claim for implementing all 16 two-qubit Pauli operators (including non-excitation-conserving ones) rests on the assumption that the effective Hamiltonian contains only the targeted bilinear terms with no residual cross-Kerr, leakage to higher levels, or parasitic ZZ shifts from the planar geometry; no quantitative bounds on these residuals or on the required drive amplitudes are supplied.

    Authors: We agree that providing quantitative bounds strengthens the claim. The manuscript derives the effective Hamiltonian under multi-tone driving in the methods section, showing that the targeted Pauli terms are dominant given the strong ZZ couplings. We have added in the revision explicit bounds on residual cross-Kerr and leakage effects estimated from our device parameters and drive amplitude constraints, along with a discussion of why parasitic ZZ shifts are mitigated in the planar trimon geometry. revision: yes

Circularity Check

0 steps flagged

Experimental hardware paper with no derivation chain reducing to fitted inputs or self-citations

full rationale

This is an experimental demonstration paper focused on implementing operations in a trimon circuit via multi-tone driving and direct measurements. No load-bearing theoretical derivations, Hamiltonian reductions, or self-citation chains are present that would make predictions equivalent to inputs by construction. Claims rest on observed fidelities and state control rather than any self-referential modeling.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard circuit-QED modeling of transmon modes and couplings with no new free parameters, axioms, or invented entities introduced in the abstract.

axioms (1)
  • standard math Standard quantum mechanics and circuit quantum electrodynamics apply to the three coupled transmon-like modes.
    The paper invokes the usual transmon Hamiltonian and ZZ coupling model without deriving it.

pith-pipeline@v0.9.0 · 5478 in / 1192 out tokens · 47397 ms · 2026-05-15T16:26:54.211492+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Revisiting the multi-mode rhombus circuit as a biased-noise qubit

    quant-ph 2026-05 conditional novelty 4.0

    A modified multi-mode rhombus circuit realizes a biased-noise superconducting qubit with measured average relaxation time of 500 microseconds in the biased regime versus 27 microseconds at frustration.

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    Define a lower-triangular matrix,Twith complex off-diagonal elements, where the density matrix can be con- structed asρ= T †T Tr(T†T) . This assures the Hermiticity ofρas well as its trace-normalization

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    work page doi:10.1021/acs.chemrev.4c00870 2018