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arXiv:2603.04566 · Physical Review Applied

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

quant-phSubmitted Mar 4, 2026• Announced Mar 6, 2026• 0 citations• Revised Mar 10, 2026 (v2)
v1 · Mar 4, 2026v2 · Mar 10, 2026v3 · May 8, 2026
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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.

Comments
9 pages, 6 figures

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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 ZZZZZZ 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.
Superconducting circuits offer great flexibility in designing quantum hardware. The authors present a multimodal ``trimon'' circuit implementing three qubits, and exploit the strong all-to-all longitudinal coupling to demonstrate high-fidelity multiqubit gates. Their design is a marked departure from conventional ones that combine individual, decoupled qubits. Nonetheless, this scheme allows fairly straightforward scale-up using established multiqubit architectures. The trimon mimics natural molecules, as used in NMR techniques, and shows significant potential for applications in quantum information processing.
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Superconducting circuits are well established as a viable candidate for the realisation of quantum computers. Circuits based on the transmon qubit are now ubiquitous, owing to its simple design and reduced control wiring overhead. An issue with transmon qubit-based architectures is the always-on unwanted interactions that impose limits on gate speeds and introduce errors into their operation. In addition, understanding sources of noise and decoherence is essential to the low-error operation quantum computers. This thesis describes the implementation of a multi-mode superconducting qubit in a coaxial circuit QED architecture. Constructed from three superconducting islands, connected via two Josephson junctions, the device possesses two transmon-like modes with orthogonal field symmetries. The unique polarisation of each mode allows for engineering dissipation and coupling in the system, extending functionality beyond the single-mode transmon. Experimental results on the unit-cell of the two-mode coaxial transmon are presented, demonstrating coherent control and simultaneous dispersive readout of the modes of the device. A predictive theory of charge sensitivity in a multi-mode superconducting qubit is presented, and experimental results in agreement of this theory are shown, observing sensitivity to four charge-parity configurations and two independent gate-charge offsets. The utility of a multi-mode qubit as a charge detector in spatially tracking local-charge drift of ≃ 100 µm length scales is also shown, demonstrating the use of these devices as tools in understanding charge noise in superconducting circuits. Finally, a system of a pair of coupled two-mode coaxial transmons is introduced, demonstrating a highly mode-selective coupling architecture. A suppressed quantum crosstalk of 2 kHz between protected modes of the devices is measured, along with equal single qubit gate fidelities when operated both individually and simultaneously. A first characterisation of a microwave activated conditional phase interaction between computational modes driven via ancillary transitions (AT-MAP) is presented. Whilst not shown in this work, this state-dependent two-qubit interaction can be used to generate entanglement. Combined with the low crosstalk demonstrated, this shows the multi-mode qubit architecture is a promising candidate for the construction of larger scale quantum processors with fast gates and low crosstalk-related errors.
Gate-based quantum computers typically encode and process information in two-dimensional units called qubits.Using d-dimensional qudits instead may offer intrinsic advantages, including more efficient circuit synthesis, problem-tailored encodings and embedded error correction.In this work, we design a superconducting qudit-based quantum processor wherein the logical space of transmon qubits is extended to higher-excited levels.We propose a universal gate set featuring a two-qudit cross-resonance entangling gate, for which we predict fidelities beyond 99% in the d = 4 case of ququarts with realistic experimental parameters.Furthermore, we present a decomposition routine that compiles general qudit unitaries into these elementary gates, requiring fewer entangling gates than qubit alternatives.As proof-of-concept applications, we numerically demonstrate the synthesis of SU(16) gates for noisy quantum hardware and an embedded error-correction sequence that encodes a qubit memory in a transmon ququart to protect against pure dephasing noise.We conclude that universal qudit control-a valuable extension to the operational toolbox of superconducting quantum information processing-is within reach of current transmon-based architectures and has applications to near-term and long-term hardware.
The existing scalable superconducting quantum processors have only nearest-neighbor coupling. This leads to a reduced circuit depth, requiring a large series of gates to perform an arbitrary unitary operation in such systems. Recently, multi-modal devices have been demonstrated as a promising candidate for small quantum processor units. Always on longitudinal coupling in such circuits leads to implementation of native high fidelity multi-qubit gates. We propose an architecture using such devices as building blocks for a highly connected larger quantum circuit. To demonstrate a quantum operation between such blocks, a standard transmon is coupled to the multi-modal circuit using a 3D bus cavity giving rise to small exchange interaction between the transmon and one of the modes. We study the cross-resonance interaction in such systems and characterize the entangling operation and the unitary imperfections and crosstalk as a function of device parameters. Finally, we tune up the cross-resonance drive to implement multi-qubit gates in this architecture.
Qubit connectivity is an important property of a quantum processor, with an ideal processor having random access-the ability of arbitrary qubit pairs to interact directly. This a challenge with superconducting circuits, as state-of-the-art architectures rely on only nearest-neighbor coupling. Here, we implement a random access superconducting quantum information processor, demonstrating universal operations on a nine-qubit memory, with a Josephson junction transmon circuit serving as the central processor. The quantum memory uses the eigenmodes of a linear array of coupled superconducting resonators. We selectively stimulate vacuum Rabi oscillations between the transmon and individual eigenmodes through parametric flux modulation of the transmon frequency. Utilizing these oscillations, we perform a universal set of quantum gates on 38 arbitrary pairs of modes and prepare multimode entangled states, all using only two control lines. We thus achieve hardware-efficient random access multi-qubit control in an architecture compatible with long-lived microwave cavity-based quantum memories.