Transmon Qutrit Processors

• Transmon qutrit processors are superconducting quantum devices that encode information in three energy levels, enabling native SU(3) operations for high-dimensional quantum computing.
• They achieve high-fidelity state preparation, tomography, and entangling gate operations through tailored pulse protocols and dynamic coupling in both single-device and chain architectures.
• The architectures support complex simulations like spin-1 many-body physics and efficient state transfer, demonstrating robust control and error mitigation in multi-qutrit setups.

Searching arXiv for recent and foundational papers on transmon qutrit processors to ground the article in the literature. Transmon qutrit processors are superconducting quantum processors that use the three lowest levels of a transmon, $|0\rangle$, $|1\rangle$, and $|2\rangle$, as a genuine three-level computational unit rather than truncating the device to a qubit. In this encoding, a transmon realizes a spin-1 local Hilbert space, supports native SU(3) control, and can be used for qutrit state preparation, entangling gates, state transfer, many-body simulation, and high-dimensional algorithmic primitives on architectures ranging from single devices to coupled chains and small multi-qutrit processors (Bianchetti et al., 2010, Goss et al., 2022, Kumaran et al., 2024).

1. Physical basis and effective processor models

A transmon qutrit exploits the weakly anharmonic ladder of a superconducting artificial atom. In the standard ladder or $\Xi$-type description, the allowed transitions are $|0\rangle\leftrightarrow|1\rangle$ and $|1\rangle\leftrightarrow|2\rangle$, while the direct $|0\rangle\leftrightarrow|2\rangle$ transition is selection-rule suppressed. For coherent drives on the two allowed transitions, the effective three-level rotating-frame Hamiltonian used for single-qutrit control is

$$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$

with $\Delta$ the detuning and $\Omega_{1,2}$ the complex Rabi frequencies (Yu et al., 9 Jul 2025). This model is the basic control layer for transmon qutrit processors.

In chain architectures, the same three-level encoding can be used to emulate a spin-1 lattice. For a one-dimensional array of nearest-neighbor-coupled transmons operated as qutrits, the rotating-frame Hamiltonian can be written as

$|1\rangle$0

where $|1\rangle$1 is a tunable nearest-neighbor coupling and $|1\rangle$2 is the transmon anharmonicity (Ghosh, 2014). In the resonant operating mode used for qutrit state transfer, $|1\rangle$3 and only the couplers are pulsed.

The same physical interpretation underlies direct spin-1 simulations. In the spin-1 AKLT and Abelian Higgs implementations, each qutrit is treated as a local three-dimensional spin degree of freedom rather than as an embedded qubit pair. This suggests that transmon qutrit processors are particularly natural when the target model already has local dimension three, because the hardware Hilbert space matches the problem Hilbert space without an auxiliary encoding overhead (Kumaran et al., 2024, Asaduzzaman et al., 12 Mar 2026).

2. Single-qutrit control, tomography, and readout

The first milestone for the field was the demonstration that a transmon can be prepared in arbitrary three-level superposition states and fully characterized. Using DRAG pulses extended to three levels, quadrature compensation, and time-dependent phase ramps, arbitrary states of the form $|1\rangle$4 were prepared in a circuit-QED transmon, followed by full qutrit state tomography with an average fidelity of $|1\rangle$5 over 14 states; the reported fidelities included $|1\rangle$6 for $|1\rangle$7 and $|1\rangle$8 for $|1\rangle$9 (Bianchetti et al., 2010). The same work established level-resolved dispersive readout through state-dependent cavity shifts $|2\rangle$0 MHz, $|2\rangle$1 MHz, and $|2\rangle$2 MHz.

Subsequent work moved from state preparation to direct SU(3) gate synthesis. A coherent-control framework based on SU(3) dynamics and Lewis–Riesenfeld invariants realized a qutrit Hadamard and a chiral qutrit $|2\rangle$3 gate on a superconducting transmon in $|2\rangle$4 ns each, with interleaved randomized-benchmarking errors $|2\rangle$5 and $|2\rangle$6, corresponding to $|2\rangle$7 and $|2\rangle$8 (Yu et al., 9 Jul 2025). In that framework, $|2\rangle$9 and $\Xi$0 are implemented as virtual phase gates, so the physically nontrivial control task reduces to realizing fast one-step $\Xi$1 and $\Xi$2 pulses on the native $\Xi$3-system.

A complementary line of work developed generic SU($\Xi$4) synthesis directly on a transmon, with explicit demonstrations for $\Xi$5 and $\Xi$6. For the qutrit case, SU(3) randomized benchmarking reported a Clifford error of $\Xi$7, an average of $\Xi$8 $\Xi$9 pulses per Clifford, and an inferred per-$|0\rangle\leftrightarrow|1\rangle$0-pulse error of $|0\rangle\leftrightarrow|1\rangle$1, corresponding to a per-gate fidelity of about $|0\rangle\leftrightarrow|1\rangle$2 (Liu et al., 2023). This places transmon qutrit control in the regime where nontrivial three-level circuits are practical.

Alternative control paradigms have also been demonstrated. Non-Abelian, non-adiabatic holonomic gates were implemented in the $|0\rangle\leftrightarrow|1\rangle$3 subspace of a transmon, with $|0\rangle\leftrightarrow|1\rangle$4 used as an auxiliary level and simultaneous driving of the first two transitions arranged so that the cyclic condition

$|0\rangle\leftrightarrow|1\rangle$5

and parallel-transport constraint are satisfied (1804.01759). This realizes geometric single-qutrit control using the same three-level hardware, but with a distinct robustness principle.

Readout remains a central technical issue. On IBM transmons promoted to qutrits via pulse-level control, a dispersive three-cluster readout combined with a support vector classifier yielded readout accuracies of about $|0\rangle\leftrightarrow|1\rangle$6 for $|0\rangle\leftrightarrow|1\rangle$7, $|0\rangle\leftrightarrow|1\rangle$8 for $|0\rangle\leftrightarrow|1\rangle$9, and $|1\rangle\leftrightarrow|2\rangle$0 for $|1\rangle\leftrightarrow|2\rangle$1, with SPAM mitigation based on inversion of the confusion matrix (Nguyen et al., 2022). In higher-dimensional single-transmon qudit experiments, single-shot discrimination reached $|1\rangle\leftrightarrow|2\rangle$2, $|1\rangle\leftrightarrow|2\rangle$3, $|1\rangle\leftrightarrow|2\rangle$4, and $|1\rangle\leftrightarrow|2\rangle$5 for $|1\rangle\leftrightarrow|2\rangle$6 through $|1\rangle\leftrightarrow|2\rangle$7, indicating that qutrit readout is significantly easier than ququart readout on the same hardware (Liu et al., 2023).

3. Entangling gates, transport primitives, and processor connectivity

The central multi-qutrit primitive is a genuine two-qutrit entangling gate. A dynamic cross-Kerr mechanism based on differential AC Stark shifts yielded an effective interaction

$|1\rangle\leftrightarrow|2\rangle$8

which was then shaped with echoed sequences and local phase corrections into qutrit $|1\rangle\leftrightarrow|2\rangle$9 and $|0\rangle\leftrightarrow|2\rangle$0 gates (Goss et al., 2022). The reported estimated process fidelities were $|0\rangle\leftrightarrow|2\rangle$1 for $|0\rangle\leftrightarrow|2\rangle$2 and $|0\rangle\leftrightarrow|2\rangle$3 for $|0\rangle\leftrightarrow|2\rangle$4. Because these are full two-qutrit Clifford entanglers in the $|0\rangle\leftrightarrow|2\rangle$5 computational space, they are appropriate building blocks for genuinely ternary processors rather than qubit gates embedded in a larger space.

A distinct route uses parametric coupling in a tunable-bus architecture. For two fixed-frequency transmon qutrits coupled through a flux-tunable transmon, flux modulation at a resonant difference frequency generates an effective exchange Hamiltonian

$|0\rangle\leftrightarrow|2\rangle$6

which selectively addresses chosen two-state subspaces inside the $|0\rangle\leftrightarrow|2\rangle$7-dimensional two-qutrit Hilbert space (Subramanian et al., 2023). In that setting, $|0\rangle\leftrightarrow|2\rangle$8 and $|0\rangle\leftrightarrow|2\rangle$9 were simulated with durations $$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$0 ns and $$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$1 ns and fidelities $$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$2 and $$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$3, and a two-qutrit CZ compiled from these partial swaps plus local operations had an entangling time of about $$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$4 ns and fidelity $$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$5. This suggests that frequency-selective parametric exchange is a viable route to scalable two-qutrit gates on fixed-frequency transmon hardware.

Transmon qutrit processors also require routing primitives. In a one-dimensional gmon-style chain, a qutrit state-transfer protocol was derived by matching the dynamics of the single- and double-excitation manifolds. For a trapezoidal coupler pulse and $$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$6 MHz, the analytic estimates

$$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$7

give $$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$8 MHz and $$H/\hbar = \Delta \,|1\rangle\langle 1| + \frac{1}{2}\left( \Omega_1\,|0\rangle\langle 1| + \Omega_2\,|1\rangle\langle 2| + \text{h.c.} \right),$$9 ns, and numerical optimization refined these to $\Delta$0 MHz and $\Delta$1 ns with unitary fidelity $\Delta$2 for the elementary two-qutrit transfer step (Ghosh, 2014). In processor terms, this is a qutrit SWAP-like nearest-neighbor routing gate, and the same work found linear decoherence error scaling $\Delta$3 with $\Delta$4 and quartic intrinsic-error scaling $\Delta$5 with $\Delta$6.

4. Processor architectures, benchmarking, and noise tailoring

Small multi-qutrit processors have now been realized in several architectural forms. One platform used an 8-qutrit ring of fixed-frequency transmons and experimentally focused on a 3-qutrit subset, with measured single-qutrit randomized-benchmarking Clifford fidelities of $\Delta$7, $\Delta$8, and $\Delta$9 in isolation and $\Omega_{1,2}$0, $\Omega_{1,2}$1, and $\Omega_{1,2}$2 under simultaneous operation (Goss et al., 2023). Another platform demonstrated three-qutrit GHZ entanglement on a cloud-accessible IBM processor by adding custom $\Omega_{1,2}$3-subspace pulses to the standard qubit control stack (Cervera-Lierta et al., 2021). A plausible implication is that the distinction between “qubit” and “qutrit” processors is increasingly a control-and-calibration distinction rather than a fundamentally different hardware class.

Noise is more structured in qutrit systems than in qubit systems. Beyond $\Omega_{1,2}$4 and $\Omega_{1,2}$5, one must account for $\Omega_{1,2}$6, $\Omega_{1,2}$7, level-dependent Stark shifts, leakage, and spectator-dependent phases. In the 3-qutrit processor used for noise tailoring, the relevant coherence times were approximately $\Omega_{1,2}$8s, $\Omega_{1,2}$9s, $|1\rangle$00s, and $|1\rangle$01s across the three sites (Goss et al., 2023). The same work generalized randomized compiling from Pauli twirling to Weyl twirling and combined it with noiseless output extrapolation and readout calibration. For a three-qutrit GHZ state, the fidelity improved from $|1\rangle$02 with readout calibration only to $|1\rangle$03 with randomized compiling, NOX, and RCAL, and random-circuit-sampling benchmarks exhibited up to $|1\rangle$04 improvement. This directly counters the common assumption that qutrit noise complexity necessarily precludes useful mitigation.

Frequency allocation remains a scaling bottleneck. A fixed-frequency transmon program based on laser annealing reported an anharmonicity nominally engineered to $|1\rangle$05 MHz, an empirical tuning precision of $|1\rangle$06 MHz on tuned qubits, an intrinsic frequency-equivalent tuning precision of $|1\rangle$07 MHz, and no measurable impact on coherence, together with a 65-qubit processor median two-qubit gate fidelity of $|1\rangle$08 (Zhang et al., 2020). Although that work did not operate qutrit gates, its collision taxonomy explicitly included type-2 and type-3 collisions involving $|1\rangle$09, so it is directly relevant to qutrit frequency planning. This suggests that large-scale transmon qutrit processors will require qubit-style frequency engineering, but with additional forbidden bands arising from $|1\rangle$10, $|1\rangle$11, and higher-manifold resonances.

5. Representative workloads and demonstrated capabilities

The practical value of transmon qutrit processors is most evident in the range of workloads already demonstrated.

Workload	Processor realization	Reported outcome
Three-qutrit GHZ entanglement (Cervera-Lierta et al., 2021)	Three IBM transmons promoted to qutrits	Fidelity $|1\rangle$12; genuine three-partite and three-dimensional entanglement
Neutrino oscillations (Nguyen et al., 2022)	Single IBM transmon qutrit via Qiskit Pulse	Vacuum, matter, and CP-violation simulations matched analytical calculations; qutrit PMNS schedule $|1\rangle$13 versus $|1\rangle$14 for a two-qubit version
Qutrit classifier (Cao et al., 2023)	Single fixed-frequency transmon qutrit	Hardware test accuracy $|1\rangle$15; simulated test accuracy $|1\rangle$16
Spin-1 AKLT states (Kumaran et al., 2024)	IBM transmon qutrits with calibrated 1–2 pulses	OBC ground-state fidelities up to $|1\rangle$17; qutrit implementation outperformed qubit encoding in noisy tensor-network simulations
Abelian Higgs model (Asaduzzaman et al., 12 Mar 2026)	Two-site transmon qutrit processor	Real-time dynamics observed with both hybrid analog-digital and gate-based protocols

The GHZ experiment is also significant as a certification protocol. For the target state

$|1\rangle$18

the maximal fidelity with any state of Schmidt-rank vector $|1\rangle$19, $|1\rangle$20, or $|1\rangle$21 is $|1\rangle$22, so the measured value $|1\rangle$23 proves genuine three-partite, three-dimensional entanglement (Cervera-Lierta et al., 2021). This made superconducting hardware the first non-photonic platform reported in the provided corpus to create and certify this form of entanglement.

Single-qutrit algorithms have also become concrete. A transmon qutrit platform demonstrated qutrit Ramsey interferometry with final populations

$|1\rangle$24

and a parity-check algorithm that distinguishes even and odd qutrit permutations with a single oracle query, whereas the classical task requires at least two queries (Yu et al., 9 Jul 2025). A separate qudit experiment on a transmon carried out SU(3) and SU(4) operations, discrete Fourier transforms, permutation-parity protocols, and single-qudit Grover and VQE demonstrations, with a qutrit SU(3) state tomography example reaching $|1\rangle$25 state fidelity and a qutrit DFT$|1\rangle$26 process fidelity of $|1\rangle$27 (Liu et al., 2023).

For physics simulation, the qutrit advantage is especially direct. In the AKLT work, each spin-1 degree of freedom was encoded in one transmon qutrit rather than in two qubits plus a symmetry projection, and hardware state preparations for open-boundary chains achieved $|1\rangle$28, $|1\rangle$29, $|1\rangle$30, $|1\rangle$31, $|1\rangle$32, and $|1\rangle$33 Hellinger fidelities across the reported $|1\rangle$34 cases (Kumaran et al., 2024). In the 2026 Abelian Higgs experiment, the three-level truncation of the transmon Hilbert space was mapped directly to the spin-1 truncated model, and both a pulse-based hybrid analog-digital Floquet simulation and a Trotterized digital implementation were realized on transmon qutrit hardware (Asaduzzaman et al., 12 Mar 2026).

6. Limitations, misconceptions, and outlook

A frequent misconception is that qutrit processors are simply qubit processors with an extra basis state turned on. The literature shows that this is incomplete. In the transmon ladder, single- and double-excitation manifolds generally evolve with different effective couplings, so qubit SWAP protocols do not transfer unchanged to qutrits; the state-transfer protocol had to impose a specific joint constraint on the pulse areas in both manifolds to realize a high-fidelity qutrit SWAP-like operation (Ghosh, 2014). Likewise, the chiral qutrit $|1\rangle$35 gate could not be generated by a real, time-independent Hamiltonian, so a time-dependent control field was required to break time-reversal symmetry effectively (Yu et al., 9 Jul 2025). These examples show that multilevel control is not a superficial extension of qubit control.

Another misconception is that qutrit processing requires wholly new hardware. In the neutrino-oscillation study, a standard IBM transmon was promoted to a qutrit using only pulse-level access, custom $|1\rangle$36 calibrations, and three-level readout classification (Nguyen et al., 2022). This suggests that a significant fraction of near-term qutrit progress will come from reprogramming and recalibrating existing transmon platforms rather than fabricating entirely different devices.

The principal limitations are consistently reported. They include leakage to $|1\rangle$37 and higher levels under strong pulses, control crosstalk, state-dependent Stark phases, the absence of native and scalable $|1\rangle$38–$|1\rangle$39–$|1\rangle$40 discriminators on some cloud platforms, and the difficulty of extending current methods to long chains or two-dimensional qutrit lattices (Ghosh, 2014, Cervera-Lierta et al., 2021, Kumaran et al., 2024). In the AKLT study, the authors explicitly stated that higher levels in real transmons are affected by various channels of decoherence and are unsuitable for encoding higher spin systems, motivating a deliberate restriction to qutrits rather than larger qudits (Kumaran et al., 2024).

The outlook is correspondingly specific. Available results already combine high-fidelity single-qutrit SU(3) control, two-qutrit entangling gates, qutrit transport, error mitigation, and domain-specific simulations. What remains is the consolidation of these components into larger processor stacks with frequency-engineered layouts, native multi-qutrit entanglers, scalable three-level readout, and compiler support that treats SU(3) as a first-class target rather than as a byproduct of qubit control. The existing evidence suggests that transmon qutrit processors are most compelling when the target task is intrinsically three-dimensional—spin-1 many-body physics, qutrit communication primitives, qudit algorithms, or compact encodings—because in that regime the third level is not overhead but the native computational substrate (Goss et al., 2022, Goss et al., 2023, Asaduzzaman et al., 12 Mar 2026).