Universal Hamiltonian control in a planar trimon circuit

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.

Figures (6)

• Figure 1: (a) Optical image of the planar trimon device. The central trimon circuit (orange box) consists of four capacitor pads connected via four Josephson junctions. (Right) A zoomed-in Scanning Electron Microscope (SEM) image of the junctions at the center of the circuit. Two $\lambda/4$ coplanar waveguide readout resonators (red and green) are capacitively coupled to adjacent trimon pads, while a dedicated drive line (blue) couples capacitively to the circuit to enable direct control of the modes. (b) Lumped-element circuit model of the planar trimon. Self capacitances (red) represent the shunt capacitance from each pad to ground. Adjacent pad capacitances (purple) arise from nearest neighbor coupling between the pads. Cross-capacitances (green) correspond to coupling between opposite pads and are approximately an order of magnitude smaller than the self capacitance. The brown elements denote the Josephson junctions connecting the four pads. Numbers 1, 2, 3, and 4 (red dots) indicate the four nodes of the circuit. (c) Energy level diagram of the three-qubit subspace, showing the $12$ allowed dipole transitions between the $8$ computational basis states. Transitions associated with the A, B, and C modes are indicated in red, blue, and green, respectively.
• Figure 2: SPAM corrected two-qubit QPT results for a $60$ns (a) $cX_{\pi/2}$ which implements a $X_{\pi/2}$ rotation on qubit B conditioned on qubit A being in $\ket{0}$, and (b) $X_{\pi}$, realized by applying simultaneous drives at $\omega_{0B0}$ and $\omega_{1B0}$. Qubit C is kept in the ground state throughout. When embedded in the full three-qubit computational subspace (with qubit C prepared in the ground state), these gates correspond to $ccX_{\pi/2}$ and a $cX_\pi$ gate, respectively. Bar heights indicate matrix element magnitude and color indicates the associated complex phase; the color of amplitudes smaller than $0.01$ is suppressed for clarity.
• Figure 3: Tomographic reconstruction of the four Bell states: (a) $\ket{\Phi_{+}}$, (b) $\ket{\Phi_{-}}$, (c) $\ket{\Psi_{+}}$, and (d) $\ket{\Psi_{-}}$, obtained after applying Readout Error Mitigation (REM) and maximum-likelihood estimation (MLE) (see Supplementary Information). The bars indicate the magnitude of each matrix element, while the color denotes its phase.
• Figure 4: Quantum process and state tomography of Raman-mediated entangling gates. (a) Process matrix of the $\sqrt{i\text{SWAP}}$ gate and (b) of the $\sqrt{i\text{bSWAP}}$ gate. (c) Reconstructed density matrix of the state $(\ket{01}-i\ket{10})/\sqrt{2}$ prepared by initializing $\ket{100}$ and applying the $\sqrt{i\text{SWAP}}$ gate. (d) Reconstructed density matrix of the state $(\ket{00}+i\ket{11})/\sqrt{2}$ produced directly using a single $\sqrt{i\text{bSWAP}}$ gate. Bar height indicates the magnitude of each matrix element and color denotes its phase; for QPT, the color of amplitudes smaller than $0.015$ is suppressed for clarity.
• Figure 5: (a) Energy level structure used in the qudit dynamical decoupling (DD) experiments. The red shaded box indicates the three levels forming the qutrit, the green-shaded box indicates the four level ququart, and all six levels together constitute the qud6 system. (b-d) Experimental results for the qutrit, ququart, and qud6 single axis DD sequence. The three sequences shown in each plot were interleaved and executed as a single experiment. For each plot, the fidelity is normalized by the maximum fidelity achieved in that experiment, defined as the maximum value among the three sequences. In each case, an effective $X$ pulse on the qudit space is decomposed using $2$, $3$ and $5$ native CC$X$ gates, corresponding to the qutrit, ququart, and qud6, respectively. Error bars correspond to $\pm2\sigma$.