High coherence and low cross-talk in a tileable 3D integrated superconducting circuit architecture

Abstract

We report high qubit coherence as well as low cross-talk and single-qubit gate errors in a superconducting circuit architecture that promises to be tileable to two-dimensional (2D) lattices of qubits. The architecture integrates an inductively shunted cavity enclosure into a design featuring nongalvanic out-of-plane control wiring and qubits and resonators fabricated on opposing sides of a substrate. The proof-of-principle device features four uncoupled transmon qubits and exhibits average energy relaxation times T₁ = 149(38) μs, pure echoed dephasing times T_ϕ,e = 189(34) μs, and single-qubit gate fidelities F = 99.982(4)% as measured by simultaneous randomized benchmarking. The 3D integrated nature of the control wiring means that qubits will remain addressable as the architecture is tiled to form larger qubit lattices. Band structure simulations are used to predict that the tiled enclosure will still provide a clean electromagnetic environment to enclosed qubits at arbitrary scale.

Fig. 1.. Optical images of cavity enclosure and circuit.

(A) Enclosure base with cavity, central pillar, and four tapered through-holes for out-of-plane wiring access. (B) Enclosure lid with a central cylindrical recess and identical through-holes for out-of-plane wiring. (C) Cylindrical recess in the lid filled with a ball of indium. (D) (Grayscale) Four-qubit circuit mounted inside the enclosure base. The four qubits are visible, arranged in a square lattice with 2-mm spacing. (E) A spiral resonator and (F) a transmon qubit with identical electrode dimensions to those in the device.

Fig. 2.. Device schematics.

(A) Cross section of the out-of-plane wiring design (not to scale), here shown addressing a qubit. PTFE, polytetrafluoroethylene. (B) Cross section of the bulk via inductive shunt design (to scale). The designed dimensions are shown in micrometers. (C) Circuit layout illustration (not to scale). The substrate and enclosure are partially shown, and the out-of-plane wiring is shown for Q₂. Examples of the coupling terms and drive voltages in the Hamiltonian in Eqs. 1 and 2 are shown.

Fig. 3.. Qubit relaxation characterization.

(A) Two hundred fifty-one consecutive T₁ measurements over an approximately 12-hour period. (B) Resultant histograms of T₁. The inset shows an example T₁ time trace for Q₃, and the measurement pulse sequence. The four qubits were measured simultaneously; the data are shown across two graphs for legibility.

Fig. 4.. Cross-talk characterization.

(A) Experimentally measured qubit control line selectivity ${\mathrm{\phi }}_{\mathit{i}\mathit{j}}^q={({\mathrm{\epsilon }}_{\mathit{i}\mathit{j}}^q/{\mathrm{\epsilon }}_{\mathit{j}\mathit{j}}^q)}^2$ from qubit i to qubit control line j, expressed in units of dB as $10{\text{log}}_{10}({\mathrm{\phi }}_{\mathit{i}\mathit{j}}^q)$. (B) Experimentally measured resonator control line selectivity ${\mathrm{\phi }}_{\mathit{i}\mathit{j}}^r={({\mathrm{\epsilon }}_{\mathit{i}\mathit{j}}^r/{\mathrm{\epsilon }}_{\mathit{j}\mathit{j}}^r)}^2$ from resonator i to resonator control line j, expressed in units of dB as $10{\text{log}}_{10}({\mathrm{\phi }}_{\mathit{i}\mathit{j}}^r)$. (C) Frequency variation in Q₁ found from 20 repeated Ramsey experiments, with either no drive on any resonator or a continuous drive applied to R₂, R₃, or R₄ at frequency ω_{r, j} that populates it with a photon number ${\overline{n}}_j$ of at least n_{low, j} ≝ n_{crit, j}/10.

Fig. 5.. Randomized benchmarking.

(A) RB curves for simultaneous single-qubit RB on the four qubits. Points and error bars are the average and SD of the results for the k = 80 different Clifford sequences. (B) Pauli-Z correlators 〈ZZII〉, 〈ZZZI〉, and 〈ZZZZ〉 versus number of Clifford gates for the single-shot simultaneous RB data. The fitted dashed curves provide the depolarizing parameters α₁₁₀₀, α₁₁₁₀, and α₁₁₁₁. The associated Pauli-Z products versus number of Clifford gates are also shown (triangles). The close similarity of the correlator and product curves is indicative of low cross-talk (34, 37). (C) Leakage RB curve on Q₃. The final anomalous data point is excluded from the fit.

Fig. 6.. Depolarizing fixed-weight parameters.

The four-qubit system depolarizing fixed-weight parameters ϵ_S in each subspace S for S ≠ ∅. The 15 subspaces are expressed as bitstrings, where if bit n (here indexed left to right) is 1, then qubit n is in that subspace.

Fig. 7.. Band structure simulation.

(A) HFSS model of a unit cell featuring a single addressable and measurable qubit (4 × 1/4) and a single pillar that inductively shunts the enclosure. The unit cell has identical dimensions to the 2 mm by 2 mm central region of the device measured in this work. (B) Simulated lowest-band dispersion for the infinite enclosure formed by tiling the plane with the unit cell, with (solid) and without (dashed) the inductively shunting pillar and associated substrate aperture. The wave vector k traces between the symmetry points Γ : (k_x = 0, k_y = 0), X : (k_x = π/a, k_y = 0), M : (k_x = π/a, k_y = π/a). The colored curves show the predicted curvature around the Γ point with (red) and without (blue) the inductively shunting pillar and associated substrate aperture, using no free fit parameters (see the Supplementary Materials).