A Superconducting Qubit-Resonator Quantum Processor with Effective All-to-All Connectivity

Abstract

In this work we introduce a superconducting quantum processor architecture that uses a transmission-line resonator to implement effective all-to-all connectivity between six transmon qubits. This architecture can be used as a test-bed for algorithms that benefit from high connectivity. We show that the central resonator can be used as a computational element, which offers the flexibility to encode a qubit for quantum computation or to utilize its bosonic modes which further enables quantum simulation of bosonic systems. To operate the quantum processing unit (QPU), we develop and benchmark the qubit-resonator conditional Z gate and the qubit-resonator MOVE operation. The latter allows for transferring a quantum state between one of the peripheral qubits and the computational resonator. We benchmark the QPU performance and achieve a genuinely multi-qubit entangled Greenberger-Horne-Zeilinger (GHZ) state over all six qubits with a readout-error mitigated fidelity of $0.86$.

Figures (7)

• Figure 1: (a) Schematic illustration of the qubit-resonator QPU. The readout resonators (one for each qubit) have been omitted for the sake of clarity. (b) Operational frequencies of the qubits (blue circles), the tunable couplers (green squares), the computational resonator (red line), and the dispersively coupled resonators used for multiplexed readout (black diamonds). The qubits and couplers are biased at their first-order flux-insensitive point and their frequencies are tunable from this maximum attainable value down to nearly zero.
• Figure 2: Qubit-resonator gate calibration. (a), (b) Pulse level schedules used for tuning up the population exchange of the MOVE operation and the CZ gate, respectively. For the MOVE operation, initially only the qubit is in the excited state, while for the CZ gate both the qubit and the computational resonator start in the first excited state. (c), (d) Energy level diagrams showing the relevant states involved in the MOVE operation and the CZ gate, respectively. Both diagrams depict the diabatic (dotted grey line) and dressed (black solid line) energy levels. The energy splittings ($2\Tilde{g}_\mathrm{MOVE},\ 2\Tilde{g}_\mathrm{CZ}$) are tuned by adjusting the coupler frequency $\omega_\mathrm{TC}$. (e), (f) Population oscillations between the energy levels shown in (c) and (d), respectively, are obtained by scanning the qubit frequency during the gate, $\omega_\mathrm{QB}$, over the resonance condition (indicated by the black dashed line), and by tuning the effective interaction strength between the qubit and the computational resonator during the gate by adjusting the coupler frequency, $\omega_\mathrm{TC}$. The white crosses indicate the initial guesses for the operating point of the gates based on the population oscillations.
• Figure 3: Interleaved randomized benchmarking experiments for qubit-resonator gates. (a) Circuit for benchmarking the MOVE operation via interleaved randomized benchmarking. The sequence consists of $m$ single-qubit Clifford gates $\mathcal{C}_1$ interleaved with $k$ repetitions of two subsequent MOVE operations, which effectively implement an identity. The final operation $\mathcal{U}^{-1}$ inverts the applied sequence. (b) Circuit for benchmarking the CZ gate via interleaved randomized benchmarking. Two-qubit Clifford gates $\mathcal{C}_2$ are interleaved with MOVE-$l$CZ-MOVE operations for a varying number of CZ gates $l$. (c) Experimental data of the sequence fidelity for randomized benchmarking with $k=1, .., 4$ interleaved double MOVE operations and the reference single-qubit Clifford sequence (open blue circles) as a function of the number of Clifford gates. (d) Extracted fidelity of the interleaved gate sequence as a function of $k$ (solid black circles) and quadratic fit (dashed line). (e) Experimental data of the sequence fidelity for randomized benchmarking with interleaved MOVE-$l$CZ-MOVE gate sequences and the reference two-qubit Clifford sequence (open blue circles) as a function of the number of Clifford gates. (f) Extracted fidelity of the interleaved MOVE-$l$CZ-MOVE gate sequence as a function of $l$ (solid black circles) and quadratic fit (dashed line).
• Figure 4: GHZ state characterization. (a) Circuit for preparing a GHZ state with a variable number of entangled qubits $N$ on a qubit-resonator QPU with star topology. (b) The fidelity $F_{\ket{\psi}_{\rm GHZ}}$ is calculated from the GHZ state population and its coherence, inferred via multiple quantum coherences. We show the GHZ state fidelity as a function of the qubit number $N$, obtained by analysing the data both with (blue circles) and without (red triangles) applying readout-error mitigation.
• Figure 5: Measured Q-score ratio as a function of problem size $n$. For each problem size, the average is taken over 60 randomly sampled Erdős–Rényi graphs. The error bars show the standard error of the mean.