Genuine 12-Qubit Entanglement on a Superconducting Quantum Processor

We report the preparation and verification of a genuine 12-qubit entanglement in a superconducting processor. The processor that we designed and fabricated has qubits lying on a 1D chain with relaxation times ranging from 29.6 to $54.6\mu \mathrm{s}$. The fidelity of the 12-qubit entanglement was measured to be above $0.5544\pm 0.0025$, exceeding the genuine multipartite entanglement threshold by 21 statistical standard deviations. After thermal cycling, the 12-qubit state fidelity was further improved to be above $0.707\pm 0.008$. Our entangling circuit to generate linear cluster states is depth invariant in the number of qubits and uses single- and double-qubit gates instead of collective interactions. Our results are a substantial step towards large-scale random circuit sampling and scalable measurement-based quantum computing.

Figure 1

(a) Circuit diagram. There are 12 neighboring qubits illustrated in two colors (green/dark blue) that correspond to two groups of working frequencies. The green ones are around 5 GHz and the dark-blue ones are around 4.2 GHz. All readout resonators (light blue) are coupled to a common transmission line (purple). By using frequency-domain multiplexing, joint readout for all qubits can be performed. For each qubit, individual capacitively coupled microwave control lines ($XY$) and inductively coupled bias lines ($Z$) enable full control of qubit operations. (b) The idling frequencies of both $f_{01}$ (solid red line) and $f_{12}$ (dotted black line) for all qubits. The color of the vertical bars on qubit levels indicates the energy relaxation rate ${\mathrm{\Gamma }}_1$. All qubit operations are performed within this frequency range.

Figure 2

(a) Algorithm to generate linear cluster state. The initial state for each qubit is $|0⟩$. $Y/2$ gates are applied to bring each qubit to $|+⟩$, then the CZ gates are applied to generate the GME state. Finally, joint measurements are performed to obtain the state fidelity. (b) The fidelities of $Y/2$ single qubit gates obtained by randomized benchmarking. The error bars represent a 95% confidence interval, determined from nonlinear least-squares fits. (c) CZ gate fidelities obtained by performing quantum process tomography. Error bars on the data are calculated via the bootstrapping method, with a 95% confidence interval.

Figure 3

(a) Experimental and theoretical distribution of the $XZ\dots XZ$ component in the 12 qubit linear cluster state. (b) Same as (a), but use $ZX\dots ZX$ instead. In both (a) and (b), the states are in the form of $|Q_{12}\dots Q_1⟩$. Experimental and theoretical results are presented in dark blue and brown, respectively. (c) Linear cluster state fidelities from 4 to 12 qubits, which are 0.9176(28), 0.9196(28), 0.8870(27), 0.8827(27), 0.8536(27), 0.7988(27), 0.7136(26), 0.5720(25), and 0.5544(25), exceed GME threshold by 149, 149, 143, 141, 130, 110, 82, 28, and 21 statistical standard deviations, respectively. State fidelities are calculated from two components, $XZ\dots XZ$ and $ZX\dots ZX$, of the linear cluster state. Error bars have a confidence interval of 95%, obtained from statistical calculation. A threshold of 50% for genuine entanglement is marked with a blue dashed line.