Global Parametric Gates for Multi-qubit Entanglement

TL;DR

The work introduces a global parametric gate that uses a multi-tone drive on a common, tunable qubit to mediate bus-based, all-to-all coupling to multiple fixed-frequency qubits, implementing an effective exchange Hamiltonian with g_{j,eff}=g_j J_1(ε_j) ∏_{k≠j} J_0(ε_k). In experiments on a ring-network superconducting processor, the authors generate two-, three-, and four-qubit W-state entanglement with fidelities of 99.4%, 93.4%, and 91.4%, respectively, and demonstrate thorough calibration via XEB, Cryoscope, and QST. Numerical simulations project even higher performance, predicting up to 99.70% entanglement fidelity for six qubits, signaling strong scalability as coherence and control improve. The approach offers microwave-only, reconfigurable control for fixed-frequency qubits, leveraging a shared bus to enable robust, high-connectivity multipartite entanglement with reduced circuit depth.

Abstract

We propose and experimentally demonstrate a global parametric gate that generates multi-qubit entangled states in a single step. By applying a parametric drive to a common qubit at precise detunings relative to computational qubits, we directly produce two-, three-, and four-qubit entanglement with state fidelities of 99.4\%\pm0.2\%, 93.4\%\pm0.3\%, and 91.4\%\pm0.3\%, respectively. This scheme enables efficient, reconfigurable control using only microwave drives and is compatible with fixed-frequency qubits. Error analyses indicate that infidelity stems primarily from decoherence and coherent control errors, with negligible contributions from static ZZ coupling and flux noise. Furthermore, simulations with state-of-the-art parameters predict this global gate can generate high-fidelity (99.70\%) entanglement in systems of up to six qubits.

Figures (11)

• Figure 1: Device architecture and gate principle. (a-b) Working principle of the global parametric gate. Multiple computational qubits (red, blue, green…) couple to a shared bus resonator, enabling all-to-all connectivity. Entanglement across multiple qubits is generated in a single step by applying a microwave parametric drive to a flux-tunable common qubit (yellow). The drive consists of a superposition of frequency components detuned from the fixed-frequency computational qubits. (c) Schematic circuit of the superconducting architecture featuring the shared bus resonator. The parametric drive is applied to the common qubit via its dedicated flux line. (d) False-colored optical image of the fabricated device.
• Figure 2: Real part (a) and imaginary part (b) of a reconstructed 2-qubit density matrix for $Q_0$-$Q_1$ (F = 0.994(2), $t_{gate}=320\,\mathrm{ns}$). Experimental results (colored bars) are compared to the ideal state (transparent bars). (c) Circuit schematic of the XEB sequence for the $\sqrt{\mathrm{iSWAP}}$gate. The single-qubit gates S are randomly chosen from a set of 64 distinct single-qubit gates. (d) Fidelity decay for the $\sqrt{\mathrm{iSWAP}}$ gate ($t_{gate}=316\,\mathrm{ns}$) and the reference gates as a function of the circuit depth m. (e) The exchange oscillation between $\ket{10}$ and $\ket{01}$ for $Q_0$-$Q_1$ as a function of drive length and drive frequency $\nu_{1,\Omega_1}$ relative to the qubit frequency detuning $\Delta_1$ at $\Omega_1=0$. The parametric modulation induces a 8.3 MHz DC shift in $Q_0$'s frequency, offsetting the resonant exchange from $\nu_{1,\Omega_1=0}$.
• Figure 3: (a) Qubit occupation probabilities during multi-qubit exchange oscillations. The upper, middle, and lower panels correspond to the two-qubit ($Q_0$-$Q_1$, initial state $\ket{01}$), three-qubit ($Q_0$-$Q_1$-$Q_2$, initial state $\ket{100}$), and four-qubit ($Q_0$-$Q_1$-$Q_2$-$Q_3$, initial state $\ket{1000}$) systems, respectively. Experimental data are shown as colored markers, with simulation results as solid lines ($Q_0$: yellow, cycle $Q_1$: red, cycle $Q_2$: green, diamond $Q_3$: blue, pentagram). For the two-, three-, and four-qubit cases, the parametric drive frequencies are shifted by 8.3 MHz, 7.6 MHz, and 10.8 MHz, respectively, relative to the detuning between each computational qubit and the common qubit. Simulation parameters: $\Omega_1/2\pi$=41.4 MHz, $\nu_1/2\pi$=58.4 MHz ($Q_0$-$Q_1$); $\Omega_1/2\pi$=29.9 MHz, $\Omega_1$:$\Omega_2$=1:3, $\nu_1/2\pi$=58.4 MHz, $\nu_2/2\pi$= 164.8 MHz ($Q_0$-$Q_1$-$Q_2$); $\Omega_1/2\pi$=18.3 MHz, $\Omega_1$:$\Omega_2$:$\Omega_3$=1:3:4, $\nu_1/2\pi$ = 58.4 MHz, $\nu_2/2\pi$ = 164.8 MHz, $\nu_3/2\pi$ = 193.9 MHz ($Q_0$-$Q_1$-$Q_2$-$Q_3$). (b, c) Pulse sequences used for quantum state tomography (QST) in three- and four-qubit entanglement experiments, respectively. (d, e) Real and imaginary parts of the reconstructed three-qubit density matrix for qubits $Q_0$-$Q_1$-$Q_2$ (F = 0.934(3), $t_{gate}$=460 ns). Experimental results (colored bars) are compared to the ideal state (transparent bars).
• Figure 4: Quantum state tomography of four-qubit entanglement. Real (a) and imaginary (b) parts of the reconstructed four-qubit density matrix for qubits $Q_0$-$Q_1$-$Q_2$-$Q_3$, measured after a gate time ($t_{gate}$) of 720 ns. The achieved state fidelity is 0.914(3). Experimental results are shown as colored bars, overlaid with the ideal state (transparent bars) for comparison.
• Figure S1: Experimental setup and cryogenic wiring diagram. The schematic illustrates the signal path for qubit control and measurement. Control signals (XY, Z, parametric drive) generated at room temperature are progressively attenuated and filtered at different temperature stages of the dilution refrigerator before reaching the quantum processor at $\sim$10 mK. Readout signals from the device are amplified by a near-quantum-limited Josephson Parametric Amplifier (JPA) at the base temperature, followed by a HEMT amplifier at 4 K and further amplification at room temperature before demodulation and acquisition.