Scalable native multiqubit gates via engineered noncomputational-state interactions in superconducting fluxonium qubits

TL;DR

This work tackles the challenge of implementing native multi-qubit gates in superconducting qubits by leveraging engineered interactions in noncomputational manifolds of fluxonium qubits to realize $C^{\otimes N}Z$ gates. The authors derive an effective Hamiltonian in a central-fluxonium–neighbor architecture and show that neighbor-state-dependent plasmon frequency shifts enable selective activation of multi-qubit transitions. They demonstrate, through analysis and simulations, that CCZ, CCCZ, and CCCCZ gates with high fidelity can be executed rapidly (tens to a few hundred nanoseconds) while coexisting with primitive gates, with gate errors on the order of $10^{-2}$ (or $10^{-3}$ when incoherence is considered) for $N=1$–$4$. The results indicate a scalable route to integrate native multi-qubit gates into a unified processor, potentially reducing circuit depth and overhead for near-term and fault-tolerant quantum computing, though larger $N$ faces engineering challenges from level repulsion and capacitive loading.

Abstract

Native multiqubit gates could be essential for bridging the gap from current noisy devices to future utility-scale quantum computers, as they can substantially reduce circuit depth for near-term applications on noisy devices and may also lower the physical overhead of fault-tolerant quantum computation. Here we introduce a scalable protocol for implementing native multi-controlled gates on fluxonium qubits, supporting an arbitrary number of control qubits ($N > 1$) while remaining compatible with existing single- and two-qubit gate realizations. Our approach leverages engineered interactions in noncomputational state manifolds to enable qubit-state selective transitions, which is activated for the direct implementation of $(C^{\otimes N})Z$ gates. We show that in square lattices with fluxonium qubits, $CCZ$, $CCCZ$, and $CCCCZ$ gates with errors around 0.01 (0.001) are achievable, with gate lengths of $50\,(100)\,\text{ns}$, $100\,(250)\,\text{ns}$, and $150\,(300)\,\text{ns}$, respectively. Looking forward, integrating these native multi-controlled gates with primitive single- and two-qubit gate sets within a single quantum processor could significantly enhance flexibility in circuit synthesis and offer a promising alternative pathway toward utility-scale quantum computing.

Figures (10)

• Figure 1: (a) A 2D square qubit lattice comprising fluxoniums (circles) coupled via couplers (squares). The inset depicts the fluxonium architecture featuring tunable plasmon interactions and qubit-state decoupling, where fluxoniums are coupled via a transmon-based tunable coupler. (b) The energy levels of a three-fluxonium system (with the system-state notation $|Q_{1},Q_{0},Q_{2}\rangle$), where $Q_{0}$ is coupled to two neighbors $Q_{1}$ and $Q_{2}$. The coupler-mediated flip-flop interactions in the noncomputational-state manifolds (curved arrows, $|210\rangle\leftrightarrow|120\rangle$, $|021\rangle\leftrightarrow|012\rangle$, and $|211(112)\rangle\leftrightarrow|121\rangle$) cause neighbor-state-dependent frequency shifts in $Q_{0}$'s plasmon transition $|1\rangle\leftrightarrow|2\rangle$ through interaction-induced level repulsions.
• Figure 2: The neighbor-state-dependent frequency shift in the central fluxonium versus the the coupler-fluxonium coupling strength $J_{ck}$ for $N=2$ (a) and $N=3$ (b). Black circles denote the accumulated shift contributing from all neighbors, i.e., $(\delta_{\overrightarrow{01}}+\delta_{\overrightarrow{10}})$ and $(\delta_{\overrightarrow{001}}+\delta_{\overrightarrow{010}} +\delta_{\overrightarrow{100}})$ are for $N=2$ and $N=3$, respectively. The gray regions show the parameter space where the relation of $\delta_{\overrightarrow{s}}\equiv\sum_{j}s_{j}\chi_{j}$ breaks down (where the negative values of $\delta_{\overrightarrow{100}}$ are excluded from the data presented in (b)).
• Figure 3: State-dependent plasmon frequencies for each fluxonium under varying neighbor-state configurations. The gray boxes highlight the gate frequency (i.e., the frequency of the central fluxonium's $|1\rangle\leftrightarrow|2\rangle$ with all neighbors in state $|1\rangle$) for implementing $(C^{\otimes N})Z$ gates. In (a-d), minimum detunings between the gate transition and other nearby transitions are $(\delta^{'}_{\overrightarrow{s}})_{\rm Min}/2\pi=\{-78.8,\,-59.7,\,-28.7,\,-18.0\}\, {\rm MHz}$ for $N=\{1,\,2,\,3,\,4\}$, respectively.
• Figure 4: Gate errors (a) and leakage (b) of $(C^{\otimes N})Z$ ($N=1,\,2,\,3,\,4$) versus gate lengths (excluding the coupler flux ramping) with different drive pulse shapes. Here, the DRAG pulse parameters are chosen to suppress the spurious transition nearest to the target gate transition, see Fig. \ref{['fig3']}, and for $CCZ$, $CCCZ$, and $CCCCZ$ gates, the cosine ramp times of the flat-top pulses are $10$ ns, $20$ ns, and $30$ ns, respectively. In (a), the calculated incoherence gate errors arising from relaxation and dephasing of noncomputational gate levels are represented by dotted lines in distinct colors: gray for $CZ$, green for $CCZ$, red for $CCCZ$, and blue for $CCCCZ$ gates.
• Figure 5: The neighbor-state-dependent frequency shift $\delta_{\overrightarrow{100}}$ versus the the coupler-fluxonium coupling strength $J_{ck}$ for $N=3$. The gray regions show the parameter space where the approximate model breaks down, characterized by $\delta_{\overrightarrow{100}}$ undergoing discontinuous transitions between positive and negative values. Here the coupler biases are listed in Table \ref{['tab:qubit_parameters']} (namely [0.403, 0.420, 0.410]).