Controlled-SWAP gates by tuning of interfering transition pathways in neutral atom arrays

TL;DR

The paper tackles the lack of native exchange gates in neutral-atom quantum processors by introducing an interaction-enabled destructive-interference mechanism that mediates exchange via Rydberg interactions. A single-step controlled-SWAP (Fredkin) gate is demonstrated conceptually and extended to an exchange family with phase programmability, achieving fidelities above 99% while suppressing Rydberg-state exposure by over an order of magnitude compared with decomposed gate sequences. The approach generalizes to multi-control SWAP (C_k-SWAP) and conditional multiplexed SWAP gates, enabling programmable routing, multi-copy state verification, and syndrome-conditioned operations in scalable lattice geometries. This work elevates exchange from a mediated primitive to a native operation in neutral-atom processors, with significant implications for verification protocols, fermionic and XY-model simulations, and hardware-level quantum routing and compilation across quantum architectures.

Abstract

Neutral-atom quantum processors employ Rydberg blockade for multiqubit phase operations but lack similar native exchange and conditional exchange gates, which are essential primitives for state verification, fermionic and XY-model simulation, and efficient routing in large qubit arrays. We demonstrate that by lifting the degeneracy between interfering transition pathways, a single Rydberg-excited atom can control state exchange between pairs of atoms. Using this mechanism, we realize a direct controlled-SWAP (Fredkin) operation with more than 99\% fidelity and an order-of-magnitude reduction in circuit depth and reduced exposure to decay and decoherence of Rydberg state components compared with decomposed implementations. The mechanism operates robustly under Doppler broadening at ~150 $μ$K and realistic laser-intensity noise and extends naturally to an entire family of useful gates, including multi-control conditional exchanges (C$_k$-SWAP) and conditional multiplexed SWAP gates. By incorporating controlled exchange operations as native physical operations on neutral atoms, our work provides multiqubit gates that enable higher-order state-verification protocols, occupation-dependent simulations, and conditional routing across optical lattices.

Figures (5)

• Figure 1: Level Scheme and the time diagram of the laser pulse orders for the controlled-SWAP operation
• Figure 2: Controlled-SWAP Operation -- Panels 1–6 illustrate the operation for different qubit configurations. Series (a) shows the level scheme in the collective basis of the target atoms. Series (b) and (c) depict, respectively, the population dynamics and phase evolution during the application of the target pulses in step (ii) of gate operation. (a1,b1) When the control atom is in the Rydberg state $|r\rangle$ and targets are in $|10\rangle$ or $|01\rangle$, the interaction with the target atoms shifts the energy levels such that two eigenstates of Eq. \ref{['Eq_H']} become nearly degenerate. This degeneracy leads to destructive interference, effectively blocking the SWAP between target atoms. (a2,b2) In the absence of control Rydberg excitation, the four-photon transition via the symmetric state $|\overline{1r}\rangle$ enables the SWAP between $|01\rangle$ and $|10\rangle$. Note that it is essential that neither of the target atoms is Rydberg-blocked by the control atom. The dashed lines in (b2) correspond to a case where one of the targets is blocked by the control under a non-isotropic interaction, illustrating that the SWAP operation cannot proceed via $|1r\rangle$ or $|r1\rangle$ alone but requires the symmetric state $|\overline{1r}\rangle = (|1r\rangle + |r1\rangle)/\sqrt{2}$. The same principle will be employed for a conditional multiplexed SWAP operation in the end of the paper. (a3) For the initial state $|1\rangle_c |00\rangle_t$, the only resonant two-photon transitions are to $|0r\rangle$ and $|r0\rangle$, which form a dark state with zero eigen energy, see text and hence generate no phase, see (c3), but it acquires a transient excited state population proportional to $(\Omega_1(t)/\Omega_2)^2$ until the system returns fully to $|00\rangle$ at the end of the Gaussian pulse, see (b3). All other computational basis states, including $|100\rangle$, $|r11\rangle$, and $|111\rangle$, involve far-detuned transitions and thus preserve their populations throughout the operation, see panels (b4, b5, b6), while acquiring phases due to AC Stark shift as quantified in panels (c4, c5, c6) and in the text. Applied parameters are presented in Table \ref{['tab_1']}. The gate output amplitudes are tabulated in Table \ref{['tab_3']} consistent with the desired controlled SWAP gates.
• Figure 3: Stability of the gate scheme against parameter fluctuations in (a) detuning, (b) $\Omega_1$, and (c) $\Omega_2$. (a) The infidelity caused by Doppler broadening due to atomic thermal motion is plotted as a function of temperature. The scattered signs denote the present scheme; the dotted–dashed curve shows the anti‐blockade Fredkin‐gate model from Ref. Wu21. (b,c) Infidelity versus the relative Gaussian width of laser‐intensity fluctuations for (b) $\Omega_1$ and (c) $\Omega_2$. Each data point represents an average over 40 independent trials. The applied parameters are listed in Table \ref{['tab_1']}.
• Figure 4: Optimum Parameters for LongRange Operation -- (a-c) Effects of the relative controlling parameters, on the rotation fidelity (excluding the phase adjustment). (d) The infidelity of C-SWAP versus interatomic distance, encountering the population rotation errors, and Rydberg loss. The applied parameters are the same as in Table I, except that in (a) $\Omega_{1max}$, in (b) $\Omega_2$, in (c) $V$, and in (d), all parameters are optimized for each interatomic distance.
• Figure 5: Geometry of extended SWAP and C-SWAP variants with higher-order generalizations. Control and target qubits are represented by hollow and solid circles, respectively. Panels (a)–(c) illustrate the geometries of (a) a SWAP gate, (b) a controlled-SWAP (C-SWAP) gate, and (c) a multi-control SWAP (C$_k$-SWAP) gate, arranged in a triangular lattice configuration in which every pair of atoms resides within the mutual Rydberg blockade range. Panels (d,e) illustrate the geometries of conditional multiplexed SWAP gates. Different logical states of the control atom are coupled to distinct Rydberg levels, $|nP_{3/2},3/2\rangle$ or $|(n-1)D_{5/2},5/2\rangle$, while the targets are driven to $|nS_{1/2},1/2\rangle$. The resulting anisotropic control–target blockade regions, shown as green and yellow shaded areas, selectively inhibit the SWAP operation for blockaded targets. (d) Four-target configuration implementing Eq. \ref{['Eq_10']}. (e) Three-target architecture implementing Eq. \ref{['Eq_11']}, where target 1 always lies outside the control blockade, while targets 2 and 3 are blockaded conditionally on the control-qubit state.