Demonstration of two-dimensional connectivity for a scalable error-corrected ion-trap quantum processor architecture

TL;DR

The paper addresses scalability in trapped-ion quantum processors by introducing the Quantum Spring Array (QSA), a two-dimensional lattice of ion-string subregisters whose nearest-neighbor connectivity is achieved by controllable axial and radial separations rather than transport through junctions. It develops a theory of coupling between separated ion chains, showing that inter-string coupling rates $\Omega_c$ can scale favorably with ion number $n$ and be tuned via double-well potentials, with axial and radial motional modes providing resilient entangling channels. Experimentally, the authors demonstrate axial and radial well-to-well coupling, observe coherent phonon exchange, and realize entanglement between radially separated ions, while also implementing radial transport and RF control to adjust separations and coupling. They further map the architecture to fault-tolerant quantum error correction primitives and propose parallel transversal gate schemes, outlining a feasible path toward scalable, fault-tolerant quantum computation on an ion-trap platform.

Abstract

A major hurdle for building a large-scale quantum computer is increasing the number of qubits while maintaining connectivity between them. In trapped-ion devices, this connectivity can be achieved by moving subregisters consisting of a few ions across the processor. Here, we focus on an architecture, which we refer to as the Quantum Spring Array (QSA), that is based on a rectangular two-dimensional lattice of linear strings of ions. Connectivity between adjacent ion strings can be controlled by adjusting their separation. This requires control of trapping potentials along two directions, one along the axis of the ion string and one radial to it. In this work, we investigate key elements of the QSA architecture along both directions: We show that the coupling rate between neighboring lattice sites increases with the number of ions per site and the motion of the coupled system can be resilient to electrical noise, both being key requisites for fast and high-fidelity quantum gate operations. The coherence of the coupling is assessed and an entangling gate between qubits stored in radially separated trapping regions is demonstrated. Moreover, we demonstrate control over radio-frequency signals to adjust the radial separation, and thus the coupling rate, between strings. We further present constructions for the implementation of parallelized, transversal gate operations, and map the QSA architecture to code primitives for fault-tolerant quantum error correction, providing a step towards a quantum processor architecture that is optimized for large-scale operation.

Figures (27)

• Figure 1: Overview of the main features of the proposed QSA architecture. (a) A chain of ionic qubits are confined in a single well of an ion trap, with full connectivity between all qubits. (b) Multiple separate trapping regions are distributed over a 2D lattice. Trapping sites have connectivity between nearest neighbors. (c) A shuttling-based approach is used to bring ion chains close enough to couple them, with an interaction constant $k_{\mathrm{int}}$, symbolically depicted in purple as springs. Axial shuttling is achieved by displacing an ion string along a linear trap's RF null, and radial shuttling is achieved by displacing the RF null itself. When coupled, all-to-all connectivity between ions in separate strings is enabled; the use of such an architecture for quantum error correction codes, and the ability to apply transversal operations between chains of ions, as depicted in (d), are both theoretically investigated in this work. (e) Experimental highlights discussed in this work include: (i) the favorable scaling of coupling rate with number of ions, (ii) the insensitivity to electric field noise of the double well stretch mode of the coupled-ion system compared to the common mode, and (iii) generation of an entangled state, $\ket{SS}+\ket{DD}$, in radially separated ions, mediated by an oscillatory exchange of motion between two separated wells.
• Figure 2: (a) Schematic depiction of an ion trap layout that enables axial (purple arrows) and radial (blue arrows) shuttling to adjust the separation between trapping sites in two dimensions. The direction of separation $\hat{e}_d$ lies along the (b) axial and (c) radial direction with respect to the ion chain's axial mode of oscillation leading, respectively, to axial and radial coupling of ion chains. In both cases, coupled ions exhibit shared axial modes of motion, and can oscillate in phase (COM - common), or out of phase (STR - stretch). In this work, the two means of coupling are investigated in separate ion traps, whose layouts are shown in (d) and (e).
• Figure 3: Simulated coupling rate as a function of number of ions per well, for various separations of the individual wells. The common mode frequency of the individual wells is set to 400 for each point. If the axis of separation is along the ion chains' axial direction (axial coupling, left), the coupling of axial modes scales almost quadratically with number of ions, while for a separation along the radial direction (radial coupling, right) the scaling is sub-linear. Dashed lines are the coupling rates predicted from the point-charge model (Eq. \ref{['eq:couplingrate']}), which has a linear scaling with number of ions.
• Figure 4: (a) Electrode layout of the trap used for the axial coupling experiments. (b) Double-well potential along the trap axis. The plots show the same data, at different scales. In this particular example, local trap frequencies are 830, with a double well separation of 89.
• Figure 5: (a) Example of the avoided crossing in the coupling rate measurement for $n=6$ ions per well. (b) Measured coupling rate for various numbers $n$ of ions per well, and various separations. Lines are simulated values. Insets display chains of ions detected with an EMCCD camera. The error bars represent the 95$\%$ confidence interval coming from the the fits to the avoided crossing measurements using Eq.\ref{['eq:avoidedcrossing_fit']}.