Multiplexed bi-layered realization of fault-tolerant quantum computation over optically networked trapped-ion modules

Abstract

We study an architecture for fault-tolerant measurement-based quantum computation (FT-MBQC) over optically-networked trapped-ion modules. The architecture is implemented with a finite number of modules and ions per module, and leverages photonic interactions for generating remote entanglement between modules and local Coulomb interactions for intra-modular entangling gates. We focus on generating the topologically protected Raussendorf-Harrington-Goyal (RHG) lattice cluster state, which is known to be robust against lattice bond failures and qubit noise, with the modules acting as lattice sites. To ensure that the remote entanglement generation rates surpass the bond-failure tolerance threshold of the RHG lattice, we employ spatial and temporal multiplexing. For realistic system timing parameters, we estimate the code cycle time of the RHG lattice and the ion resources required in a bi-layered implementation, where the number of modules matches the number of sites in two lattice layers, and qubits are reinitialized after measurement. For large distances between modules, we incorporate quantum repeaters between sites and analyze the benefits in terms of cumulative resource requirements. Finally, we derive and analyze a qubit noise-tolerance threshold inequality for the RHG lattice generation in the proposed architecture that accounts for noise from various sources. This includes the depolarizing noise arising from the photonically-mediated remote entanglement generation between modules due to finite optical detection efficiency, limited visibility, and the presence of dark clicks, in addition to the noise from imperfect gates and measurements, and memory decoherence with time. Our work thus underscores the hardware and channel threshold requirements to realize distributed FT-MBQC in a leading qubit platform today -- trapped ions.

Figures (19)

• Figure 1: Illustration of the MUSIQC architecture, consisting of $N$ ELUs that are interconnected via an optical switch.
• Figure 2: Essential components of an Elementary Logic Unit (ELU). It comprises of 50–100 trapped ions.
• Figure 3: Schematic illustration of probabilistic entanglement generation between two ions situated in separate Elementary Logical Units (ELUs). The configuration includes detectors D1 and D2, along with a beam splitter. Entanglement generation is heralded by distinct detector click patterns, enabling the identification of successful entangled pairs.
• Figure 4: A ($2 \times 2 \times 2$) unit cell of the Rausendorff-Harrington-Goyal (RHG) lattice. The cell contains sites at each edge and face center of the 3D cubic lattice, represented as green and black colors, respectively. Two different kinds of layers exist within the lattice, marked by green and black sites. Black sites are connected by red bonds, while green sites are linked by orange bonds. Blue bond connects the inter-layer bonds. The faces of the cells are referred to as either primal or dual.
• Figure 5: An adaptation of the RHG lattice into a 2+1D architecture. The lattice can be implemented using just two layers of 2D lattices, with memories being efficiently recycled post-measurement.