Saikat Guha

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.

Trapped ions form an advanced technology platform for quantum information processing with long qubit coherence times, high-fidelity quantum logic gates, optically active qubits, and a potential to scale up in size while preserving a high level of connectivity between qubits. These traits make them attractive not only for quantum computing but also for quantum networking. Dedicated, special-purpose trapped-ion processors in conjunction with suitable interconnecting hardware can be used to form quantum repeaters that enable high-rate quantum communications between distant trapped-ion quantum computers in a network. In this regard, hybrid traps with two distinct species of ions, where one ion species can generate ion-photon entanglement that is useful for optically interfacing with the network and the other has long memory lifetimes, useful for qubit storage, have been proposed for entanglement distribution. We consider an architecture for a repeater based on such dual-species trapped-ion systems. We propose and analyze a protocol based on spatial and temporal mode multiplexing for entanglement distribution across a line network of such repeaters. Our protocol offers enhanced rates compared to rates previously reported for such repeaters. We determine the ion resources required at the repeaters to attain the enhanced rates, and the best rates attainable when constraints are placed on the number of repeaters and the number of ions per repeater. Our results bolster the case for near-term trapped-ion systems as quantum repeaters for long-distance quantum communications.

Demonstrations of quantum advantage have largely focused on computational speedups and on quantum simulation of many-body physics, limited by fidelity and capability of current devices. Discriminating laser-pulse-modulated classical-communication codewords at the minimum allowable probability of error using universal-quantum processing presents a promising parallel direction, one that is of both fundamental importance in quantum state discrimination, as well as of technological relevance in deep-space laser communications. Here we present an experimental realization of a quantum joint detection receiver for binary phase shift keying modulated codewords of a 3-bit linear tree code using a recently-proposed quantum algorithm: belief propagation with quantum messages. The receiver, translated to a quantum circuit, was experimentally implemented on a trapped-ion device -- the recently released Honeywell LT-1.0 system using ${}^{171}Yb+ $ ions, which possesses all-to-all connectivity and mid-circuit measurement capabilities that are essential to this demonstration. We conclusively realize a previously postulated but hitherto not-demonstrated joint quantum detection scheme, and provide an experimental framework that surpasses the quantum limit on the minimum average decoding error probability associated with pulse-by-pulse detection in the low mean photon number limit. The full joint-detection scheme bridges across photonic and trapped-ion based quantum information science, mapping the photonic coherent states of the modulation alphabet onto inner product-preserving states of single-ion qubits. Looking ahead, our work opens new avenues in hybrid realizations of quantum-enhanced receivers with applications in astronomy and emerging space-based platforms.