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1. Generating Fault-Tolerant Cluster States from Crystal Structures

   https://doi.org/10.22331/q-2020-07-13-295  

   Newman, Michael; de Castro, Leonardo Andreta; Brown, Kenneth R. (July 2020, Quantum)

   null (Ed.)

   Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states. Recent work has demonstrated that MBQC provides a more general framework for fault-tolerance that extends beyond foliated quantum error-correcting codes. We systematically expand on that paradigm, and use combinatorial tiling theory to study and construct new examples of fault-tolerant cluster states derived from crystal structures. Included among these is a robust self-dual cluster state requiring only degree- 3 connectivity. We benchmark several of these cluster states in the presence of circuit-level noise, and find a variety of promising candidates whose performance depends on the specifics of the noise model. By eschewing the distinction between data and ancilla, this malleable framework lays a foundation for the development of creative and competitive fault-tolerance schemes beyond conventional error-correcting codes. 

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2. Fault-tolerant optical interconnects for neutral-atom arrays

   https://doi.org/10.1103/PhysRevResearch.7.013313  

   Sinclair, Josiah; Ramette, Joshua; Grinkemeyer, Brandon; Bluvstein, Dolev; Lukin, Mikhail D; Vuletić, Vladan (March 2025, Physical Review Research)

   We analyze the use of photonic links to enable large-scale fault-tolerant connectivity of locally error-corrected modules based on neutral atom arrays. Our approach makes use of recent theoretical results showing the robustness of surface codes to boundary noise and combines recent experimental advances in atom-array quantum computing with logical qubits with optical quantum networking techniques. We find the conditions for fault tolerance can be achieved with local two-qubit Rydberg gate and nonlocal Bell-pair errors below 1% and 10%, respectively, without requiring distillation or space-time overheads. Realizing the interconnects with a lens, a single optical cavity, or an array of cavities enables—with sufficient multiplexing—a Bell-pair generation rate in the 1–50 MHz range. When directly interfacing logical qubits, this rate translates to error-correction cycles in the 25–2000 kHz range, satisfying all requirements for fault tolerance and in the upper range fast enough for 100 kHz logical clock cycles. Published by the American Physical Society2025 

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3. Fault-Tolerant Quantum Computation Using Large Spin-Cat Codes

   https://doi.org/10.1103/PRXQuantum.5.020355  

   Omanakuttan, Sivaprasad; Buchemmavari, Vikas; Gross, Jonathan A; Deutsch, Ivan H; Marvian, Milad (June 2024, PRX Quantum)

   We construct a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, analogous to the continuous-variable cat encoding. With this, we can correct the dominant error sources, namely processes that can be expressed as error operators that are linear or quadratic in the components of angular momentum. Such codes tailored to dominant error sources can exhibit superior thresholds and lower resource overheads when compared to those designed for unstructured noise models. A key component is the gate that preserves the rank of spherical tensor operators. Categorizing the dominant errors as phase and amplitude errors, we demonstrate how phase errors, analogous to phase-flip errors for qubits, can be effectively corrected. Furthermore, we propose a measurement-free error-correction scheme to address amplitude errors without relying on syndrome measurements. Through an in-depth analysis of logical gate errors, we establish that the fault-tolerant threshold for error correction in the spin-cat encoding surpasses that of standard qubit-based encodings. We consider a specific implementation based on neutral-atom quantum computing, with qudits encoded in the nuclear spin of 87Sr, and show how to generate the universal gate set, including the rank-preserving gate, using quantum control and the Rydberg blockade. These findings pave the way for encoding a qubit in a large spin with the potential to achieve fault tolerance, high threshold, and reduced resource overhead in quantum information processing. 

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4. Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae

   https://doi.org/10.1103/PhysRevX.14.031016  

   Xu, Qian; Zeng, Pei; Xu, Daohong; Jiang, Liang (July 2024, Physical Review X)

   Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control. Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single-photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction requires only dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is comprised of only a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits. 

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5. Strict area law implies commuting parent Hamiltonian

   Kim, I H; Lin, T-C; Ranard, D; Shi, B (April 2024, arXiv)

   arXiv (Ed.)

   We propose a fault-tolerant quantum error correction architecture consisting of a linear array of emitters and delay lines. In our scheme, a resource state for fault-tolerant quantum computation is generated by letting the emitters interact with a stream of photons and their neighboring emitters. Depending on the number of emitters ne, we study the effect of delay line errors in two regimes: when ne is a small constant of order unity and when ne scales with the code distance. Between these two regimes, the logical error rate steadily decreases as ne increases, from a scaling of exp(−cη−1/2) to exp(−c′η−1), where η is the error rate per unit length in the delay line, for some constants c,c′>0. We also carry out a detailed study of the break-even point and the fault-tolerance overhead. These studies suggest that the multi-emitter architecture, using the state-of-the-art delay lines, can be used to demonstrate error suppression, assuming other sources of errors are sufficiently small. 

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