Fault-tolerant magic state preparation with flag qubits

Magic state distillation is one of the leading candidates for implementing universal fault-tolerant logical gates. However, the distillation circuits themselves are not fault-tolerant, so there is additional cost to first implement encoded Clifford gates with negligible error. In this paper we present a scheme to fault-tolerantly and directly prepare magic states using flag qubits. One of these schemes uses a single extra ancilla, even with noisy Clifford gates. We compare the physical qubit and gate cost of this scheme to the magic state distillation protocol of Meier, Eastin, and Knill, which is efficient and uses a small stabilizer circuit. In some regimes, we show that the overhead can be improved by several orders of magnitude.Comment: 26 pages, 17 figures, 5 tables. Comments welcome! v2 (published version): quantumarticle documentclass and expanded discussions on the fault-tolerant scheme

Error suppression via complementary gauge choices in Reed-Muller codes

Concatenation of two quantum error correcting codes with complementary sets of transversal gates can provide a means towards universal fault-tolerant computation. We first show that it is generally preferable to choose the inner code with the higher pseudo-threshold in order to achieve lower logical failure rates. We then explore the threshold properties of a wide range of concatenation schemes. Notably, we demonstrate that the concatenation of complementary sets of Reed-Muller codes can increase the code capacity threshold under depolarizing noise when compared to extensions of previously proposed concatenation models. We also analyze the properties of logical errors under circuit level noise, showing that smaller codes perform better for all sampled physical error rates. Our work provides new insights into the performance of universal concatenated quantum codes for both code capacity and circuit level noise.Comment: 11 pages + 4 appendices, 6 figures. In v2, Fig.1 was added to conform to journal specification

Flag fault-tolerant error correction with arbitrary distance codes

In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for the first time, our protocol also applies to a broader class of distance-three codes than was previously known. Flag circuits use extra ancilla qubits to signal when errors resulting from $v$ faults in the circuit have weight greater than $v$. The flag error correction protocol is applicable to stabilizer codes of arbitrary distance which satisfy a set of conditions and uses fewer qubits than other schemes such as Shor, Steane and Knill error correction. We give examples of infinite code families which satisfy these conditions and analyze the behaviour of distance-three and -five examples numerically. Requiring fewer resources than Shor error correction, flag error correction could potentially be used in low-overhead fault-tolerant error correction protocols using low density parity check quantum codes of large code length.Comment: 29 pages (18 pages main text), 22 figures, 7 tables. Comments welcome! V3 represents the version accepted to quantu

The Small Stellated Dodecahedron Code and Friends

We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges resp. vertices of a small stellated dodecahedron, making this code suitable for 3D connectivity. This code encodes 8 logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity check measurements) as compared to 1 logical qubit into 9 physical qubits (plus 8 ancilla qubits) for the surface code. We develop fault-tolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuit-based pseudo-threshold.Comment: 19 pages, 14 figures, comments welcome! v2 includes updates which conforms with the journal versio

A Direct, Early Stage Guanidinylation Protocol for the Synthesis of Complex Aminoguanidine-containing Natural Products

The guanidine functional group, displayed most prominently in the amino acid arginine, one of the fundamental building blocks of life, is an important structural element found in many complex natural products and pharmaceuticals. Owing to the continual discovery of new guanidinecontaining natural products and designed small molecules, rapid and efficient guanidinylation methods are of keen interest to synthetic and medicinal organic chemists. Because the nucleophilicity and basicity of guanidines can affect subsequent chemical transformations, traditional, indirect guanidinylation is typically pursued. Indirect methods commonly employ multiple protection steps involving a latent amine precursor, such as an azide, phthalimide, or carbamate. By circumventing these circuitous methods and employing a direct guanidinylation reaction early in the synthetic sequence, it was possible to forge the linear terminal guanidine containing backbone of clavatadine A to realize a short and streamlined synthesis of this potent factor XIa inhibitor. In practice, guanidine hydrochloride is elaborated with a carefully constructed protecting array that is optimized to survive the synthetic steps to come. In the preparation of clavatadine A, direct guanidinylation of a commercially available diamine eliminated two unnecessary steps from its synthesis. Coupled with the wide variety of known guanidine protecting groups, direct guanidinylation evinces a succinct and efficient practicality inherent to methods that find a home in a synthetic chemist\u27s toolbox