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Circuit synthesis is the task of decomposing a given logical functionality into a sequence of elementary gates. It is (depth-)optimal if it is impossible to achieve the desired functionality with even shorter circuits. Optimal synthesis is…

We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be…

With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation -- magic state preparation. Using an…

Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…

We present a blueprint for building a fault-tolerant universal quantum computer with Rydberg atoms. Our scheme, which is based on the surface code, uses individually-addressable optically-trapped atoms as qubits and exploits…

The failure susceptibility of the quantum hardware will force quantum computers to execute fault-tolerant quantum circuits. These circuits are based on quantum error correcting codes, and there is increasing evidence that one of the most…

We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. Namely, other than computational basis state preparation as required by the DiVincenzo criteria [1], our scheme requires…

Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods that apply to codes of high rate, encoding k qubits per block with k>1. It is shown that the logical qubits within a given block can…

We propose a scheme for the fault-tolerant implementation of arbitrary Clifford circuits. To achieve this, we extend previous work on flag gadgets for syndrome extraction to a general framework that flags any Clifford circuit. This…

A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-K\"onig bound for $n$-dimensional topological stabilizer codes. In this work, we extend…

A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…

Flag qubits have recently been proposed in syndrome extraction circuits to detect high-weight errors arising from fewer faults. The use of flag qubits allows the construction of fault-tolerant protocols with the fewest number of ancillas…

Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and…

The color code is remarkable for its ability to perform fault-tolerant logic gates. This motivates the design of practical decoders that minimise the resource cost of color-code quantum computation. Here we propose a decoder for the planar…

As quantum computing machines move towards the utility regime, it is essential that users are able to verify their delegated quantum computations with security guarantees that are (i) robust to noise (ii) composable with other secure…

We propose a novel technique for optimizing a modular fault-tolerant quantum computing architecture, taking into account any desired space-time trade-offs between the number of physical qubits and the fault-tolerant execution time of a…

Steane's 7-qubit quantum error-correcting code admits a set of fault-tolerant gates that generate the Clifford group, which in itself is not universal for quantum computation. The 15-qubit Reed-Muller code also does not admit a universal…

We consider the problem of fault-tolerant quantum computation in the presence of slow error diagnostics, either caused by measurement latencies or slow decoding algorithms. Our scheme offers a few improvements over previously existing…

An important approach to the fault-tolerant quantum computation is protecting the logical information using the quantum error correction. Usually, the logical information is in the form of logical qubits, which are encoded in physical…

Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory. Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and…