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Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes,…
Quantum gate benchmarking is unavoidably influenced by state preparation and measurement errors. Randomized benchmarking addresses this challenge by employing group twirling to regularize the noise channel, then provides a characterization…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Fault-tolerant quantum error correction provides a strategy to protect information processed by a quantum computer against noise which would otherwise corrupt the data. A fault-tolerant universal quantum computer must implement a universal…
The surface code is currently the primary proposed method for performing quantum error correction. However, despite its many advantages, it has no native method to fault-tolerantly apply non-Clifford gates. Additional techniques are…
We introduce a family of scalable planar fault-tolerant circuits that implement logical non-Clifford operations on a 2D color code, such as a logical $T$ gate or a logical non-Pauli measurement that prepares a magic $|T\rangle$ state. The…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a…
Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a…
Estimating and reducing the overhead of fault tolerance (FT) schemes is a crucial step toward realizing scalable quantum computers. Of particular interest are schemes based on two-dimensional (2D) topological codes such as the surface and…
Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom…
Quantum computing can be realized with numerous different hardware platforms and computational protocols. A highly promising approach to foster scalability is to apply a photonic platform combined with a measurement-induced quantum…
We present a 1D repetition code based on the so-called cat qubits as a viable approach toward hardware-efficient universal and fault-tolerant quantum computation. The cat qubits that are stabilized by a two-photon driven-dissipative…
Given a quantum error correcting code, an important task is to find encoded operations that can be implemented efficiently and fault-tolerantly. In this Letter we focus on topological stabilizer codes and encoded unitary gates that can be…
As experimental platforms for quantum information processing continue to mature, characterization of the quality of unitary gates that can be applied to their quantum bits (qubits) becomes essential. Eventually, the quality must be…
I present a new approach for designing quantum error-correcting codes that guarantees a physically natural implementation of Clifford operations. Inspired by the scheme put forward by Gottesman, Kitaev, and Preskill for encoding a qubit in…
We establish a unified framework for Majorana-based fault-tolerant quantum computation with Majorana surface codes and Majorana color codes. All logical Clifford gates are implemented with zero time overhead. This is done by introducing a…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
Lattice surgery protocols allow for the efficient implementation of universal gate sets with two-dimensional topological codes where qubits are constrained to interact with one another locally. In this work, we first introduce a decoder…