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We propose a unifying paradigm for analyzing and constructing topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. To this end, we relate such circuits to discrete fixed-point…
Conventional approaches to fault-tolerant quantum computing realize logical circuits gate-by-gate, synthesizing each gate independently on one or more code blocks. This incurs excess overhead and doesn't leverage common structures in…
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
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…
We describe a fault-tolerant version of the one-way quantum computer using a cluster state in three spatial dimensions. Topologically protected quantum gates are realized by choosing appropriate boundary conditions on the cluster. We…
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…
Quantum computing promises a new approach to solving difficult computational problems, and the quest of building a quantum computer has started. While the first attempts on construction were succesful, scalability has never been achieved,…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow…
Topological quantum computing has recently proven itself to be a very powerful model when considering large- scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
In order to achieve fault-tolerant quantum computation, we need to repeat the following sequence of four steps: First, perform 1 or 2 qubit quantum gates (in parallel if possible). Second, do a syndrome measurement on a subset of the…
Fault-tolerant quantum computation using two-dimensional topological quantum error correcting codes can benefit from multi-qubit long-range operations. By using simple commutation rules, a quantum circuit can be transpiled into a sequence…
We introduce several dynamical schemes that take advantage of mid-circuit measurement and nearest-neighbor gates on a lattice with maximum vertex degree three to implement topological codes and perform logic gates between them. We first…
Lattice surgery with two-dimensional quantum error correcting codes is among the leading schemes for fault-tolerant quantum computation, motivated by superconducting hardware architectures. In conventional lattice surgery compilation…
Floquet quantum error-correcting codes provide an operationally economical route to fault tolerance by dynamically generating stabilizer structures using only two-body Pauli measurements. But while it is well established that stabilizer…
Photonics provides a viable path to a scalable fault-tolerant quantum computer. The natural framework for this platform is measurement-based quantum computation, where fault-tolerant graph states supersede traditional quantum…
Fault-tolerant quantum error correction is a necessity for any quantum architecture destined to tackle interesting, large-scale problems. Its theoretical formalism has been well founded for nearly two decades. However, we still do not have…
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…
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…