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While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
Large-scale quantum computation requires to be performed in the fault-tolerant manner. One crucial challenge of fault-tolerant quantum computing (FTQC) is reducing the overhead of implementing logical gates. Recently work proposed…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
We construct quantum codes that support transversal $CCZ$ gates over qudits of arbitrary prime power dimension $q$ (including $q=2$) such that the code dimension and distance grow linearly in the block length. The only previously known…
Dynamic quantum circuits incorporate mid-circuit measurements and feed-forward operations originally intended to realize Quantum Error Correction. This paradigm has recently been utilized to prepare certain states and long-range entangling…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
We give an asymptotically good family of quantum CSS codes on qubits with a transversal CCZ gate, meaning that the parallel logical CCZ on all logical qubits is performed by parallel physical CCZs on (a subset of) physical qubits. The…
Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state…
Transversal gates play a crucial role in suppressing error propagation in fault-tolerant quantum computation, yet they are intrinsically constrained: any nontrivial code encoding a single logical qubit admits only a finite subgroup of…
One of the main problems for the future of practical quantum computing is to stabilize the computation against unwanted interactions with the environment and imperfections in the applied operations. Existing proposals for quantum memories…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…
We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an…
Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary…
Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and…
This is a short review on an interdisciplinary field of quantum information science and statistical mechanics. We first give a pedagogical introduction to the stabilizer formalism, which is an efficient way to describe an important class of…
We show how to perform a fault-tolerant universal quantum computation in 2D architectures using only transversal unitary operators and local syndrome measurements. Our approach is based on a doubled version of the 2D color code. It enables…
Universal fault-tolerant quantum computation requires overcoming the Eastin--Knill theorem on quantum error correction (QEC) codes that protect information from noise. This is often accomplished through strategies like magic state…