Related papers: The X-Cube Floquet Code
Bosonic systems offer unique advantages for quantum error correction, as a single bosonic mode provides a large Hilbert space to redundantly encode quantum information. However, previous studies have been limited to exploiting symmetries in…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such…
This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
Quantum computing as a promising technology can utilize stochastic solutions instead of deterministic approaches for complicated scenarios for which classical computing is inefficient, provided that both the concerns of the error-prone…
Bias-tailored codes such as the XZZX surface code and the domain wall color code achieve high dephasing-biased thresholds because, in the infinite-bias limit, their $Z$ syndromes decouple into one-dimensional repetition-like chains; the…
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…
Floquet codes have recently emerged as a new family of error-correcting codes, and have drawn significant interest across both theoretical and practical quantum computing. A central open question has been how to implement logical operations…
Analyzing and developing new quantum error-correcting schemes is one of the most prominent tasks in quantum computing research. In such efforts, introducing time dynamics explicitly in both analysis and design of error-correcting protocols…
Universal quantum computers require fault-tolerant logical qudits, as qudits naturally align with the simulation of multi-level physical systems. Here, we present a general framework and working examples for encoding fault-tolerant logical…
The existence of self-correcting quantum memories in three dimensions is a long-standing open question at the interface between quantum computing and many-body physics. We take the perspective that large contributions to the entropy arising…
Bosonic codes, leveraging infinite-dimensional Hilbert spaces for redundancy, offer great potential for encoding quantum information. However, the realization of a practical continuous-variable bosonic code that can simultaneously correct…
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…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted $Z$-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on…
We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which…
From the perspective of quantum many-body physics, the Floquet code of Hastings and Haah can be thought of as a measurement-only version of the Kitaev honeycomb model where a periodic sequence of two-qubit XX, YY, and ZZ measurements…
Quantum computation requires qubits that satisfy often-conflicting criteria, including scalable control and long-lasting coherence. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits.…
To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the…