Related papers: Tessellation codes: encoded quantum gates by geome…
The typical time-independent view of quantum error correction (QEC) codes hides significant freedom in the decomposition into circuits that are executable on hardware. Using the concept of detecting regions, we design time-dynamic QEC…
The stable operation of quantum computers will rely on error-correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many…
The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated…
We consider geometric methods of ``rotating" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric code states using single shot techniques, and in turn these…
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…
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…
Surface codes$\unicode{x2014}$leading candidates for quantum error correction (QEC)$\unicode{x2014}$and entanglement phases$\unicode{x2014}$a key notion for many-body quantum dynamics$\unicode{x2014}$have heretofore been unrelated. Here, we…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…
We propose a scheme to implement geometric entangling gates for two logical qubits in a coupled cavity system in decoherence-free subspaces. Each logical qubit is encoded with two atoms trapped in a single cavity and the geometric…
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions…
An economy of scale is found when storing many qubits in one highly entangled block of a topological quantum code. The code is defined by construction of a topologically convoluted 2-d surface and does not work by compressing redundancy in…
We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming…
The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
Quantum networks serve as the means to transmit information, encoded in quantum bits or qubits, between quantum processors that are physically separated. Given the instability of qubits, the design of such networks is challenging,…
We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes…
We consider realistic, multi-parameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli…
Most quantum computing architectures can be realized as two-dimensional lattices of qubits that interact with each other. We take transmon qubits and transmission line resonators as promising candidates for qubits and couplers; we use them…
Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a…