Related papers: Logic Functions and Quantum Error Correcting Codes
We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the…
Descriptions of quantum algorithms, communication etc. protocols assume the existence of closed quantum system. However, real life quantum systems are open and are highly sensitive to errors. Hence error correction is of utmost importance…
The gauge field formalism, or operator-valued cochain formalism, has recently emerged as a powerful framework for describing quantum Calderbank-Shor-Steane (CSS) codes. In this work, we extend this framework to construct a broad class of…
In the realm of quantum computing, quantum circuits serve as essential depictions of quantum algorithms, which are then compiled into executable operations for quantum computations. Quantum compilers are responsible for converting these…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
Quantum error correction (QEC) is crucial for realizing scalable quantum technologies, and topological quantum error correction (TQEC) has emerged as the most experimentally advanced paradigm of QEC. Existing homological and topological…
In this paper we present a new unified theoretical framework that describes the full dynamics of quantum computation. Our formulation allows any questions pertaining to the physical behavior of a quantum computer to be framed, and in…
We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to…
We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we apply a random unitary error channel and subsequently measure stabilizer checks,…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
Quantum computers have the potential to solve certain complex problems in a much more efficient way than classical computers. Nevertheless, current quantum computer implementations are limited by high physical error rates. This issue is…
Quantum error correction and fault-tolerant quantum computation are two fundamental concepts which make quantum computing feasible. While providing a theoretical means with which to ensure the arbitrary accuracy of any quantum circuit,…
Quantum computers are highly susceptible to errors due to unintended interactions with their environment. It is crucial to correct these errors without gaining information about the quantum state, which would result in its destruction…
A common assumption in analyses of error thresholds and quantum computing in general is that one applies fault-tolerant quantum error correction (FTQEC) after every gate. This, however, is known not to always be optimal if the FTQEC…
In coding theory, constructing codes with good parameters is one of the most important and fundamental problems. Though a great many of good codes have been produced, most of them are defined over alphabets of sizes equal to prime powers.…
Scaling quantum computing to practical applications necessitates reliable quantum error correction. Although numerous correction codes have been proposed, the overall correction efficiency critically limited by the decode algorithms. We…
The ultimate goal of quantum error correction is to create logical qubits with very low error rates (e.g. 1e-12) and assemble them into large-scale quantum computers capable of performing many (e.g. billions) of logical gates on many (e.g.…
Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral…
The realization of large-scale quantum computers requires not only quantum error correction (QEC) but also fault-tolerant operations to handle errors that propagate into harmful errors. Recently, flag-based protocols have been introduced…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…