Related papers: Entanglement-Assisted Quantum Error-Correcting Cod…
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…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
In this paper we extend to asymmetric quantum error-correcting codes (AQECC) the construction methods, namely: puncturing, extending, expanding, direct sum and the (u|u + v) construction. By applying these methods, several families of…
Quantum error-correction codes (QECCs) are a vital ingredient of quantum computation and communication systems. In that context it is highly desirable to design QECCs that can be represented by graphical models which possess a structure…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
We propose and prove an existential theorem for entanglement-assisted asymmetric quantum error correction. Then we demonstrate its superiority over the conventional one.
We examine the transformation of noise under a quantum error correcting code (QECC) concatenated repeatedly with itself, by analyzing the effects of a quantum channel after each level of concatenation using recovery operators that are…
Correlation functions and entanglement are two different aspects to characterize quantum many-body states. While many correlation functions are experimentally accessible, entanglement entropy (EE), the simplest characterization of quantum…
We study the performance of quantum error correction codes (QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the…
Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…
The entanglement of formation gives a necessary and sufficient condition for the existence of a perfect quantum error correction procedure.
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
It is often assumed that the ancilla qubits required for encoding a qubit in quantum error correction (QEC) have to be in pure states, $|00...0>$ for example. In this letter, we seek an encoding scheme, in which the ancillae may be in a…
A toric quantum error-correcting code construction procedure is presented in this work. A new class of an infinite family of toric quantum codes is provided by constructing a classical cyclic code on the square lattice $\mathbb{Z}_{q}\times…
We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…
Quantum error correcting codes (QECC) is becoming an increasingly important branch of coding theory. For classical block codes, a \href{codetables.de} {comprehensive database of best known codes} exists which is available online at…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building…
Generating entanglement between distributed network nodes is a prerequisite for the quantum internet. Entanglement distribution protocols based on high-dimensional photonic qudits enable the simultaneous generation of multiple entangled…
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum…