相关论文: Non-catastrophic Encoders and Encoder Inverses for…
Poulin, Tillich, and Ollivier discovered an important separation between the classical and quantum theories of convolutional coding, by proving that a quantum convolutional encoder cannot be both non-catastrophic and recursive.…
Quantum convolutional coding is a technique for encoding a stream of quantum information before transmitting it over a noisy quantum channel. Two important goals in the design of quantum convolutional encoders are to minimize the memory…
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to…
Classical turbo codes efficiently approach the Shannon limit, and so bringing these over to the quantum scenario would allow for rapid transmission of quantum information. Early on in the work of defining the quantum analogue, it was shown…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum…
Transversal gates are logical gate operations on encoded quantum information that are efficient in gate count and depth, and are designed to minimize error propagation. Efficient encoding circuits for quantum codes that admit transversal…
We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
A quantum shift register circuit acts on a set of input qubits and memory qubits, outputs a set of output qubits and updated memory qubits, and feeds the memory back into the device for the next cycle (similar to the operation of a…
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…
Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the…
One of the most important open questions in the theory of quantum convolutional coding is to determine a minimal-memory, non-catastrophic, polynomial-depth convolutional encoder for an arbitrary quantum convolutional code. Here, we present…
We transfer the concept of linear feed-back shift registers to quantum circuits. It is shown how to use these quantum linear shift registers for encoding and decoding cyclic quantum error-correcting codes.
In this paper, we show how to construct non-binary entanglement-assisted stabilizer quantum codes by using pre-shared entanglement between the sender and receiver. We also give an algorithm to determine the circuit for non-binary…
We present two methods for the construction of quantum circuits for quantum error-correcting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC…
Quantum autoencoder is a quantum neural network model for compressing information stored in quantum states. However, one needs to process information stored in quantum circuits for many tasks in the emerging quantum information technology.…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…