Related papers: Examples of minimal-memory, non-catastrophic quant…
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…
Quantum convolutional codes, like their classical counterparts, promise to offer higher error correction performance than block codes of equivalent encoding complexity, and are expected to find important applications in reliable quantum…
One of the major goals in quantum information processing is to reduce the overhead associated with the practical implementation of quantum protocols, and often, routines for quantum error correction account for most of this overhead. A…
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…
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…
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…
We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First,…
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…
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…
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.…
We present an algorithm to construct quantum circuits for encoding and inverse encoding of quantum convolutional codes. We show that any quantum convolutional code contains a subcode of finite index which has a non-catastrophic encoding…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
We show how extra entanglement shared between sender and receiver reduces the memory requirements for a general entanglement-assisted quantum convolutional code. We construct quantum convolutional codes with good error-correcting properties…
Efficiently encoding classical visual data into quantum states is essential for realizing practical quantum neural networks (QNNs). However, existing encoding schemes often discard spatial and semantic information when adapting…
Simulation of fermionic Hamiltonians with gate-based quantum computers requires the selection of an encoding from fermionic operators to quantum gates, the most widely used being the Jordan-Wigner transform. Many alternative encodings…
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…
A novel decoding algorithm is developed for general quantum convolutional codes. Exploiting useful ideas from classical coding theory, the new decoder introduces two innovations that drastically reduce the decoding complexity compared to…
A significant obstacle for practical quantum computation is the loss of physical qubits in quantum computers, a decoherence mechanism most notably in optical systems. Here we experimentally demonstrate, both in the quantum circuit model and…
We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary single-qubit error. Our first example is a degenerate six-qubit quantum error-correcting code. We explicitly provide the…
The rapid scaling of Large Language Models (LLMs) elevates inference costs and compounds substantial deployment barriers. While quantization to 8 or 4 bits mitigates this, sub-3-bit methods face severe accuracy, scalability, and efficiency…