Related papers: Stabilizer quantum codes defined by trace-dependin…
Locating the boundaries of consecutive blocks of quantum information is a fundamental building block for advanced quantum computation and quantum communication systems. We develop a coding theoretic method for properly locating boundaries…
Non-stabilizerness is a fundamental resource for quantum computational advantage, differentiating classically simulable circuits from those capable of universal quantum computation. Recently, non-stabilizerness has been shown to be relevant…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
Product codes are a concatenated error-correction scheme that has been often considered for applications requiring very low bit-error rates, which demand that the error floor be decreased as much as possible. In this work, we consider…
Quantum stabilizer codes often struggle with syndrome errors due to measurement imperfections. Typically, multiple rounds of syndrome extraction are employed to ensure reliable error information. In this paper, we consider phenomenological…
It is important to study the behavior of a t-error correcting quantum code when the number of errors is greater than t, because it is likely that there are also small errors besides t large correctable errors. We give a lower bound for the…
A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements.…
The ubiquity of stabilizer circuits in the design and operation of quantum computers makes techniques to verify their correctness essential. The simulation of stabilizer circuits, which aims to replicate their behavior using a classical…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
We introduce a class of bosonic quantum error-correcting codes, termed \emph{extended binomial codes}, which generalize the structure of one-mode binomial codes by incorporating ideas from high-rate qubit stabilizer codes. These codes are…
There is a connection between classical codes, highly entangled pure states (called k-uniform or absolutely maximally entangled (AME) states), and quantum error correcting codes (QECCs). This leads to a systematic method to construct…
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
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…
We demonstrate that small quantum memories, realized via quantum error correction in multi-qubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant error model of the system. For a biased noise…
Quantum error correction is one of the fundamental building blocks of digital quantum computation. The Quantum Lego formalism has introduced a systematic way of constructing new stabilizer codes out of basic lego-like building blocks, which…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum…
We present a method for implementing stabilizer-based codes with encoding schemes of the operator quantum error correction paradigm, e.g., the "standard" five-qubit and CSS codes, on solid-state qubits with Ising or XY-type interactions.…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…