相关论文: Creating Boolean Functions for the Five-EPR-Pair, …
This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the…
Quantum states have high affinity for errors and hence error correction is of utmost importance to realise a quantum computer. Laflamme showed that 5 qubits are necessary to correct a single error on a qubit. In a Pauli error model, four…
The future of quantum repeater networking will require interoperability between various error correcting codes. A few specific code conversions and even a generalized method are known, however, no detailed analysis of these techniques in…
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph…
The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. 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…
In this paper, based on the relationship between logic functions and quantum error correcting codes(QECCs), we unify the construction of QECCs via graphs, projectors and logic functions. A construction of QECCs over a prime field GF(p) is…
Quantum error correction in general is experimentally challenging as it requires significant expansion of the size of quantum circuits and accurate performance of quantum gates to fulfill the error threshold requirement. Here we propose a…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
We investigate novel protocols for entanglement purification of qubit Bell pairs. Employing genetic algorithms for the design of the purification circuit, we obtain shorter circuits achieving higher success rates and better final fidelities…
This study explores the feasibility of utilizing quantum error correction (QEC) to generate and store logical Bell states in heralded quantum entanglement protocols, crucial for quantum repeater networks. Two lattice surgery-based protocols…
We present a method to conduct both quantum state reconstruction and entanglement purification simultaneously that is advantageous in several respects over previous work in this direction, showing that the number of Bell pairs necessary to…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…
We study how different types of quantum correlations can be established as the consequence of a generalized entanglement swapping protocol where starting from two Bell pairs (1, 2) and (3, 4), a general quantum measurement (denoted by a…
In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial…
Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean…
It is often difficult to correctly implement a Boolean controller for a complex system, especially when concurrency is involved. Yet, it may be easy to formally specify a controller. For instance, for a pipelined processor it suffices to…
Boolean functions are mathematical objects with numerous applications in domains like coding theory, cryptography, and telecommunications. Finding Boolean functions with specific properties is a complex combinatorial optimization problem…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…