Related papers: On the logical operators of quantum codes
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
In this dissertation, I present a general method for studying quantum error correction codes (QECCs). This method not only provides us an intuitive way of understanding QECCs, but also leads to several extensions of standard QECCs,…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
Working within the framework of Loop Quantum Gravity (LQG), we construct a set of three operators suitable for identifying coordinate-like quantities on a spin-network configuration. In doing so, we rely on known properties of operators for…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose…
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium…
We utilize the symmetry groups of regular tessellations on two-dimensional surfaces of different constant curvatures, including spheres, Euclidean planes and hyperbolic planes, to encode a qubit or qudit into the physical degrees of freedom…
We present a canonical way of assigning to each magnitude of a classical mechanical system a differential operator in the configuration space, thus rigorously establishing the Correspondence Principle for such systems. Here we show how each…
Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the…
We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new…
This Diplom thesis provides an explicit construction of a quantum Goppa code for any hyperelliptic curve over a non-binary field. Hyperelliptic curves have conjugate pairs of rational places. We use these pairs to construct self-orthogonal…
We consider the problem of coding for quantum channels with side information that is available ahead of time at the transmitter but not at the receiver. We find a single-letter expression for the entanglement-assisted quantum capacity of…
Operator entanglement of two-qubit joint unitary operations is revisited. Schmidt number is an important attribute of a two-qubit unitary operation, and may have connection with the entanglement measure of the unitary operator. We found the…