相关论文: Shifts on a finite qubit string: A class of quantu…

We consider to treat the usual probabilistic cloning, state separation, unambiguous state discrimination, \emph{etc} in a uniform framework. All these transformations can be regarded as special examples of generalized completely positive…

We develop a unified quantum framework for subgraph counting in graphs. We encode a graph on $N$ vertices into a quantum state on $2\lceil \log_2 N \rceil$ working qubits and $2$ ancilla qubits using its adjacency list, with worst-case gate…

Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction…

We discuss an approach to quantum gerbes over quantum groups in terms of q-deformation of transition functions for a loop group bundle. The case of the quantum group SUq(2) is treated in some detail.

Quantum computing has the potential to significantly speed up complex computational tasks, and arguably the most promising application area for near-term quantum computers is the simulation of quantum mechanics. To make the most of our…

String problems in general can be solved faster by using special data structures such as suffixes in many cases structured as trees and arrays. In this paper, we show that suffixes used in those data structures can be obtained by using…

The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…

Quantum information processing protocols are efficiently implemented on spin-$\frac{1}{2}$ networks. A quantum communication protocol generally involves a certain number of parties having local access to a subset of a larger system, whose…

We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…

We develop a quasisymmetric analogue of the theory of Schubert cycles, building off of our previous work on a quasisymmetric analogue of Schubert polynomials and divided differences. Our constructions result in a natural geometric…

Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…

We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discrete analogs of completely integrable transformation on closed…

While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…

In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…

A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…

A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This raises the question where the usual algebraic argument --…

Using the concept of mixable shuffles, we formulate explicitly the quantum quasi-shuffle product. We also provide a desirable description of the subalgebra generated by the set of primitive elements of the quantum quasi-shuffle bialgebra. A…

We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis…

The Hamming distance is ubiquitous in computing. Its computation gets expensive when one needs to compare a string against many strings. Quantum computers (QCs) may speed up the comparison. In this paper, we extend an existing algorithm for…

A system of unitary transformations providing two optimal copies of an arbitrary input cubit is obtained. An algorithm based on classical Boolean algebra and allowing one to find any unitary transformation realized by the quantum CNOT…