Related papers: Biunitary constructions in quantum information
We show that maximal families of mutually unbiased bases are characterized in all dimensions by partitioned unitary error bases, up to a choice of a family of Hadamards. Furthermore, we give a new construction of partitioned unitary error…
This paper explores the representation of quantum computing in terms of unitary reflections (unitary transformations that leave invariant a hyperplane of a vector space). The symmetries of qubit systems are found to be supported by…
Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…
We study bipartite unitary operators which stay invariant under the local actions of diagonal unitary and orthogonal groups. We investigate structural properties of these operators, arguing that the diagonal symmetry makes them suitable for…
From the set of operators for errors and its correction code, we introduce the so-called complete unitary transformation. It can be used for encoding while the inverse of it can be applied for correcting the errors of the encoded qubit. We…
We show how to construct an arbitrary robust one-qubit unitary operation with a control Hamiltonian of $A_x(t) \sigma_x + A_y(t) \sigma_y$, where $\sigma_i$ is a Pauli matrix and $A_i(t)$ is piecewise constant. Our method, based on planar…
A problem of universality in simulation of evolution of quantum system and in theory of quantum computations is related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific…
All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always…
The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work…
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…
Errors in the control of quantum systems may be classified as unitary, decoherent and incoherent. Unitary errors are systematic, and result in a density matrix that differs from the desired one by a unitary operation. Decoherent errors…
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…
A family of two-unitary complex Hadamard matrices (CHM) stemming from a particular matrix, of size $36$ is constructed. Every matrix in this orbit remains unitary after operations of partial transpose and reshuffling which makes it a…
The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated by physics, or information theory, etc., the respective symmetry objects might become more…
Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze…
Although Hadamard matrices have been investigated since the nineteenth century, relatively little is known about their higher-dimensional analogues. In this paper, we introduce two constructions of Hadamard hypercubes. The first…
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes that obey (are covariant with respect to) continuous symmetries in a certain sense cannot…
In classical computational chemistry, the coupled-cluster ansatz is one of the most commonly used $ab~initio$ methods, which is critically limited by its non-unitary nature. The unitary modification as an ideal solution to the problem is,…
We studied the construction problem of the unextendible product basis (UPB). We mainly give a method to construct a UPB of a quantum system through the UPBs of its subsystem. Using this method and the UPBs which are known for us, we…
Binary classification is a fundamental problem in machine learning. Recent development of quantum similarity-based binary classifiers and kernel method that exploit quantum interference and feature quantum Hilbert space opened up tremendous…