Related papers: Remark on Quantum Nambu Bracket
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…
This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the…
First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity.…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
We introduce an affinization of the quantum Kac-Moody algebra associated to a symmetric generalized Cartan matrix. Based on the affinization, we construct a representation of the quantum Kac-Moody algebra by vertex operators from bosonic…
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…
We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing's tket compiler. We present…
Current implementations of quantum computers suffer from large numbers of control lines per qubit, becoming unmanageable with system scale up. Here, we discuss a sparse spin-qubit architecture featuring integrated control electronics…
We enhance the tribracket counting invariant with \textit{tribracket brackets}, skein invariants of tribracket-colored oriented knots and links analogously to biquandle brackets. This infinite family of invariants includes the classical…
We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it…
We demonstrate that, in certain cases, quantization and the classical limit provide functors that are "almost inverse" to each other. These functors map between categories of algebraic structures for classical and quantum physics,…
We propose a solution to the quantum measurement paradox by first identifying its classical counterpart.
We present an implementation of the three-neutron quantization condition (QC) derived in previous work. We construct the matrices appearing in the QC and determine solutions numerically. The symmetries of the QC allow the projection onto…
A class of exact membrane solutions is quantized.
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
We review single-qubit quantum process tomography for trace-preserving and nontrace-preserving processes, and derive explicit forms of the general constraints for fitting experimental data. These forms provide additional insight into the…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
The characterization of quantum correlations is crucial to the development of new quantum technologies and to understand how dramatically quantum theory departs from classical physics. Here we systematically study single- and multiparticle…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…