Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as those of E_8, have been used extensively in the literature. The present paper analyses such Coxeter groups in the Clifford Geometric Algebra framework, which aff...
An intuitive programming package for simulating and analyzing Clifford-dominated circuits, quantum measurement, and stabilizer states with applications to many-body localization, classical shadows, quantum chemistry and error correction code. (⭐ 87)
quantum computing and quantum information theory, the Clifford gates are the elements of the Clifford group, a set of mathematical transformations which
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The negative solution to the famous problem of $36$ officers of Euler implies that there are no two orthogonal Latin squares of order six. We show that the problem has a solution, provided the officers are entangled, and construct orthogonal quantum...
There exist pairs of orthogonal Latin squares of any order n except if n=2 or n=6 [Bose, Shrikhande and Parker, 1960]. In particular, the problem of Euler's thirty-six officers does not have a solution. However, it has a "quantum solution": there exi...
We present a new theorem describing stable solutions for a driven quantum system. The theorem, coined `inertial theorem', is applicable for fast driving, provided the acceleration rate is small. The theorem states that in the inertial limit eigenoper...
This paper develops a simplified model for sexual replication within the quasispecies formalism. We assume that the genomes of the replicating organisms are two-chromosomed and diploid, and that the fitness is determined by the number of chromosome...
For an electrically driven electron confined in a nanowire quantum dot with spin-orbit coupling (SOC), we find a SOC-magnetism phase-locked condition under which we derive a complete set of Schrödinger kitten states which contains some novel degener...
A powerful tool in control and systems engineering is represented by Nyquist plots, for which a qualitative representation often gives a clearer visualization of the frequency response function that is typically not given by computer programs, especi...
What magnitude of torque must be supplied by the anchor to keep the structure upright?Hint: Consider working with gauge pressure and noting I. 2: One quarter of a circular cylinder (radius a, depth into …
Quantum metrology protocols are typically designed around the assumption that we have an abundance of measurement data, but recent practical applications are increasingly driving interest in cases with very limited data. In this regime the best appro...
We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition....
We consider electron spin qubits in quantum dots and define a measurement efficiency e to characterize reliable measurements via n-shot read outs. We propose various implementations based on a double dot and quantum point contact (QPC) and show tha...
The first quantitative neural network model of feelings and emotions is proposed on the base of available data on their neuroscience and evolutionary biology nature, and on a neural network human memory model which admits distinct description of co...
Dec 22, 2021 · What's the difference between these types of adjective usages? For example: This is more of a prerequisite than a necessary quality. This is more a prerequisite than a necessary quality. …
We investigate the estimation of dephasing-induced decoherence in continuous-variable quantum systems using non-Gaussian probe states. By purifying the open system, we identify optimal probes, specifically squeezed cat and symmetric squeezed compass...
A proof of the Quadratic Reciprocity Law is presented using a Lemma of Gauss, the theory of finite fields and the Frobenius automorfism....