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Quantum Rep., Volume 7, Issue 3 (September 2025) – 4 articles

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16 pages, 2739 KiB  
Article
Efficient Encoding of the Traveling Salesperson Problem on a Quantum Computer
by John P. T. Stenger, Sean T. Crowe, Joseph A. Diaz, Ramiro Rodriguez, Daniel Gunlycke and Joanna N. Ptasinski
Quantum Rep. 2025, 7(3), 32; https://doi.org/10.3390/quantum7030032 - 17 Jul 2025
Abstract
We propose an amplitude encoding of the traveling salesperson problem along with a method for calculating the cost function using a probability distribution obtained on a quantum computer. Our encoding requires a number of qubits that grows logarithmically with the number of cities. [...] Read more.
We propose an amplitude encoding of the traveling salesperson problem along with a method for calculating the cost function using a probability distribution obtained on a quantum computer. Our encoding requires a number of qubits that grows logarithmically with the number of cities. We propose to calculate the cost function using a nonlinear function of expectation values of quantum operators. This is in contrast to the typical method of evaluating the cost function by summing expectation values of quantum operators. We demonstrate our method using a variational quantum eigensolver algorithm to find the shortest route for a given graph. We find that there is a broad range in the hyperparameters of the optimization procedure for which the best route is found. Full article
16 pages, 8172 KiB  
Article
A Comparative Analysis of a Nonlinear Phase Space Evolution of SU(2) and SU(1,1) Coherent States
by Rodrigo D. Aceves, Miguel Baltazar, Iván F. Valtierra and Andrei B. Klimov
Quantum Rep. 2025, 7(3), 31; https://doi.org/10.3390/quantum7030031 - 5 Jul 2025
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Abstract
We carried out a comparative study of the phase space evolution of SU(2) and SU(1,1) coherent states generated by the same nonlinear two-mode Hamiltonian. We analyze the dynamics of the Wigner functions in the respective phase spaces and discuss the principal associated physical [...] Read more.
We carried out a comparative study of the phase space evolution of SU(2) and SU(1,1) coherent states generated by the same nonlinear two-mode Hamiltonian. We analyze the dynamics of the Wigner functions in the respective phase spaces and discuss the principal associated physical effects: the squeezing of the appropriate observables and the Schrödinger’s cat state generation characteristic of both the considered symmetry groups. Full article
(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)
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9 pages, 283 KiB  
Article
Neutrino Mixing Matrix with SU(2)4 Anyon Braids
by Michel Planat
Quantum Rep. 2025, 7(3), 30; https://doi.org/10.3390/quantum7030030 - 23 Jun 2025
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Abstract
We recently classified baryonic matter in the ground and first excited states thanks to the discrete group of braids inherent to SU(2)2 Ising anyons. Remarkably, the braids of SU(2)4 anyons allow the neutrino [...] Read more.
We recently classified baryonic matter in the ground and first excited states thanks to the discrete group of braids inherent to SU(2)2 Ising anyons. Remarkably, the braids of SU(2)4 anyons allow the neutrino mixing matrix to be generated with an accuracy close to measurements. This is an improvement over the model based on tribimaximal neutrino mixing, which predicts a vanishing solar neutrino angle θ13, which has now been ruled out. The discrete group of braids for SU(2)4 anyons is isomorphic to the small group (162,14), generated by a diagonal matrix σ1=R and a symmetric complex matrix σ2=FRF1, where the (3×3) matrices F and R correspond to the fusion and exchange of anyons, respectively. We make use of the Takagi decomposition σ2=UTDU of σ2, where U is the expected PMNS unitary matrix and D is real and diagonal. We obtain agreement with the experimental results in about the 3σ range for the complex entries of the PMNS matrix with the angles θ1310°, θ1230°, θ2338°, and δCP240°. Potential physical consequences of our model are discussed. Full article
(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)
15 pages, 468 KiB  
Article
Contextual Hidden Fields Preclude the Derivation of Bell-Type Inequalities
by Álvaro G. López
Quantum Rep. 2025, 7(3), 29; https://doi.org/10.3390/quantum7030029 - 20 Jun 2025
Viewed by 254
Abstract
We show that loophole-free Bell-type no-go theorems cannot be derived in theories involving local hidden fields. At the time of measurement, a contextuality loophole appears because each particle’s electromagnetic field interacts with the field of its respective apparatus, preventing the expression of the [...] Read more.
We show that loophole-free Bell-type no-go theorems cannot be derived in theories involving local hidden fields. At the time of measurement, a contextuality loophole appears because each particle’s electromagnetic field interacts with the field of its respective apparatus, preventing the expression of the probability density as a function independent of the orientation of the measuring devices. Then, we use the dynamical evolution of the probability distribution to show that the spin-correlation integral cannot be expressed in terms of initial Cauchy data restricted to the particles. A measurement independence loophole ensues, which prevents the usage of the non-contextual correlation integrals required to demonstrate the CHSH-Bell inequality. We propose that correlated fields are the missing hidden variable triggering the coupled nonlinear oscillations of the particles, which bring about the synchronicities observed in the Einstein–Podolsky–Rosen–Bohm (EPRB) experiment. Full article
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