The Particle in a Box Warrants an Examination

• URL: http://arxiv.org/abs/2204.07577v3
• Date: Sat, 4 Jun 2022 13:41:44 GMT
• Title: The Particle in a Box Warrants an Examination
• Authors: John R. Klauder
• Abstract summary: Using canonical quantization, this example has been fully studied thanks to its simplicity. Despite its repeated analysis, there is a feature that puts the past results into question. In addition to pointing out the quantization issue, the procedures of affine quantization can lead to a proper quantization.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The particle in a box is a simple model that has a classical Hamiltonian $H=p^2$ (using $2m=1$), with a limited coordinate space, $-b<q<b$, where $0<b<\infty$. Using canonical quantization, this example has been fully studied thanks to its simplicity, and it is a common example for beginners to understand. Despite its repeated analysis, there is a feature that puts the past results into question. In addition to pointing out the quantization issue, the procedures of affine quantization can lead to a proper quantization that nesaeccsrily points toward more complicated eigenfunctions and eigenvalues, which deserve to be solved.

Related papers

• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. Even with sublinear barriers, we use Feynman-Kac techniques to lift classical to quantum ones establishing tight lower bound $T_mathrmmix = 2Omega(nalpha)$.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Calculating response functions of coupled oscillators using quantum phase estimation [40.31060267062305]
  We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. Our proposed quantum algorithm operates in the standard $s-sparse, oracle-based query access model. We show that a simple adaptation of our algorithm solves the random glued-trees problem in time.
  arXiv  Detail & Related papers  (2024-05-14T15:28:37Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Approximation Algorithms for Quantum Max-$d$-Cut [42.248442410060946]
  The Quantum Max-$d$-Cut problem involves finding a quantum state that maximizes the expected energy associated with the projector onto the antisymmetric subspace of two, $d$-dimensional qudits over all local interactions. We develop an algorithm that finds product-state solutions of mixed states with bounded purity that achieve non-trivial performance guarantees.
  arXiv  Detail & Related papers  (2023-09-19T22:53:17Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Affine Quantization of the Harmonic Oscillator on the Semi-bounded domain $(-b,\infty)$ for $b: 0 \rightarrow \infty$ [0.0]
  We study the transformation of a classical system into its quantum counterpart using it affine quantization (AQ) Fantoni and Klauder (arXiv:2109.13447,Phys. Rev. D bf 103, 076013 (2021) We numerically solve this problem for $b rightarrow infty$, confirming the results of Gouba ( arXiv:2005.08696,J. High Energy Phys., Gravitation Cosmol.
  arXiv  Detail & Related papers  (2021-11-20T22:52:45Z)
• Quantum Heaviside Eigen Solver [1.027974860479791]
  We propose a quantum algorithm named as a quantum Heaviside eigen solver to calculate both the eigen values and eigen states of the general Hamiltonian for quantum computers. The present algorithm is a universal quantum eigen solver for Hamiltonian in quantum many-body systems and quantum chemistry.
  arXiv  Detail & Related papers  (2021-11-16T08:26:47Z)
• Estimating Gibbs partition function with quantumClifford sampling [6.656454497798153]
  We develop a hybrid quantum-classical algorithm to estimate the partition function. Our algorithm requires only a shallow $mathcalO(1)$-depth quantum circuit. Shallow-depth quantum circuits are considered vitally important for currently available NISQ (Noisy Intermediate-Scale Quantum) devices.
  arXiv  Detail & Related papers  (2021-09-22T02:03:35Z)
• Affine Quantization on the Half Line [0.0]
  Dirac's canonical quantization works reasonably well in the case of conventional quantum mechanics over $mathbbRn$. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in situations for which canonical quantization fails.
  arXiv  Detail & Related papers  (2020-05-18T13:20:36Z)
• Quantization of the 1-D forced harmonic oscillator in the space ($x, v$) [0.0]
  For the resonant case, both forms of quantization are different. The average energy of the system is higher in ($x,hat p$) quantization than on the $(x,hat v$) quantization. The Boltzmann-Shannon entropy on the ($x,hat p$) quantization is higher than on the ($x,hat v$) quantization.
  arXiv  Detail & Related papers  (2020-04-29T21:29:20Z)
• Quantum Coupon Collector [62.58209964224025]
  We study how efficiently a $k$-element set $Ssubseteq[n]$ can be learned from a uniform superposition $|Srangle of its elements. We give tight bounds on the number of quantum samples needed for every $k$ and $n$, and we give efficient quantum learning algorithms.
  arXiv  Detail & Related papers  (2020-02-18T16:14:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.