Super Quantum Mechanics

• URL: http://arxiv.org/abs/2502.00037v1
• Date: Sat, 25 Jan 2025 19:41:04 GMT
• Title: Super Quantum Mechanics
• Authors: Mikhail Gennadievich Belov, Victor Victorovich Dubov, Vadim Konstantinovich Ivanov, Alexander Yurievich Maslov, Olga Vladimirovna Proshina, Vladislav Gennadievich Malyshkin,
• Abstract summary: We introduce Super Quantum Mechanics (SQM) as a theory that considers states in Hilbert space subject to multiple quadratic constraints.<n>In this case, the stationary SQM problem is a quantum inverse problem with multiple applications in machine learning and artificial intelligence.
• Score: 37.69303106863453
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce Super Quantum Mechanics (SQM) as a theory that considers states in Hilbert space subject to multiple quadratic constraints. Traditional quantum mechanics corresponds to a single quadratic constraint of wavefunction normalization. In its simplest form, SQM considers states in the form of unitary operators, where the quadratic constraints are conditions of unitarity. In this case, the stationary SQM problem is a quantum inverse problem with multiple applications in machine learning and artificial intelligence. The SQM stationary problem is equivalent to a new algebraic problem that we address in this paper. The SQM non-stationary problem considers the evolution of a quantum system, distinct from the explicit time dependence of the Hamiltonian, $H(t)$. Several options for the SQM dynamic equation are considered, and quantum circuits of 2D type are introduced, which transform one quantum system into another. Although no known physical process currently describes such dynamics, this approach naturally bridges direct and inverse quantum mechanics problems, allowing for the development of a new type of computer algorithm. Beyond computer modeling, the developed theory could be directly applied if or when a physical process capable of solving an inverse quantum problem in a single measurement act (analogous to wavefunction measurement in traditional quantum mechanics) is discovered in the future.

Related papers

• On the generalized eigenvalue problem in subspace-based excited state methods for quantum computers [0.0]
  Solving challenging problems in quantum chemistry is one of the leading promised applications of quantum computers. Within the quantum algorithms proposed for problems in excited state quantum chemistry, subspace-based quantum algorithms are promising for pre-fault-tolerant quantum devices. We show that errors in eigenvalues increase drastically with an increase in the condition number of the overlap matrix when a generalized eigenvalue equation is solved in the presence of statistical sampling errors. We also show that excited-state methods that have an eigenvalue equation as the working equation, such as q-sc-EOM, do not have such problems and
  arXiv  Detail & Related papers  (2025-03-12T17:26:11Z)
• Correcting and extending Trotterized quantum many-body dynamics [0.0]
  We develop a hybrid ansatz that combines the strengths of quantum and classical methods. We show how this hybrid ansatz can avoid SWAP gates in the quantum circuit. We also show how it can extend the system size while keeping the number of qubits on the quantum device constant.
  arXiv  Detail & Related papers  (2025-02-19T14:50:12Z)
• Rapidly Achieving Chemical Accuracy with Quantum Computing Enforced Language Model [22.163742052849432]
  QiankunNet-VQE is a transformer based language models enforced with quantum computing to learn and generate quantum states. It has been implemented using up to 12 qubits and attaining an accuracy level competitive with state-of-the-art classical methods.
  arXiv  Detail & Related papers  (2024-05-15T07:50:57Z)
• Quantum Zeno Monte Carlo for computing observables [0.0]
  We introduce Quantum Zeno Monte Carlo (QZMC), a classical-quantum hybrid algorithm that demonstrates resilience to device noise and Trotter errors while showing computational cost for a gapped system.<n>QZMC computes static and dynamic properties without requiring initial state overlap or variational parameters, offering reduced quantum circuit depth.
  arXiv  Detail & Related papers  (2024-03-05T08:32:17Z)
• Computational supremacy in quantum simulation [22.596358764113624]
  We show that superconducting quantum annealing processors can generate samples in close agreement with solutions of the Schr"odinger equation. We conclude that no known approach can achieve the same accuracy as the quantum annealer within a reasonable timeframe.
  arXiv  Detail & Related papers  (2024-03-01T19:00:04Z)
• State-Averaged Orbital-Optimized VQE: A quantum algorithm for the democratic description of ground and excited electronic states [0.0]
  The SA-OO-VQE package aims to answer both problems with its hybrid quantum-classical conception based on a typical Variational Quantum Eigensolver approach. The SA-OO-VQE has the ability to treat degenerate (or quasi-degenerate) states on the same footing, thus avoiding known numerical optimization problems around avoided crossings or conical intersections.
  arXiv  Detail & Related papers  (2024-01-22T12:16:37Z)
• Quantum Merlin-Arthur proof systems for synthesizing quantum states [0.0]
  We investigate a state synthesizing counterpart of the class NP-synthesizing. We establish that the family of UQMA witnesses, considered as one of the most natural candidates, is in stateQMA. We demonstrate that stateQCMA achieves perfect completeness.
  arXiv  Detail & Related papers  (2023-03-03T12:14:07Z)
• An Introduction to Quantum Machine Learning for Engineers [36.18344598412261]
  Quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. This book provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra.
  arXiv  Detail & Related papers  (2022-05-11T12:10:52Z)
• Variational Quantum Simulation of Chemical Dynamics with Quantum Computers [23.13347792805101]
  We present variational simulations of real-space quantum dynamics suitable for implementation in Noisy Intermediate-Scale Quantum (NISQ) devices. Motivated by the insights that most chemical dynamics occur in the low energy subspace, we propose a subspace expansion method.
  arXiv  Detail & Related papers  (2021-10-12T16:28:52Z)
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation [55.41644538483948]
  Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates. We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
  arXiv  Detail & Related papers  (2021-08-06T19:38:03Z)
• Testing Quantum Mechanics using Noisy Quantum Computers [0.0]
  We propose to test quantum mechanics in the high-complexity regime using noisy quantum devices. We show that quantum mechanics predicts that the fidelity of our procedure decays exponentially with circuit depth. We find that highly informative experiments should require only thousands qubits.
  arXiv  Detail & Related papers  (2021-08-04T17:59:59Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms [105.54048699217668]
  A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
  arXiv  Detail & Related papers  (2020-08-03T18:00:05Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

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.