Extended quantum state result for gl_n weight systems.
problem Quantum states associated with gl_n weight systems.
method Extended Corfield et al. result to all gl_n weight systems.
result All gl_n weight systems are quantum states.
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48 results for “quantum state systems”
Fundamental weight systems identified as quantum states.
problem Identifying which weight systems are quantum states.
method Analyzing the Cayley distance kernel on the symmetric group and its positivity.
result All fundamental gl(n)-weight systems are quantum states.
Quantum Knots and Mosaicsquant-ph
In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This definition can be viewed as a blueprint for the construction of an actual physical quantum system. Moreover, this definition of a quantum knot system is intended to represent the "quantu…
Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of Restricted Boltzmann Machines and some classes of Tensor-Network states in arbitrary dime…
The paper studies distributions and controllability in quantum mechanical systems.
problem Controlling quantum mechanical systems and their evolution.
method Analysis of distributions, controllability, and geodesics on sub-Finsler manifolds.
result Proves the Lie group decomposition and geodesics equivalence for quantum system steering.
New method uses single quantum state for machine learning tasks, improving accuracy.
problem Challenges in unsupervised learning with quantum data.
method SIngle-Preparation Quantum Information Processing (SIPQIP) concept.
result Significantly more accurate estimation compared to traditional methods.
A Theory of Complex Adaptive Learning and a Non-Localized Wave Equation in Quantum Mechanicsq-fin.GN
The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.
problem Understanding the underlying mechanism of distribution formation in complex quantum entanglement.
method Exploring the logical relationship between Schrödinger's wave equation and Shi's trading volume-price wave equation in finance.
result A non-localized wave equation in quantum mechanics reveals the invariance of interaction as a universal law.
A reinforcement learning approach prepares quantum squeezed states in open spin systems.
problem Generating non-classical states in open quantum systems with dissipation and dephasing.
method Reinforcement learning to determine optimal control pulses for spin-squeezing.
result Optimal control sequences enhance collective spin squeezing and entanglement.
Quantum states can be learned efficiently using gentle measurements.
problem Efficiently learning quantum states with minimal measurements.
method Introducing α-LGM measurements and proving strong quantum DPI.
result The number of states needed for accurate learning is of order 1/(ε^2 α^2).
Meta-learning algorithms prepare quantum Gibbs states efficiently for NISQ devices.
problem Efficiently preparing quantum Gibbs states for NISQ devices.
method Meta-Variational Quantum Thermalizer (Meta-VQT) and Neural Network Meta-VQT (NN-Meta VQT) algorithms.
result Meta-learned parameters significantly outperform random initializations in optimization tasks.
New method uses kernel methods to approximate ground states of quantum Hamiltonians efficiently.
problem Approximating ground states of quantum Hamiltonians using neural networks is computationally expensive.
method Introduces a statistical learning approach using kernel methods to make optimization trivial.
result Ground state properties of arbitrary gapped quantum Hamiltonians can be reached with polynomial resources.
The paper introduces a quantum state system to count perfect matchings in graphs.
problem Counting perfect matchings in graphs using quantum state systems.
method Topological quantum field theory (TQFT) and spectral sequences.
result The filtered -color vertex homology for is generated by perfect matchings.
New MBL hidden Born machine learns various tasks.
problem Learning from quantum many-body systems.
method MBL dynamics and hidden units for training.
result Enhanced trainability and stability in learning.
We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These quantum states are contained in a density operator which describes the new quan…
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By lifting the problem from the state space to the space of unitary gates realising the…
New definitions of ESP for quantum reservoir computing handle non-stationary systems.
problem Traditional ESP does not apply to non-stationary systems.
method Introduce two new categories of ESP: non-stationary ESP and subset/subspace ESP.
result Demonstrates correspondence between non-stationary ESP and QRC with NARMA tasks.
New method uses adiabatic principles to improve ground-state preparation in quantum computing.
problem Challenges in variational training of complex energy landscapes.
method Iterative Hamiltonian deformation complemented with adiabatic principles.
result Consistent convergence to target ground state through sequence of intermediate problems.
Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTscond-mat.str-el
New pseudo-Hermitian models from non-semisimple TQFTs.
problem Constructing exactly solvable pseudo-Hermitian spin Hamiltonians.
method Identifying ground states on surfaces using non-semisimple TQFTs.
result Ground states depend only on spatial topology and can be assigned by non-semisimple TQFTs.
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concernin…
Enumeration on graph mosaicsmath.GT
Since the Jones polynomial was discovered, the connection between knot theory and quantum physics has been of great interest. Lomonaco and Kauffman introduced the knot mosaic system to give a definition of the quantum knot system that is intended to represent an actual physical quantum system. Recently the authors deve…
Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical…
We study the quantum synchronization between a pair of two-level systems inside two coupled cavities. By using a digital-analog decomposition of the master equation that rules the system dynamics, we show that this approach leads to quantum synchronization between both two-level systems. Moreover, we can identify in th…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum s…
How useful can machine learning be in a quantum laboratory? Here we raise the question of the potential of intelligent machines in the context of scientific research. A major motivation for the present work is the unknown reachability of various entanglement classes in quantum experiments. We investigate this question …
In this contribution we review results on the kinematics of a quantum system localized on a connected configuration manifold and compatible dynamics for the quantum system including external fields and leading to non-linear Schrödinger equations for pure states.
Machine learning employs dynamical algorithms that mimic the human capacity to learn, where the reinforcement learning ones are among the most similar to humans in this respect. On the other hand, adaptability is an essential aspect to perform any task efficiently in a changing environment, and it is fundamental for ma…
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Ha…
Quantum learning complexity reviewed using information theory.
problem Learning properties of quantum systems or processing data via quantum computing.
method Information-theoretic techniques focusing on data, copy, and model complexity.
result Copy complexity due to irreversible quantum measurements limits information extraction.
New quantum state reconstruction method accelerates convergence.
problem Quantum state reconstruction for larger systems.
method Momentum-Inspired Factored Gradient Descent (MiFGD) combining compressed sensing, non-convex optimization, and acceleration.
result Converges to true density matrix at an accelerated linear rate, provably close to the true matrix.
Study on spontaneous symmetry breaking in financial markets using quantum mechanics.
problem Analyzing spontaneous symmetry breaking in financial markets.
method Using Hamiltonian form of Black-Scholes and Merton-Garman equations, analyzing symmetry breaking and interpreting Nambu-Goldstone bosons.
result Interpretation of Nambu-Goldstone bosons in financial markets.
New machine learning method detects quantum separability in large-scale systems.
problem Deciding quantum separability of large-scale bipartite density matrices.
method Frank-Wolfe-based algorithm for finding nearest separable density matrices and classification of density matrices as separable or entangled.
result The method scales up to thousands of density matrices and achieves high quantum entanglement detection accuracy.
MPE framework proves universal approximation for quantum data distribution.
problem Challenges in generating quantum data from underlying distributions.
method Many-body Projected Ensemble (MPE) framework for quantum state design.
result MPE can approximate any quantum distribution within 1-Wasserstein distance error.
Sketch Tomography improves quantum state estimation accuracy.
problem Efficiently estimating quantum states, especially MPS states.
method Hybridizes classical shadow protocol with tensor train ansatz.
result Proven convergence with quadratic sample complexity.
Novel quantum algorithm for financial market modeling.
problem Accurate quantum state preparation for financial simulation.
method Multi-Split-Steps Quantum Walk (multi-SSQW) with PQC and variational solver.
result Highly accurate modeling of complex financial distributions.
Model financial markets using open quantum systems to understand market imperfections.
problem Understanding market imperfections through imperfect trading mechanisms.
method Using open quantum systems to represent financial markets, characterizing orbits, and analyzing reduced density matrices.
result Non-classical modes of time evolution can incorporate factors like illiquid trades and imperfect trading mechanisms.
A quantum state generation method that respects physical constraints.
problem Generating quantum states with complex-valued Hermitian, positive semi-definite, and trace one properties.
method Mirror diffusion model with von Neumann entropy to enforce structural constraints.
result Demonstrated effective generation of quantum states with conditional guidance.
Information Entropy of the Financial Market: Modelling Random Processes Using Open Quantum Systemsq-fin.MF
The financial market entropy is modeled using open quantum systems.
problem Understanding entropy in financial market dynamics.
method Using Open Quantum Systems to model entropy gain in financial markets.
result Interesting non-classical results generated by relaxing assumptions.
Global EQG sums boundary states over manifold diffeomorphism classes.
problem Summing boundary states over manifold diffeomorphism classes.
method Formulated as classical statistical physics, weights determined by general principles.
result Hartle-Hawking state as a probability measure.
Bayesian control prepares GHZ states in Rydberg atoms.
problem Preparing non-classical states robustly for quantum sensors.
method Bayesian optimal control of trapped Rydberg atoms.
result Control pulses drive atoms into GHZ states with scalable preparation times.
Quantum reservoir computing needs coherence influx for effective information processing.
problem Understanding and optimizing quantum reservoir computing.
method Theoretical and numerical analysis of quantum systems, focusing on coherence influx and spectral radius of Pauli transfer matrix.
result Coherence influx is essential for realizing nonstationary echo state property in quantum reservoir computing.
This review covers quantum computing applications in finance and blockchain.
problem Challenges in finance and blockchain security with quantum computing.
method Systematic review of recent quantum finance and blockchain work.
result Quantum-resistant blockchain systems and security measures.
In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to define a dynamic-dependent metric tensor on the principal manifold, such that the…
Quantum systems with scrambling improve temporal information processing, but scaling requires exponential overhead.
problem Scalability and memory retention of quantum reservoirs in temporal information processing.
method Examined a quantum reservoir processing framework with scrambling reservoirs modeled by high-order unitary designs, analyzed in noiseless and noisy settings.
result Memory retention improves exponentially with reservoir size but worsens with reservoir iterations, requiring exponential shot overhead for scaling.
The idea is considered that a quantum wormhole in a spacetime foam can be described as a Ricci flow. In this interpretation the Ricci flow is a statistical system and every metric in the Ricci flow is a microscopical state. The probability density of the microscopical state is connected with a Perelman's functional of …
Bandits roaming Hilbert spacequant-ph
The thesis optimizes quantum state exploration using bandit algorithms.
problem Maximizing reward in online learning of quantum state properties.
method Multi-armed bandit approach to select observables, minimizing regret.
result Optimal strategies with matching upper and lower bounds for regret.
Physicists use quantum models to describe the behavior of physical systems. Quantum models owe their success to their interpretability, to their relation to probabilistic models (quantization of classical models) and to their high predictive power. Beyond physics, these properties are valuable in general data science. …
Inference-Based Quantum Sensingquant-ph
New method infers unknown parameters in quantum sensing with high probability.
problem Estimating unknown parameters in quantum sensing with limited measurements.
method Inference-based scheme for characterizing system response at 2n+1 parameters.
result Inference error is smaller than δ with a number of shots scaling as Ω(log^3(n)/δ^2).
Study uses supervised learning to classify quantum phases with limited measurements.
problem Classifying quantum phases of matter with incomplete phase diagrams.
method Combines classical and quantum techniques, including tensor networks, kernel methods, and quantum algorithms.
result Certification of new ground states can be achieved with polynomial measurements.