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.
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.
Study on learning quantum dynamics without direct interaction.
problem Learning quantum dynamics incoherently without direct interaction.
method Analyze sample complexity and prove bounds for incoherent learning.
result Prove that arbitrary measurements allow efficient learning of unitary processes incoherently.
A quantum reinforcement learning algorithm reduces sample complexity.
problem Quantum reinforcement learning under model-free settings with quantum oracle access.
method Quantum Natural Policy Gradient (QNPG) algorithm replacing random sampling with deterministic gradient estimation.
result QNPG achieves a sample complexity of ildeO(ε−1.5) for queries to the quantum oracle, significantly improving classical lower bound. Distributed Quantum Gaussian Processes improve modeling in multi-agent systems.
problem Limited expressivity of classical kernels in complex domains.
method Distributed Quantum Gaussian Process (DQGP) with DR-ADMM algorithm.
result Enhanced modeling capabilities and scalability in multi-agent systems.
Paper tackles interpretability issues in deep learning models.
problem Lack of understanding of deep learning models' decision-making processes.
method Integrates concepts from machine learning, quantum computation, and quantum field theory.
result Demonstrates a many valued quantum logic system in Convolutional Deep Belief Networks.
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 …
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. …
Study characterizes memory capacity of quantum reservoirs using transmon qubits.
problem Understanding the memory capacity of quantum reservoirs built with transmon qubits.
method Characterized memory capacity of quantum reservoirs using transmon qubits from IBM, focusing on NMSE and topology complexity.
result Found a peak in memory capacity for configurations with n-1 self-loops, suggesting optimal design for forecasting tasks.
This work explores using deep NNs to learn quantum systems from probability distributions.
problem Learning quantum systems from limited probability distribution data.
method Using deep neural networks to reconstruct quantum Hamiltonian from probability distributions.
result Deep neural networks can learn quantum Hamiltonians from probability distributions.
New quantum kernels avoid overfitting by combining local and global components.
problem Exponential concentration in quantum kernels leads to overfitting.
method Local-global quantum kernels combining small subsystem and full-system measurements.
result Demonstrated benign overfitting in local-global quantum kernels.
Quantum crypto-economics models price risks in blockchain technology.
problem Quantum technology's potential to undermine blockchain security.
method Building financial models to price quantum risk in blockchain scenarios.
result Quantum crypto-economics models can assess and price quantum risks in blockchain.
New algorithm improves efficiency of quantum system modeling.
problem Intractable complexities in quantum Hamiltonian learning and Gibbs sampling.
method Generalized quantum natural gradient descent and Quantum-Probabilistic Mirror Descent.
result Data sample efficiency proven using information geometry and quantum metrology.
Quantum machine learning improves satellite image alignment.
problem Align satellite images taken at different times and angles.
method Quantum machine learning techniques for feature extraction and matching.
result Quantum methods show potential for future improvements.
The paper introduces reservoir computing models for complex systems.
problem Modeling complex engineering systems using nonlinear autoregression.
method Introduces reservoir computing with output feedback as stationary and ergodic infinite-order nonlinear autoregressive models.
result Demonstrates versatility of classical and quantum reservoir computers in modeling synthetic and real data.
Flow-VQE uses generative flows to optimize VQE efficiently.
problem Complex objective functions and expensive optimization in VQE.
method Generative normalizing flows with parameterized quantum circuits.
result Flow-VQE accelerates convergence and reduces circuit evaluations.
Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of optio…
Quantum systems learn like machine learning models, influenced by dissipation.
problem Understanding how quantum systems learn and evolve.
method Hydrodynamical formulation of quantum mechanics, gradient descent model, empirical demonstration.
result Quantum systems follow a disrupted gradient descent model, influenced by dissipation.
Classical clients can verify quantum learning tasks efficiently.
problem Making quantum learning accessible to classical clients.
method Developed a framework for classical verification of quantum learning.
result Quantum learning tasks can be efficiently verified by classical verifiers.
Physics: Similar long-distance properties can mask vastly different short-distance metrics.
problem Classifying homogeneous metrics on group manifolds by long-distance properties.
method Apply universality concept to geometry, focusing on metrics on Lie groups.
result Many metrics on low-dimensional Lie groups have similar long-distance properties despite differing short-distance properties.
Improves VQAs by balancing classical and quantum training resources.
problem Challenges in trainability and resource costs of VQAs on quantum hardware.
method Adopting HELIA Ansatz and combining classical and quantum methods for gradient estimation and training.
result Achieves higher accuracy and success rates in VQE and improved test accuracy in quantum phase classification.
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…
Quantum ELMs use a quantum reservoir to learn from data, with limits on expressivity and scalability.
problem Understanding the limits of quantum ELMs for machine learning tasks.
method Decomposed QELM predictions into Fourier series to analyze expressivity and scalability.
result Expressivity of QELMs is limited by the number of Fourier frequencies and observables, and scalability is hindered by hardware noise and entanglement.
In this paper we present some conditions for the (strong) stabilizability of an n-D Quantum MIMO system P(X). It contains two parts. The first part is to introduce the n-D Quantum MIMO systems where the coefficients vary in the algebra of Q-meromorphic functions. Then we introduce some conditions for the stabilizabilit…
Quantum computing speeds up pricing multi-asset derivatives.
problem Exponential growth in complexity for multi-asset derivatives pricing.
method Quantum algorithm based on quantum linear system algorithms for FDM.
result Exponential speedup in derivative pricing compared to classical methods.
A quantum system can be entirely described by the Kähler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we give an explicit link between the geometrical formulation (of finite dimensional qua…
Paper presents a faster classical algorithm for principal component regression.
problem Efficiently solving principal component regression problems.
method Uses quantum-inspired linear algebra techniques.
result Achieves polylogarithmic runtime, significantly faster than state-of-the-art.
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…
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.
Unified framework for learning quantum models from limited measurements.
problem Sample complexity and measurement shots in classical learning of quantum models.
method Unified learning framework considering probabilistic quantum measurements.
result Asymmetrical effects and interplay of sample size and measurement shots on learning performance.
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.
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.
We propose a protocol to perform quantum reinforcement learning with quantum technologies. At variance with recent results on quantum reinforcement learning with superconducting circuits, in our current protocol coherent feedback during the learning process is not required, enabling its implementation in a wide variety…
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.
Quantum models improve data generation from noisy quantum processors.
problem Creating complex probability distributions from limited data.
method Quantum-noise-driven generative diffusion models.
result Quantum noise can be harnessed to generate more complex distributions efficiently.
The combination of machine learning and quantum computing has emerged as a promising approach for addressing previously untenable problems. Reservoir computing is an efficient learning paradigm that utilizes nonlinear dynamical systems for temporal information processing, i.e., processing of input sequences to produce …
Study Vassiliev invariants for virtual knots, expanding quantum theory.
problem Understanding Vassiliev invariants for virtual knots.
method Define chord diagrams, weight systems, and Lie algebra weight systems for rotational virtual knots.
result Extended quantum invariants capture more information than standard invariants.
Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black--Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches: nonlinear and quantum, both based on (adaptive form of) the Schrödinger equatio…
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.
Quantum algorithms improve VaR and CVaR estimation for financial derivatives.
problem Quantum advantage in financial risk analysis of derivatives.
method Two quantum algorithms: QSP and QSP-based approach.
result QSP-based approach requires fewer quantum resources for the same accuracy.
The statistical complexity of quantum circuits is studied using Rademacher complexity.
problem Measuring the richness of quantum hypothesis spaces.
method Applying Rademacher complexity to quantum circuits, investigating dependencies on resources, depth, width, and input/output registers.
result Bounds on the capacity of quantum neural networks constrained by circuit depth, width, and resource measures.
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.
The study examines how quantum resources enhance the complexity of quantum circuits.
problem Quantum resource enhancement on circuit complexity.
method Utilizing quantum resource theories, the study analyzes statistical complexities of quantum circuits with limited quantum resources.
result Bounds for statistical complexities of quantum circuits are derived and applied to specific cases.
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.
Quantum control is valuable for various quantum technologies such as high-fidelity gates for universal quantum computing, adaptive quantum-enhanced metrology, and ultra-cold atom manipulation. Although supervised machine learning and reinforcement learning are widely used for optimizing control parameters in classical …
In this paper we show how to place Michael Berry's discovery of knotted zeros in the quantum states of hydrogen in the context of general knot theory and in the context of our formulations for quantum knots. Berry gave a time independent wave function for hydrogen, as a map from three space to the complex plane and suc…
Unified framework for robust causal directionality in quantum systems under MNAR observation.
problem Determining causal directionality in quantum systems under MNAR observation.
method Integrates CVAE-based latent constraints, MNAR-aware selection models, GEE-stabilized regression, penalized empirical likelihood, and Bayesian optimization.
result Achieves lower bias and variance, near-nominal coverage, and superior quantum-specific diagnostics.
A decentralized online quantum cash system, called qBitcoin, is given. We design the system which has great benefits of quantization in the following sense. Firstly, quantum teleportation technology is used for coin transaction, which prevents from the owner of the coin keeping the original coin data even after sending…