Study finds no significant difference in neural network weights with quantum random numbers.
problem Effects of biased quantum random numbers on neural network initialization.
method Empirical study using quantum hardware and classical pseudo-random numbers.
result No statistically significant difference found between quantum random numbers and other types.
Quantum RNG improves financial risk metrics estimation.
problem Estimating financial risk metrics with high precision.
method Quantum-Enhanced Monte Carlo using QRNG.
result Improved accuracy in VaR and CVaR estimation.
Machine learning detects classical noise in quantum RNGs.
problem Classical noise compromises the randomness of quantum RNGs.
method Developed a machine learning model to analyze and detect correlations in QRNGs.
result Machine learning can identify and mitigate classical noise in QRNGs.
Quantum algorithm reduces qubit usage for Monte Carlo simulations.
problem High qubit requirements for Monte Carlo simulations on quantum computers.
method Use of pseudo-random number generator (PRNG) on a quantum circuit.
result Significant reduction in qubit usage without sacrificing quantum speed.
Quantum machine learning tackles large datasets with randomized measurements.
problem Efficiently process large, high-dimensional datasets on quantum computers.
method Randomized measurements to scale linearly with dataset size and quadratic for post-processing.
result Substantial speed-up for noisy quantum computers, enabling image classification.
This study compares PRNG and QRNG in machine learning models, revealing significant differences in performance.
problem Implications of PRNG and QRNG on machine learning model performances.
method Used CPU and QPU to generate random numbers for various machine learning techniques.
result Quantum Random Number Generators (QRNG) outperform Pseudo Random Number Generators (PRNG) in certain tasks.
Paper presents quantum algorithms for pricing financial derivatives using complex models.
problem Implementing complex financial models like local volatility on quantum computers.
method Developed two quantum circuit implementations for local volatility model.
result Demonstrated reduced qubit requirements for local volatility model.
Paper presents a new VMBQC model with fewer parameters for better generative modeling.
problem Limited generative power of VMBQC due to more parameters than unitary models.
method Introduces a restricted VMBQC model with a single additional trainable parameter.
result Minimal extension of VMBQC model generates distributions not learnable by unitary models.
Quantum speedup for Monte Carlo integration reduces integrand calls.
problem Reducing the number of calls to the integrand subroutine in high-dimensional Monte Carlo integration.
method Combining nested quantum amplitude estimation with pseudorandom numbers for separable integrands.
result Significant reduction in the number of integrand calls for high-dimensional integration.
Quantum algorithm estimates mean with sub-Gaussian error.
problem Estimating mean of quantum-computed random variables.
method Quantum mean estimation algorithm with sub-Gaussian error rate.
result Achieves nearly-optimal quadratic speedup over classical methods.
Quantum algorithm speeds up nested expectation estimation by nearly quadratically.
problem Estimating repeatedly nested expectations with quantum computing.
method Proposes a quantum algorithm achieving nearly quadratic speedup over classical methods.
result Achieves nearly quadratic speedup for RNEs, up to logarithmic factors.
Quantum machine learning faces 'laziness' and 'barren plateaus', but noise can mitigate the latter.
problem Quantum machine learning's loss function landscape issues.
method Theoretical analysis of quantum variational circuits, neural tangent kernels, and noise effects.
result Noise can mitigate barren plateaus in quantum machine learning.
Quantum models generalize well with little data, challenging traditional generalization theories.
problem Quantum machine learning models generalize well with few data, contradicting traditional theories.
method Systematic randomization experiments and theoretical constructions.
result Quantum neural networks can fit random states and labels, defying current generalization measures.
Quantum algorithm speeds up learning from big data exponentially.
problem Scalable learning from big data with optimized random features.
method Quantum algorithm for sampling optimized random features.
result Exponential speedup in runtime compared to classical algorithms.
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.
New MBQC algorithm uses randomness for generative modeling.
problem Designing efficient quantum algorithms for generative modeling.
method Proposes a variational MBQC algorithm that treats randomness as a resource.
result Randomness in MBQC can lead to significant gains in generative modeling performance.
Machine learning, specifically LSTM, models quantum experiments efficiently.
problem Modeling complex quantum states with high-dimensional entanglement.
method Used a long short-term memory (LSTM) neural network to predict quantum experiment outcomes.
result LSTM neural networks can accurately predict quantum experiment outcomes without computing the states themselves.
Paper develops security model and pricing for stable digital currency in quantum blockchain network.
problem Securing and pricing stable digital currency in a quantum blockchain network.
method Developed a block-based quantum channel networking technology and a FinTech platform model with dynamic pricing.
result Established a generalized IoB security model using quantum channel networking and QKD.
In this paper, we briefly discuss a mathematical concept that can be used in economics.
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).
Quantum walks blend patterns into splines when averaged.
problem Understanding the asymptotic patterns of quantum random walks.
method Averaging over quantum coins using the Haar measure.
result Patterns blend into splines, showing a unified behavior.
Quantum memory limits set by relativity theory.
problem Quantum memory efficiency and relativity constraints.
method Relativistic quantum field theory and Lieb-Robinson bounds.
result Quantum memory capacity is limited by fundamental physics.
Deeper quantum circuits can improve performance on unseen data, contrary to traditional views.
problem Understanding scaling behavior of parameterized quantum circuits and their generalization.
method Gradient-based PQCs, add-one-in perturbation techniques, spectral properties of random matrices.
result Gradient-based PQCs can exhibit improved performance on unseen data as model size increases, displaying double descent behavior.
QCNNs avoid barren plateaus, making them trainable.
problem Exponentially vanishing gradients in QNNs.
method Graph-based method to analyze Haar-distributed unitaries.
result QCNNs do not exhibit barren plateaus, implying trainability.
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation tech…
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for financial market than the classical one. A part of our analysis is devoted to study t…
Quantum UCB algorithm reduces reinforcement learning regret exponentially.
problem Episodic reinforcement learning with quantum state evolution.
method Upper Confidence Bound (UCB) quantum algorithm with quantum mean estimation.
result Exponential improvement in regret from $\Tilde{\mathcal{O}}(\sqrt{K})$ to $\Tilde{\mathcal{O}}(1)$.
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.
Researchers use quantum chaos and RMT to analyze turbulence, revealing unique scaling laws.
problem Understanding the statistical structure and scaling laws of turbulence.
method Applied tools from quantum chaos and Random Matrix Theory to analyze turbulence datasets.
result Turbulence Gram matrices exhibit power-law scalings distinct from classical chaos and random data.
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.
Quantum model investigates financial derivative price dynamics with quantum interference effects.
problem Investigate quantum drift in financial derivatives using Heisenberg Equation of Motion.
method Apply geometric techniques to integrate Heisenberg Equation of Motion, model financial market as quantum observable.
result Quantum interference effects can act as drag or boost on financial returns.
The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both, unle…
New algorithm reduces feature count and accelerates error convergence.
problem Exponential error convergence in data classification with optimized random features.
method Optimized random features accelerated by quantum machine learning.
result Achieves exponential error convergence under low-noise condition.
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from classical random walks analogs, in particular, they walk faster than classical o…
New quantum states capture more information, enabling advanced processing tasks.
problem Quantum information processing challenges with limited statistical information.
method Introducing Random-Coefficient Pure States (RCPS) and exploiting their higher-order statistics.
result RCPS provide richer information than density operators, enabling new quantum tasks.
Unified approach for learning quantum operations from measurements.
problem Accurate reconstruction of unknown quantum operations from noisy measurements.
method Matrix sensing techniques, randomized measurement design, blockwise measurement design, alternating least squares (ALS).
result The proposed method provides theoretical guarantees for the identifiability and recovery of low-rank superoperators in the presence of noise.
Analyzes dynamics of quantum neural networks, predicting exponential decay of training error.
problem Understanding convergence rate of quantum neural networks training.
method Analytic theory for gradient descent dynamics of wide quantum neural networks.
result Simple analytic formula predicts exponential decay of training error.
Quantum model captures rare financial events not seen by Gaussian statistics.
problem Underestimation of rare financial events by Gaussian statistics.
method Quantum Bohmian Mechanics applied to multifractal random walk (MRW) models.
result Rare financial events generate a potential barrier in quantum potentials.
We consider the SO(3) Witten-Reshetikhin-Turaev quantum invariants of random 3-manifolds. When the level r is prime, we show that the asymptotic distribution of the absolute value of these invariants is given by the standard Rayleigh distribution and independent of the choice of level. Hence the probability that the qu…
Quantum Boltzmann Machines trained on quantum annealers produce noisy synthetic data.
problem Training quantum Boltzmann machines on quantum annealers for financial data generation.
method Used D-Wave Advantage 4.1 quantum annealer to train QBMs and compare with classical RBMs.
result Quantum Boltzmann Machines trained on quantum annealers are noisier and less effective than classical RBMs.
Quantum-assisted Gaussian process speeds up data regression.
problem High computational complexity of Gaussian process regression for large datasets.
method Quantum-assisted sparse Gaussian process regression using random Fourier features.
result Achieves polynomial-order computational speedup compared to classical methods.
Quantum field theory connects Riemannian geometry to quantum fluctuations.
problem Generating Riemannian structures from quantum fluctuations.
method QFT approach to Riemannian Geometry, focusing on Ricci curvature.
result Ricci curvature is crucial in generating Riemannian structures.
Quantum neural networks converge to Gaussian processes as they grow.
problem Understanding the convergence of quantum neural networks to Gaussian processes.
method Analyzing Haar random unitary and orthogonal deep QNNs, considering input states, measurement observables, and non-independence of unitary matrix entries.
result Quantum neural networks outputs converge to Gaussian processes in the limit of large Hilbert space dimension.
Study noncommutative Sobolev inequalities using quantum state metrics.
problem Establishing Sobolev inequalities in noncommutative settings.
method Generalizing monotone metrics in quantum states.
result Developed new matrix-valued Beckner inequalities.
We study both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we consider the effect of a random or almost periodic potential as opposed to just periodi…
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on investigating the information-theoretic upper bounds of sample complexity - how ma…
Quantum algorithm solves SOCP and SVM problems faster than classical methods.
problem Quantum algorithms for solving SOCP and SVM problems.
method Quantum interior-point method (IPM) for SOCP, scaling as O(n^k).
result Quantum algorithm exhibits polynomial speedup over classical methods.
Study benchmarks classical models over quantum in DeFi yield prediction.
problem Accurate yield and performance forecasting for DeFi liquidity allocation.
method Benchmarked six models on Curve Finance pools' historical data.
result Classical models, especially XGBoost, outperform quantum models.