The paper uses quaternions to model quantum learning on devices.
problem Designing adaption and optimization techniques for quantum learning machines.
method Division algebra of quaternions to model computation and measurement on qubits, developing a training framework.
result Established quantum information processing units similar to neurons in classical approaches.
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.
Quantum computing improves graph neural network aggregation.
problem Limitations of classical GNNs in processing global graph features.
method Quantum computer-generated aggregation weights for graph neural networks.
result Quantum-enhanced GNN performs similarly to classical models on standard datasets.
A novel quantum model improves RBM performance and is efficiently trainable.
problem Improving the performance of RBM models.
method Quantum model with parametrically coupled fermions to classical signals.
result The model outperforms classical RBM with the same number of hidden units.
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.
Variational autoencoders (VAEs) are powerful generative models with the salient ability to perform inference. Here, we introduce a quantum variational autoencoder (QVAE): a VAE whose latent generative process is implemented as a quantum Boltzmann machine (QBM). We show that our model can be trained end-to-end by maximi…
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…
This work reveals symmetries in quantum circuits and develops a noise-aware optimization method.
problem Understanding and optimizing the cost landscape of parametrized quantum circuits.
method Analytical proof of symmetries and their resilience to noise, followed by the development of SYMH optimization method.
result Symmetries in PQCs lead to degeneracy in the cost landscape and can be exploited to improve optimization under noise.
The paper explores how the unit inclusion affects topological quantum field theories in non-semisimple categories.
problem Understanding the effects of unit inclusion in non-semisimple braided tensor categories on topological quantum field theories.
method Analyzes the dualizability of the unit inclusion morphism in Morita 4-category of braided tensor categories and applies the Cobordism Hypothesis.
result Shows that the unit inclusion in non-semisimple modular categories leads to non-compact relative 3D topological quantum field theories.
Constructs a cyclic, filtered, strictly unital curved A∞ category for Lagrangian submanifolds and develops Floer theory.
problem Proving that any Lagrangian submanifold equipped with a weak bounding cochain lies in the category split-generated by a given collection of Lagrangian submanifolds.
method Develops a cyclic, filtered, strictly unital curved A∞ category and uses it to prove the above statement. result Any Lagrangian submanifold equipped with a weak bounding cochain lies in the category split-generated by a given collection of Lagrangian submanifolds.
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.
Optimizes portfolios with discrete units using simulated annealing.
problem Finding optimal asset allocation in finance with discrete units.
method Integer simulated annealing method for combinatorial optimization.
result Classical resources can efficiently solve discretized convex portfolio optimization problems.
Optimizing quantum graphs yields geodesic nets on surfaces.
problem Finding optimal quantum graphs for geodesic nets.
method Optimizing functionals from spectral theory to find geodesic nets.
result Critical metrics for eigenvalues give rise to geodesic nets.
Lossy compression of statistical data using quantum annealing.
problem Efficiently compressing statistical floating-point data.
method Representation learning with binary variables, classical optimization of basis vectors, quantum annealing for coefficients, bias correction.
result Quantum annealing shows promising results with 3.5x better compression than neural-network autoencoders.
Quantum Gaussian processes enable scalable quantum learning.
problem Lack of simple, interpretable, scalable learning frameworks for quantum data.
method Bayesian framework using Gaussian processes with quantum kernels.
result Provable and scalable quantum Gaussian processes for quantum learning.
Quantum computing optimizes ESG portfolios efficiently.
problem Optimizing investment portfolios with risk, return, and ESG considerations.
method Formulated discrete Markowitz portfolio theory (DMPT) for quantum annealers, incorporating ESG ratings.
result Discrete portfolios converge to continuous solutions as budgets increase, outperforming traditional methods.
Improved VQE for large DPO problems in finance.
problem Dynamic Portfolio Optimization (DPO) with many assets.
method Tailored VQE workflow, ISQR routine, VQE Constrained method.
result Achieved financial performance similar to classical methods.
Quantum reservoir computing tackles noisy quantum computers for temporal tasks.
problem Efficiently process input sequences on noisy quantum computers.
method Quantum reservoir computing using dissipative quantum dynamics.
result Small and noisy quantum reservoirs can handle high-order nonlinear temporal tasks.
Quantum Signal Processing reduces derivative pricing quantum resource requirements.
problem Efficiently pricing financial derivatives on quantum computers.
method Quantum Signal Processing (QSP) to encode payoffs directly into quantum amplitudes.
result Significantly reduces quantum resources (T-gates and qubits) for practical derivative contracts.
Quantum machine learning aims to solve learning problems more efficiently.
problem Solving learning problems more efficiently using quantum processors.
method Leveraging quantum processors for optimization, supervised, unsupervised, reinforcement learning, and generative modeling.
result Quantum approaches may offer real benefits under certain conditions.
Study online learning of quantum processes, showing feasibility for certain types.
problem Learning quantum processes adaptively, especially for bounded gate complexity and Pauli channels.
method Online learning, mistake-bounded model, multiplicative weights update algorithm, Bell sampling.
result Online learning feasible for quantum channels of bounded gate complexity and Pauli channels.
A new penalty-free method optimizes portfolios without quantum annealing penalties.
problem Optimizing portfolios with quantum annealing penalties.
method Removing the penalty term and using a classical feasibility projector.
result Significant reduction in chain-break fractions and post-processed regret.
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a given quantum process. QPT is a major quantum information processing tool, since it especially allows one to characterize the actual behavior of quantum gates, which are the building blocks of quantum computers. However, usual QPT procedure…
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.
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.
This paper proposes a brain-inspired approach to quantum machine learning with the goal of circumventing many of the complications of other approaches. The fact that quantum processes are unitary presents both opportunities and challenges. A principal opportunity is that a large number of computations can be carried ou…
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 algorithm speeds up financial option pricing.
problem Optimizing stopping times in stochastic processes for finance.
method Combines quantum computing techniques with LSM for optimal stopping.
result Achieves nearly quadratic speedup in runtime.
Given an element of the Bloch group of a number field~F and a natural number~n, we construct an explicit unit in the field Fn=F(e2πi/n), well-defined up to $\nn$-th powers of nonzero elements of~Fn. The construction uses the cyclic quantum dilogarithm, and under the identification of the Bloch group of~$F…
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.
Quantum machine learning boosts financial forecasting accuracy.
problem Churn prediction and credit risk assessment in finance.
method Used quantum and classical Determinantal Point Processes for churn prediction, and quantum neural networks for credit risk assessment.
result Significant improvement in precision for churn prediction (6% increase). Quantum models match classical performance with fewer parameters.
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.
The Accardi-Boukas quantum Black-Scholes framework, provides a means by which one can apply the Hudson-Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using nonlocal diffusion processes, via a Kramers-Moyal expansion, and this provides useful tools to under…
Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work by Polyakov. In this paper, we investigate the case of simply connected domains…
Study of webs in quantum type C, proving equivalence to quantum representations.
problem Equivalence of webs and quantum representations in type C.
method Defined a linear pivotal category diagrammatically, conjectured equivalence, and proved functorial results.
result Full, essentially surjective functor between web and quantum representation categories.
Quantum computing improves fault diagnosis in industrial processes.
problem Fault detection and diagnosis in industrial process systems.
method Integrates quantum computing and deep learning to extract features and diagnose faults.
result Quantum-assisted deep learning achieves high fault detection rates (79.2% and 99.39%).
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to deep architectures has remained a major challenge. Recent results connected dee…
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 algorithm improves portfolio optimization quality measured by Wasserstein distance.
problem Optimizing financial asset portfolios using quantum computing.
method Used Quantum Approximate Optimization Algorithm (QAOA) and Normalized and Complementary Wasserstein Distance (η) to benchmark solution quality. result Solution quality increases with QAOA circuit depth p and is influenced by the portfolio budget B. New method uses quantum computing to process classical data efficiently.
problem Inefficient quantum machine learning due to data loading and trainability issues.
method Linear Hamiltonian-based machine learning with ground state problems for k-local Hamiltonians.
result Demonstrated the effectiveness and scalability of the method on up to 50 qubits.
This paper gives a generalization of the AJL algorithm and unitary braid group representation for quantum computation of the Jones polynomial to continuous ranges of values on the unit circle of the Jones parameter. We show that our 3-strand algorithm for the Jones polynomial is a special case of this generalization of…
Motivated by the work of Segal and Segal on the Black-Scholes pricing formula in the quantum context, we study a quantum extension of the Black-Scholes equation within the context of Hudson-Parthasarathy quantum stochastic calculus. Our model includes stock markets described by quantum Brownian motion and Poisson proce…
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.
The article models illiquid stocks using quantum calculus with asymptotic methods.
problem Modeling illiquid financial markets.
method Application of quantum stochastic calculus and asymptotic methods.
result Power series solutions can approximate quantum stochastic processes for longer time frames.
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.
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.
Geometric approach to quantum thermodynamics models state spaces and processes.
problem Quantum thermodynamics in the regime of non-equilibrium states.
method Contact geometry and principal fiber bundles to model quantum state spaces and processes.
result Geometric formulation reveals the fundamental thermodynamic relations and unattainability of the third law.
A quantum model classifies financial sentiment by mapping text chunks to quantum circuits.
problem Classifying financial texts with high accuracy and preserving semantic information.
method Chunked diagrams are mapped to quantum circuits, with a Transformer encoder and type embeddings added for context.
result The hybrid model improves sentiment classification over a simple averaging baseline.