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 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.
New method uses quantum simulation to price multi-asset derivatives efficiently.
problem Efficiently pricing derivatives with many underlying assets.
method Variational quantum simulation to solve Black-Scholes equation.
result Quantum speedup in derivative pricing for small quantum computers.
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.
Quantum advantage in derivative pricing requires 8k qubits and 54M T-depth.
problem Quantum advantage in pricing derivatives.
method Re-parameterization method combining pre-trained variational circuits and fault-tolerant quantum computing.
result Benchmark use cases require 8k logical qubits and a T-depth of 54 million.
The Accardi-Boukas quantum Black-Scholes equation can be used as an alternative to the classical approach to finance, and has been found to have a number of useful benefits. The quantum Kolmogorov backward equations, and associated quantum Fokker-Planck equations, that arise from this general framework, are derived usi…
Quantum computing improves Monte Carlo option pricing for complex derivatives.
problem Complex financial derivatives require extensive computations in high-dimensional spaces.
method Developed a quantum algorithm for simulating many potential asset paths in parallel.
result Quantum algorithm provides highly accurate option pricing and risk analysis.
Quantum computing speeds up interest rate derivative pricing using LMM.
problem Challenges in pricing interest rate derivatives, especially caps.
method Hybrid classical-quantum approach using quantum amplitude estimation.
result Quantum computing improves convergence in pricing interest rate derivatives.
Quantum algorithms accelerate financial risk computation.
problem Accelerating the computation of financial market risk.
method Quantum gradient estimation algorithms for market sensitivities.
result Significant reduction in resource requirements for financial quantum advantage.
Quantum circuit optimization speeds up financial derivatives pricing.
problem Efficiently pricing financial derivatives on quantum computers.
method Pretraining conditional parameterized circuits for state-dependent functions.
result Quantum circuit implementation of derivatives' payoff function is more efficient.
Quantum algorithms speed up derivative pricing beyond Black-Scholes models.
problem Quantum speedups for derivative pricing beyond Black-Scholes models.
method Utilizing fast-forwardability and quantum Milstein sampler for non-GBM models, and improved numerical integration for GBM and CIR models.
result Quadratic speedups for derivative pricing in practical models like CIR and Heston's model.
To give a Cartan calculus on the extended quantum 3d space, the noncommutative differential calculus on the extended quantum 3d space is extended by introducing inner derivations and Lie derivatives.
New quantum algorithm simplifies complex financial derivatives pricing.
problem Complex financial derivatives pricing with high dimensionality.
method Quantum-inspired variational algorithms combined with neural-network quantum states.
result Simplified pricing of European options with many correlated assets.
Alternative method for derivatives pricing using quantum computers.
problem Derivatives pricing using quantum computers.
method Combination of direct encoding and modified Real Quantum Amplitude Estimation (mRQAE) algorithm.
result Experimental comparison shows that the proposed method retains speedups.
Quantum methods improve option pricing accuracy.
problem Pricing financial derivatives using Monte Carlo integration.
method Hybrid classical-quantum methods using Fourier series and QML.
result Quantum methods achieve remarkable accuracy in option pricing.
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 algorithms for financial derivatives and credit risk.
problem Estimating credit risk and option pricing in realistic financial models.
method Developed a regime switching volatility model for financial markets, using a Markov chain to determine volatility parameters.
result Quantum algorithms can be applied to realistic financial models, bringing quantum computing closer to practical applications.
New knot invariants derived using quantum cluster algebras.
problem Deriving new knot invariants from quantum cluster algebras.
method Interpreting R-matrix of Uq(sl2) as cluster transformation, introducing auxiliary parameter ε. result Derives perturbed-Alexander invariants with higher-order terms in ε. A new quantum gauge model is proposed. From this quantum gauge model we derive a quantum invariant of 3-manifolds. We show that this quantum invariant of 3-manifolds gives a classification of closed (orientable and connected) 3-manifolds. From this classification we then prove the Poincaré conjecture.
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.
Derives Atiyah sequence for noncommutative bundles.
problem Deciding when ∗-automorphisms lift to compatible ones. method Derivation-based Atiyah sequence derivation.
result Validates existence of compatible lifts.
Quantum computer method for pricing rainbow options efficiently.
problem Pricing rainbow options with quantum computers.
method Iterative Quantum Amplitude Estimation and amplitude loading techniques.
result Validation of quantum pricing model on IBM QASM simulator.
Quantum assets are priced using a new theorem, extending classical asset pricing.
problem Quantum properties in financial markets and assets.
method Developed a new definition of arbitrage for quantum assets and proved a quantum version of the first fundamental theorem of asset pricing.
result There exists a risk-free density operator under which all quantum assets are martingales if no arbitrage exists.
Quantum algorithm for pricing European call options.
problem Accurate valuation of financial derivatives, especially for complex models and options.
method Transforms classical FFT into quantum QFT for pricing European call options.
result Quantum algorithm outperforms classical Monte Carlo simulation in NISQ era.
New invariants derived from Kauffman bracket for 3-manifolds.
problem Quantum invariants of 3-manifolds, especially non-semisimple ones.
method Combinatorial methods using Temperley-Lieb algebras and Kauffman bracket polynomials.
result Recovery of invariants from small quantum group of sl2. Quantum algorithm speeds up pricing of financial derivatives.
problem Pricing autocallable options efficiently.
method Integration-based exponential amplitude loading technique.
result 50x reduction in circuit depth for payoff component.
Explains model structures for higher orbifolds and applies them to quantum cohomology.
problem Understanding quantum cohomology of higher orbifolds.
method Develops model structures on higher orbifolds and applies them to quantum cohomology.
result Model structures provide insights into quantum cohomology of higher orbifolds.
We define invariants for a framed link equipped with a SL2 local system in its complement and additional combinatorial data based on the theory of representations of stated skein algebras at roots of unity of punctured bigons and the geometric interpretation of their centers. The gauge invariance of the link invariant …
We compute Stokes matrices and monodromy for the quantum cohomology of projective spaces. We prove that the Stokes' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves.
We define quantum exterior product wedge_h and quantum exterior differential d_h on Poisson manifolds (of which symplectic manifolds are an important class of examples). Quantum de Rham cohomology, which is a deformation quantization of de Rham cohomology, is defined as the cohomology of d_h. We also define quantum Dol…
The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones.
Derives localization formulas in Batalin-Vilkovisky formalism.
problem Localization in Batalin-Vilkovisky formalism.
method Equivariant localization formulas in Batalin-Vilkovisky formalism.
result Derives localization formulas in Batalin-Vilkovisky formalism.
Simpler equations derived for knot polynomials coefficients, forming a ring.
problem Complexity of knot polynomials colored with symmetric representations.
method Deriving two difference equations for quantum C-polynomials coefficients.
result Quantum C-polynomials form a ring and are much simpler than colored polynomials.
We propose a gauge model of quantum electrodynamics (QED) and its nonabelian generalization from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from quantum field theory based on the Chern-Simon Lagrangian. From our approach we ca…
QCML uses quantum geometry to represent data.
problem Data representation and the curse of dimensionality.
method QCML encodes data as Hermitian matrices in Hilbert space.
result Data geometry reveals intrinsic dimension and topological properties.
This paper applies quantum probability theory to model asset returns, avoiding assumptions about quantum effects.
problem Modeling asset returns with classical probability theory.
method Derives a Schrödinger-like trading equation using quantum probability, linking it to traders' decisions and market behaviors.
result Quantum probability can describe multimodal distributions of asset returns without assuming quantum effects.
Quantum algorithms improve calculation of parameter sensitivities in financial derivatives.
problem Calculating derivatives of expected values with respect to parameters in stochastic models.
method Two quantum methods based on QMCI and central difference formula.
result Sum-in-QAE method can be more advantageous for nonsmooth functions or limited qubits.
Quantum computing offers new solutions for financial optimization, pricing, risk, and security.
problem Core financial bottlenecks in combinatorial search, expectation estimation, and rare-event analysis.
method Identify bottlenecks, specify quantum primitives, compare with classical benchmarks, assess under constraints.
result Strongest near-term case for quantum finance in hybrid workflows, constrained search, and amplitude-estimation.
Quantum machine learns to clean up blurry images.
problem Cleaning up blurry images using quantum computing.
method Uses Boltzmann machines, QUBO, and quantum annealing to balance image quality and noise.
result Quantum method produces cleaner images than noisy originals on average.
In this article we model a financial derivative price as an observable on the market state function. We apply geometric techniques to integrating the Heisenberg Equation of Motion. We illustrate how the non-commutative nature of the model introduces quantum interference effects that can act as either a drag or a boost …
Propose a model-independent axiomatic framework for derived skein theory.
problem Derived skein theory of oriented 3-manifolds with coefficients in a ribbon tensor category.
method Design axioms for the 0th homology and gluing.
result Establishes relationships between derived and ordinary skein theory.
We use topological quantum field theory to derive an invariant of a three-manifold with boundary. We then show how to use this invariant as an obstruction to embedding one three-manifold in another.
QTAML models quantum tunneling errors for AI robustness.
problem Quantum tunneling errors in AI inference.
method Derives weight-error distribution using WKB approximation, introduces TAC algorithm.
result TAC achieves 95% clean accuracy with 3.4-33.6x less ECC overhead.
Quantum algorithm solves financial option pricing using Hamiltonian simulation.
problem Efficiently solving the Black-Scholes equation for option pricing dynamics.
method Mapped Black-Scholes equation to Schrödinger equation, used efficient Hamiltonian simulation techniques.
result Quantum algorithm shows feasible approach for solving financial derivatives on a quantum computer.
We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kaehler manifold). This generalizes a result of Givental and Kim relating the open Toda lattice and the quantum cohomology of the finite-dimensional flag manifold. W…
Homotopy Quantum Field Theories (HQFTs) generalize more familiar Topological Quantum Field Theories (TQFTs). In generalization of the surgery construction of 3-dimensional TQFTs from modular categories, we use surgery to derive 3-dimensional HQFTs from G-modular categories.
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the mai…
Quantum connections replace metrics with operator inner products.
problem Quantifying geometric properties in quantum systems.
method Defining quantum connections and duals using operator fields and inner products.
result Holonomy and dual connections are equivalent in quantum geometry.