Classical Tensor Network and Quantum Fourier Transform Approaches for Large-Scale Carr-Madan Option Pricing

• URL: http://arxiv.org/abs/2607.28435v1
• Date: Thu, 30 Jul 2026 16:12:44 GMT
• Title: Classical Tensor Network and Quantum Fourier Transform Approaches for Large-Scale Carr-Madan Option Pricing
• Abstract summary: We reformulate the Carr-Madan pricing framework using tensor networks.<n>We show that the proposed SFFT method maintains pricing accuracy while substantially reducing memory requirements.<n>The accompanying quantum simulations and hardware executions enable a direct comparison between the classical tensor network formulation and its QFT-based quantum counterpart.
• Score: 1.0742675209112622
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fourier-based methods are among the most widely used techniques for pricing European options when the characteristic function of the underlying asset process is available. Their applicability to increasingly fine discretizations, however, is limited by the rapidly growing memory requirements of classical Fourier transforms, which become a computational bottleneck for large-scale pricing problems. In this work, we overcome this limitation by reformulating the Carr-Madan pricing framework using tensor networks. Specifically, we employ the Superfast Fourier Transform (SFFT), a compressed Tensor Train representation of the Quantum Fourier Transform (QFT), and apply it directly to tensorized option pricing without ever explicitly constructing exponentially large vectors or Fourier operators. This formulation also enables a direct comparison between the classical tensor network algorithm and its quantum counterpart through QFT-based option pricing on quantum simulators and quantum hardware. Numerical experiments for European call options demonstrate that the proposed SFFT method maintains pricing accuracy while substantially reducing memory requirements and achieving subexponential computational scaling compared with conventional FFT-based pricing. The accompanying quantum simulations and hardware executions enable a direct comparison between the classical tensor network formulation and its QFT-based quantum counterpart, showing that both approaches avoid the exponential scaling of conventional Fourier implementations and provide complementary perspectives on large-scale option pricing. Together, these results establish a unified framework connecting classical Fourier pricing, tensor network algorithms, and quantum computing approaches, demonstrating how tensorized Fourier methods can provide scalable alternatives for high-dimensional financial computations.

Related papers

• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• Hybrid Quantum State Preparation via Data Compression [0.0]
  Quantum state preparation (QSP) for a general $n$qubit state requires $O(2n)$ CNOT and circuit depth.<n>We introduce an ancilla-free hybrid classical-quantum strategy that reduces this cost to $O(poly(n)$ for a broad class of compressible data.
  arXiv  Detail & Related papers  (2025-12-01T15:32:46Z)
• Quantum Machine Learning methods for Fourier-based distribution estimation with application in option pricing [42.79174867716636]
  We introduce two hybrid classical-quantum methods to address the option pricing problem.<n>We show that the proposed methods achieve remarkable accuracy, becoming a competitive quantum alternative for derivatives valuation.
  arXiv  Detail & Related papers  (2025-10-22T11:43:08Z)
• FFT-Accelerated Auxiliary Variable MCMC for Fermionic Lattice Models: A Determinant-Free Approach with $O(N\log N)$ Complexity [52.3171766248012]
  We introduce a Markov Chain Monte Carlo (MCMC) algorithm that dramatically accelerates the simulation of quantum many-body systems.<n>We validate our algorithm on benchmark quantum physics problems, accurately reproducing known theoretical results.<n>Our work provides a powerful tool for large-scale probabilistic inference and opens avenues for physics-inspired generative models.
  arXiv  Detail & Related papers  (2025-10-13T07:57:21Z)
• FIMA-Q: Post-Training Quantization for Vision Transformers by Fisher Information Matrix Approximation [55.12070409045766]
  Post-training quantization (PTQ) has stood out as a cost-effective and promising model compression paradigm in recent years.<n>Current PTQ methods for Vision Transformers (ViTs) still suffer from significant accuracy degradation, especially under low-bit quantization.
  arXiv  Detail & Related papers  (2025-06-13T07:57:38Z)
• AdaLog: Post-Training Quantization for Vision Transformers with Adaptive Logarithm Quantizer [54.713778961605115]
  Vision Transformer (ViT) has become one of the most prevailing fundamental backbone networks in the computer vision community. We propose a novel non-uniform quantizer, dubbed the Adaptive Logarithm AdaLog (AdaLog) quantizer.
  arXiv  Detail & Related papers  (2024-07-17T18:38:48Z)
• Pricing of European Calls with the Quantum Fourier Transform [0.0]
  We introduce and analyze a quantum algorithm for pricing European call options across a broad spectrum of asset models. We compare this novel algorithm with existing quantum algorithms for option pricing.
  arXiv  Detail & Related papers  (2024-04-22T12:03:49Z)
• Quantum Augmented Dual Attack [8.134961550216618]
  We present a quantum augmented variant of the dual lattice attack on the Learning with Errors (LWE) problem, using classical memory with quantum random access (QRACM) Applying our results to lattice parameters from the literature, we find that our algorithm outperforms previous algorithms, assuming unit cost access to a QRACM.
  arXiv  Detail & Related papers  (2022-05-27T13:54:31Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions [0.9634136878988853]
  Power-law interactions with strength decaying as $1/ralpha$ in the distance provide an experimentally realizable resource for information processing. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. We show that power-law systems with $alpha le D$ are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable.
  arXiv  Detail & Related papers  (2020-07-01T18:00:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.