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Efficient state preparation for multivariate Monte Carlo simulation

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Hitomi Mori, Kosuke Mitarai, Keisuke Fujii

Quantum Physics · Submitted 11 Sep 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For this task, we propose a quantum algorithm that only requires the number of gates linear in $D$.

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arXiv ID2409.07336 (version 1)
Pith IDFZI4MGUB, Pith's permanent record of this paper and its review
CitationHitomi Mori, Keisuke Fujii, Kosuke Mitarai. "Efficient state preparation for multivariate Monte Carlo simulation." arXiv:2409.07336 (2024). https://pith.science/paper/FZI4MGUB
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,162 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.79 · human participants 0.02 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.91 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Quantum state preparation is a task to prepare a state with a specific function encoded in the amplitude, which is an essential subroutine in many quantum algorithms. In this paper, we focus on multivariate state preparation, as it is an important extension for many application areas. Specifically in finance, multivariate state preparation is required for multivariate Monte Carlo simulation, which is used for important numerical tasks such as risk aggregation and multi-asset derivative pricing. Using existing methods, multivariate quantum state preparation requires the number of gates exponential in the number of variables $D$. For this task, we propose a quantum algorithm that only requires the number of gates linear in $D$. Our algorithm utilizes multivariable quantum signal processing (M-QSP), a technique to perform the multivariate polynomial transformation of matrix elements. Using easily prepared block-encodings corresponding to each variable, we apply the M-QSP to construct the target function. In this way, our algorithm prepares the target state efficiently for functions achievable with M-QSP.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Quantum state preparation is a task to prepare a state with a specific function encoded in the amplitude, which is an essential subroutine in many quantum algorithms. background 1.00 0.04 0.02 asserted 1.00
s1 In this paper, we focus on multivariate state preparation, as it is an important extension for many application areas. background 0.65 0.30 0.03 asserted 0.99
s2 Specifically in finance, multivariate state preparation is required for multivariate Monte Carlo simulation, which is used for important numerical tasks such as risk aggregation and multi-asset derivative pricing. background 1.00 0.06 0.03 asserted 1.00
s3 Using existing methods, multivariate quantum state preparation requires the number of gates exponential in the number of variables $D$. background 0.53 0.05 0.04 asserted 1.00
s4 For this task, we propose a quantum algorithm that only requires the number of gates linear in $D$. contribution 0.88 0.92 0.81 asserted 0.99
s5 Our algorithm utilizes multivariable quantum signal processing (M-QSP), a technique to perform the multivariate polynomial transformation of matrix elements. method 0.90 0.24 0.06 asserted 0.98
s6 Using easily prepared block-encodings corresponding to each variable, we apply the M-QSP to construct the target function. method 0.99 0.79 0.06 asserted 1.00
s7 In this way, our algorithm prepares the target state efficiently for functions achievable with M-QSP. result 0.43 0.82 0.35 asserted 0.98

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.85.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Quantum state preparation is a task to prepare a state with a specific function encoded in the amplitude, which is an essential subroutine in many quantum algorithms. In this paper, we focus on multivariate state preparation, as it is an important extension for many application areas. Specifically in finance, multivariate state preparation is required for multivariate Monte Carlo simulation, which is used for important numerical tasks such as risk aggregation and multi-asset derivative pricing. Using existing methods, multivariate quantum state preparation requires the number of gates exponential in the number of variables $D$. For this task, we propose a quantum algorithm that only requires the number of gates linear in $D$. Our algorithm utilizes multivariable quantum signal processing (M-QSP), a technique to perform the multivariate polynomial transformation of matrix elements. Using easily prepared block-encodings corresponding to each variable, we apply the M-QSP to construct the target function. In this way, our algorithm prepares the target state efficiently for functions achievable with M-QSP.

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