Toward pricing financial derivatives with an IBM quantum computer

Martin, Ana; Candelas, Bruno; Rodríguez-Rozas, Ángel; Martín-Guerrero, José D.; Chen, Xi; Lamata, Lucas; Orús, Román; Solano, E.; Sanz, Mikel

doi:10.1103/physrevresearch.3.013167

Cited by 62 publications

(42 citation statements)

References 127 publications

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“…Gate-based quantum computers are expected to help solve problems in quantum chemistry [1][2][3], machine learning [4,5], financial simulation [6][7][8][9][10][11][12][13] and combinatorial optimization [14,15]. The quantum approximate optimization algorithm (QAOA) [16][17][18], inspired by a Trotterization of adiabatic quantum computing [19][20][21], runs on gate-based quantum computers [22,23].…”

Section: Introductionmentioning

confidence: 99%

Warm-starting quantum optimization

Egger

Mareček

Woerner

2021

Quantum

148

111

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There is an increasing interest in quantum algorithms for problems of integer programming and combinatorial optimization. Classical solvers for such problems employ relaxations, which replace binary variables with continuous ones, for instance in the form of higher-dimensional matrix-valued problems (semidefinite programming). Under the Unique Games Conjecture, these relaxations often provide the best performance ratios available classically in polynomial time. Here, we discuss how to warm-start quantum optimization with an initial state corresponding to the solution of a relaxation of a combinatorial optimization problem and how to analyze properties of the associated quantum algorithms. In particular, this allows the quantum algorithm to inherit the performance guarantees of the classical algorithm. We illustrate this in the context of portfolio optimization, where our results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth. Likewise, Recursive QAOA for MAXCUT problems shows a systematic increase in the size of the obtained cut for fully connected graphs with random weights, when Goemans-Williamson randomized rounding is utilized in a warm start. It is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.

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Section: Introductionmentioning

confidence: 99%

Warm-starting quantum optimization

Egger

Mareček

Woerner

2021

Quantum

148

111

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“…, h M ) is the set of data obtained in the experiment. As mentioned in the previous subsection, θ ML asymptotically achieves the lower bound in the Cramér-Rao inequality (7) if the data is generated from the model distribution; the Fisher information matrix (8) in this case can now be calculated as…”

Section: Fisher Information In the Presence Of Depolarizing Noisementioning

confidence: 96%

“…This section is devoted to show experimental result using the real-backend device of IBM Quantum Systems called ibmq_valencia [25], to evaluate the estimation performance of the proposed ML estimate and thereby the validity of the employed depolarization model. In particular we consider the Monte Carlo integration problem, whose computational (sampling) cost can be quadratically reduced via the amplitude estimation algorithm [4][5][6][7][8][9][10]. In this section, we begin with a brief explanation on the target integration problem, followed by showing the execution results of the real device for two-qubit and three-qubit cases.…”

Section: Experiments With a Real Quantum Computing Devicementioning

confidence: 99%

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Amplitude estimation via maximum likelihood on noisy quantum computer

Tanaka

Suzuki

Uno

et al. 2021

Quantum Inf Process

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Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core subroutine in various computing tasks such as the Monte Carlo methods. One of those algorithms is based on the maximum likelihood estimate with parallelized quantum circuits. In this paper, we extend this method so that it incorporates the realistic noise effect, and then give an experimental demonstration on a superconducting IBM Quantum device. The maximum likelihood estimator is constructed based on the model assuming the depolarization noise. We then formulate the problem as a two-parameters estimation problem with respect to the target amplitude parameter and the noise parameter. In particular we show that there exist anomalous target values, where the Fisher information matrix becomes degenerate and consequently the estimation error cannot be improved even by increasing the number of amplitude amplifications. The experimental demonstration shows that the proposed maximum likelihood estimator achieves quantum speedup in the number of queries, though the estimation error saturates due to the noise. This saturated value of estimation error is consistent to the theory, which implies the validity of the depolarization noise model and thereby enables us to predict the basic requirement on the hardware components (particularly the gate error) in quantum computers to realize the quantum speedup in the amplitude estimation task.

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“…Algorithms that can be implemented in quantum circuits, such as amplitude estimation, 5 quantum principle component analysis (PCA), 6 quantum generative adversarial network (QGAN), 7 the quantum-classical hybrid variational quantum eigensolver (VQE), 8 and quantum-approximate-optimization-algorithm (QAOA), 9 spring up and begin to be applied to various financial quantitative tasks. [10][11][12][13][14][15] Within all sectors of quantitative finance, the Monte Carlo simulation always plays a significant role, [16][17][18] as only a few stochastic equations for derivative pricing have found analytical solutions, 19,20 while most can only be solved numerically by repeating random settings a great many times in an uncertainty distribution (e.g., normal or log-normal distribution), which therefore consumes much time. The quantum amplitude estimation (QAE) algorithm was raised 5 in 2002.…”

Section: Introductionmentioning

confidence: 99%

Quantum computation for pricing the collateralized debt obligations

Tang

Pal

Qiao

et al. 2021

Quantum Engineering

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Collateralized debt obligation (CDO) has been one of the most commonly used structured financial products and is intensively studied in quantitative finance.By setting the asset pool into different tranches, it effectively works out and redistributes credit risks and returns to meet the risk preferences for different tranche investors. The copula models of various kinds are normally used for pricing CDOs, and the Monte Carlo simulations are required to get their numerical solution. Here we implement two typical CDO models, the single-factor Gaussian copula model and normal inverse Gaussian copula model, and by applying the conditional independence approach, we manage to load each model of distribution in quantum circuits. We then apply quantum amplitude estimation as an alternative to Monte Carlo simulation for CDO pricing. We demonstrate the quantum computation results using IBM Qiskit. Our work addresses a useful task in finance instrument pricing, significantly broadening the application scope for quantum computing in finance.

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Toward pricing financial derivatives with an IBM quantum computer

Cited by 62 publications

References 127 publications

Warm-starting quantum optimization

Warm-starting quantum optimization

Amplitude estimation via maximum likelihood on noisy quantum computer

Quantum computation for pricing the collateralized debt obligations

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