Quantum algorithm for credit valuation adjustments

Alcazar, Javier; Cadarso, Andrea; Katabarwa, Amara; Mauri, Marta; Peropadre, Borja; Wang, Guoming; Cao, Yudong

doi:10.1088/1367-2630/ac5003

Cited by 11 publications

(10 citation statements)

References 52 publications

(104 reference statements)

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“…that acts on an ancilla qubit. After applying F to |ψ n |0 as per (2), one can use the resulting expression,…”

Section: Distributional Properties: Mean and Quantilesmentioning

confidence: 99%

“…These combine the PFE, the counterparty default probability over time, the cost of received and posted collateral and other parameters in order to adjust the 'fair value' of a portfolio PV and allow the hedging of related changes. Proposals for a quantum implementation on the example of 'CVA', the Credit Valuation Adjustment, are provided in [2,92]. Fig.…”

Section: General Setupmentioning

confidence: 99%

“…the theory to describe physical properties and effects of atoms and subatomic particles, on specially designed devices. 1 Compared to 'classical' computations on CPU and GPU hardware, 2 the use of quantum hardware and specially designed software promises a significant speed advantage, dependent on the problem at hand. For certain types of applications, such as integer factorisation-often used as a basis for encryption-quantum computing is the only known way to obtain solutions in an acceptable timeframe.…”

Section: Introductionmentioning

confidence: 99%

“…See, for example, the introductory work in[45] and the state-of-the-art technology summary in[32] 2. CPU: Central Processing Unit; GPU: Graphics Processing Unit 3.…”

mentioning

confidence: 99%

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Quantum computing for financial risk measurement

Wilkens¹,

Moorhouse

2023

Quantum Inf Process

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Quantum computing allows a significant speed-up over traditional CPU- and GPU-based algorithms when applied to particular mathematical challenges such as optimisation and simulation. Despite promising advances and extensive research in hard- and software developments, currently available quantum systems are still largely limited in their capability. In line with this, practical applications in quantitative finance are still in their infancy. This paper analyses requirements and concrete approaches for the application to risk management in a financial institution. On the examples of Value-at-Risk for market risk and Potential Future Exposure for counterparty credit risk, the main contribution lies in going beyond textbook illustrations and instead exploring must-have model features and their quantum implementations. While conceptual solutions and small-scale circuits are feasible at this stage, the leap needed for real-life applications is still significant. In order to build a usable risk measurement system, the hardware capacity—measured in number of qubits—would need to increase by several magnitudes from their current value of about $$10^2$$ 10 2 . Quantum noise poses an additional challenge, and research into its control and mitigation would need to advance in order to render risk measurement applications deployable in practice. Overall, given the maturity of established classical simulation-based approaches that allow risk computations in reasonable time and with sufficient accuracy, the business case for a move to quantum solutions is not very strong at this point.

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“…that acts on an ancilla qubit. After applying F to |ψ n |0 as per (2), one can use the resulting expression,…”

Section: Distributional Properties: Mean and Quantilesmentioning

confidence: 99%

Section: General Setupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…See, for example, the introductory work in[45] and the state-of-the-art technology summary in[32] 2. CPU: Central Processing Unit; GPU: Graphics Processing Unit 3.…”

mentioning

confidence: 99%

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Quantum computing for financial risk measurement

Wilkens¹,

Moorhouse

2023

Quantum Inf Process

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“…Originally, the implementation as a series of arithmetic circuits and controlled rotation was proposed in [53], and some extensions and modifications on this have been also proposed recently [54][55][56]. In another direction, some state preparation methods based on variational algorithms with parametric quantum circuits have been considered [57][58][59][60][61].…”

Section: Definitionmentioning

confidence: 99%

Quantum algorithm for calculating risk contributions in a credit portfolio

Miyamoto

2022

EPJ Quantum Technol.

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Finance is one of the promising field for industrial application of quantum computing. In particular, quantum algorithms for calculation of risk measures such as the value at risk and the conditional value at risk of a credit portfolio have been proposed. In this paper, we focus on another problem in credit risk management, calculation of risk contributions, which quantify the concentration of the risk on subgroups in the portfolio. Based on the recent quantum algorithm for simultaneous estimation of multiple expected values, we propose the method for credit risk contribution calculation. We also evaluate the query complexity of the proposed method and see that it scales as $\widetilde{O} (\sqrt{N_{\mathrm{gr}}}/\epsilon )$ O ˜ ( N gr / ϵ ) on the subgroup number $N_{\mathrm{gr}}$ N gr and the accuracy ϵ, in contrast with the classical method with $\widetilde{O} (\log(N_{\mathrm{gr}})/\epsilon^{2} )$ O ˜ ( log ( N gr ) / ϵ 2 ) complexity. This means that, for calculation of risk contributions of finely divided subgroups, the advantage of the quantum method is reduced compared with risk measure calculation for the entire portfolio. Nevertheless, the quantum method can be advantageous in high-accuracy calculation, and in fact yield less complexity than the classical method in some practically plausible setting.

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Variational Quantum‐Neural Hybrid Error Mitigation

Zhang,

Wan,

Hsieh

et al. 2023

Adv Quantum Tech

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Quantum error mitigation (QEM) is crucial for obtaining reliable results on quantum computers by suppressing quantum noise with moderate resources. It is a key factor for successful and practical quantum algorithm implementations in the noisy intermediate scale quantum (NISQ) era. Since quantum‐classical hybrid algorithms can be executed with moderate and noisy quantum resources, combining QEM with quantum‐classical hybrid schemes is one of the most promising directions toward practical quantum advantages. This work shows how the variational quantum‐neural hybrid eigensolver (VQNHE) algorithm, which seamlessly combines the expressive power of a parameterized quantum circuit with a neural network, is inherently noise resilient with a unique QEM capacity, which is absent in vanilla variational quantum eigensolvers (VQE). The study carefully analyzes and elucidates the asymptotic scaling of this unique QEM capacity in VQNHE from both theoretical and experimental perspectives. Finally, a variational basis transformation is proposed for the Hamiltonian to be measured under the VQNHE framework, yielding a powerful tri‐optimization setup, dubbed as VQNHE++. VQNHE++ can further enhance the quantum‐neural hybrid expressive power and error mitigation capacity.

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Quantum algorithm for credit valuation adjustments

Cited by 11 publications

References 52 publications

Quantum computing for financial risk measurement

Quantum computing for financial risk measurement

Quantum algorithm for calculating risk contributions in a credit portfolio

Variational Quantum‐Neural Hybrid Error Mitigation

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