Resource threshold for quantum advantage in derivative pricing
Bound the quantum-computing resources a fault-tolerant quantum computer would need to price derivatives — autocallable and Target Accrual Redemption Forward (TARF) instruments serving as the paper's benchmark use cases — at a scale offering a quantum advantage over classical pricing.
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Bound the quantum-computing resources a fault-tolerant quantum computer would need to price derivatives — autocallable and Target Accrual Redemption Forward (TARF) instruments serving as the paper's benchmark use cases — at a scale offering a quantum advantage over classical pricing. Chakrabarti, Krishnakumar, Mazzola, Stamatopoulos, Woerner and Zeng give an upper bound on the resources required for valuable quantum advantage in pricing derivatives, presenting what they describe as the first complete resource estimates for useful quantum derivative pricing. They use autocallable and Target Accrual Redemption Forward (TARF) derivatives together as their benchmark use cases. The authors report uncovering blocking challenges in known approaches to quantum derivative pricing, and introduce a new method they call the re-parameterization method to avoid them, which combines pre-trained variational circuits with fault-tolerant quantum computing to, in their words, dramatically reduce resource requirements. For the benchmark use cases they examine — autocallable and TARF derivatives together, without the abstract stating a separate figure for either instrument alone — they report a requirement of 8k logical qubits and a T-depth of 54 million, and estimate that reaching quantum advantage would require executing that program at the order of a second. The authors state that these resource requirements are out of reach of current systems, and offer them as a roadmap for further improvements in algorithms, implementations and planned hardware architectures.
Circuit & simulation
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What this takes and returns
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How it works
Chakrabarti, Krishnakumar, Mazzola, Stamatopoulos, Woerner and Zeng give an upper bound on the resources required for valuable quantum advantage in pricing derivatives, presenting what they describe as the first complete resource estimates for useful quantum derivative pricing. They use autocallable and Target Accrual Redemption Forward (TARF) derivatives together as their benchmark use cases. The authors report uncovering blocking challenges in known approaches to quantum derivative pricing, and introduce a new method they call the re-parameterization method to avoid them, which combines pre-trained variational circuits with fault-tolerant quantum computing to, in their words, dramatically reduce resource requirements. For the benchmark use cases they examine — autocallable and TARF derivatives together, without the abstract stating a separate figure for either instrument alone — they report a requirement of 8k logical qubits and a T-depth of 54 million, and estimate that reaching quantum advantage would require executing that program at the order of a second. The authors state that these resource requirements are out of reach of current systems, and offer them as a roadmap for further improvements in algorithms, implementations and planned hardware architectures. The Classiq library carries this subject under applications · finance. Reported cost: 8k logical qubits and a T-depth of 54 million, and execution at the order of a second to reach quantum advantage, reported by the abstract for the benchmark use cases the paper examines — autocallable and Target Accrual Redemption Forward (TARF) derivatives together. The abstract states this figure for the two benchmark use cases jointly and does not disaggregate it between the two derivative types, so it is not stated here as a resource bound specific to autocallable options alone..
Implementation
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derivative-pricing-resource-threshold.txt
ALGORITHM: Resource threshold for quantum advantage in derivative pricing
PROBLEM: Bound the quantum-computing resources a fault-tolerant quantum computer would need to price derivatives — autocallable and Target Accrual Redemption Forward (TARF) instruments serving as the paper's benchmark use cases — at a scale offering a quantum advantage over classical pricing.
IDEA: Chakrabarti, Krishnakumar, Mazzola, Stamatopoulos, Woerner and Zeng give an upper bound on the resources required for valuable quantum advantage in pricing derivatives, presenting what they describe as the first complete resource estimates for useful quantum derivative pricing. They use autocallable and Target Accrual Redemption Forward (TARF) derivatives together as their benchmark use cases. The authors report uncovering blocking challenges in known approaches to quantum derivative pricing, and introduce a new method they call the re-parameterization method to avoid them, which combines pre-trained variational circuits with fault-tolerant quantum computing to, in their words, dramatically reduce resource requirements. For the benchmark use cases they examine — autocallable and TARF derivatives together, without the abstract stating a separate figure for either instrument alone — they report a requirement of 8k logical qubits and a T-depth of 54 million, and estimate that reaching quantum advantage would require executing that program at the order of a second. The authors state that these resource requirements are out of reach of current systems, and offer them as a roadmap for further improvements in algorithms, implementations and planned hardware architectures.
REPORTED COST: 8k logical qubits and a T-depth of 54 million, and execution at the order of a second to reach quantum advantage, reported by the abstract for the benchmark use cases the paper examines — autocallable and Target Accrual Redemption Forward (TARF) derivatives together. The abstract states this figure for the two benchmark use cases jointly and does not disaggregate it between the two derivative types, so it is not stated here as a resource bound specific to autocallable options alone.
BASIS: The abstract of arXiv:2012.03819 states: "We find that the benchmark use cases we examine require 8k logical qubits and a T-depth of 54 million." The benchmark use cases are named earlier in the same abstract: "we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual Redemption Forward (TARF) derivatives as benchmark use cases". The abstract does not state the 8k logical qubits and T-depth of 54 million separately for autocallable pricing and separately for TARF pricing, and does not say whether the figure is a total, a maximum, or a per-instrument number; it is stated once, for the benchmark use cases the paper examines as a set. The abstract also states: "We estimate that quantum advantage would require executing this program at the order of a second." The Classiq index entry for applications/finance/autocallable_options gives a directory path and a file list (partial_exponential_state_preparation.ipynb, partial_exponential_state_preparation.qmod, quantum_autocallable_option_pricing.ipynb, quantum_autocallable_option_pricing.qmod) and states no bound. Because the abstract's resource figure is not disaggregated between the two benchmark use cases, this record reports it as covering both together rather than assigning it to autocallable pricing specifically.
DEMONSTRATED BY: the Classiq library entry applications/finance/autocallable_options
PRIMARY SOURCE: Shouvanik Chakrabarti, Rajiv Krishnakumar, Guglielmo Mazzola, Nikitas Stamatopoulos, Stefan Woerner, William J. Zeng (2020), A Threshold for Quantum Advantage in Derivative Pricing — https://arxiv.org/abs/2012.03819
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Quantum vs classical
Classical baseline
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Quantum claim
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How to compare
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Declared gaps
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Literature & references
A Threshold for Quantum Advantage in Derivative Pricing2020 · Shouvanik Chakrabarti, Rajiv Krishnakumar, Guglielmo Mazzola, Nikitas Stamatopoulos, Stefan Woerner, William J. Zeng
Primary source: it states the re-parameterization method combining pre-trained variational circuits with fault-tolerant quantum computing, names autocallable and TARF derivatives as its benchmark use cases, and reports the 8k logical qubit / 54 million T-depth resource estimate and the order-of-a-second execution estimate for quantum advantage. Consult it for the resource figures broken out (if given) by derivative type, the pricing models and contract parameters assumed, the pre-training cost, and the classical baseline the advantage threshold is compared against, none of which the abstract states.