Algorithms · Amplitude estimation
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.
Attested & literatureUpdated
A small worked example, computed in your browser. It is not a result from this record's papers.
Canonical amplitude estimation
3 counting qubits estimating a = sin²(θ) for the one-qubit state A|0⟩ = RY(π/4)|0⟩, θ = π/8.
Step 1 of 4 · RY(π/4)
Probability of each outcome after this step
- 000085%
- 100015%
Prepares the target qubit as A|0⟩ = cos(θ)|0⟩ + sin(θ)|1⟩; the quantity being estimated is a = sin²(θ), the probability that measuring this qubit alone would give |1⟩.
Probability spreads from 1 outcome to 2.
Spreads the 3 counting qubits into an equal superposition of all 8 values.
Probability spreads from 2 outcomes to 16.
Applies controlled powers of the Grover operator Q = A Z A⁻¹ Z, one power per counting qubit: phase estimation of Q, using A|0⟩ in place of a single eigenstate.
Probability moves between the same 16 outcomes. Down: 0110 10.7% → 1.8%, 0010 10.7% → 1.8%. This is the step that entangles the qubits: from here on no single qubit has a state of its own, only the register as a whole does.
An inverse QFT on the counting register reads the phase into a 3-bit estimate.
Probability gathers from 16 outcomes onto 4. 0001 goes from 1.8% to 25.0%.
Readout The counting register reads 001 or 111, each equally likely: these are θ/π = 1/8 and its mirror 1 − 1/8 = 7/8, both exact in 3 bits by construction. Either one gives a = sin²(π/8) = (2 − √2) / 4 exactly, the standard amplitude-estimation formula a = sin²(πλ) applied to the smaller of the two readings.
Open in Studio- Record typeLiterature reference
- Reference implementationautocallable_options
- Reported cost8k 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.
- Papers1
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.
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
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..
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
- Record type
- Literature reference
- Reference implementation
- autocallable_options
- 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.
- Complexity 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 demonstration this record covers 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.
- Circuit
- Not supplied
This record is not a concrete circuit.
Quantum vs classical
Classical baseline
Compare Amplitude estimation with the strongest classical method for the same instance, input budget, and output metric.
Quantum claim
This reference exposes a quantum circuit pattern; it does not imply an application-level speedup without a matched benchmark.
How to compare
Report input loading, circuit depth, repetitions, classical preprocessing, post-processing, and wall-clock time together.
Nobody has reviewed this record for gaps yet.
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 demonstration this record covers 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.
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
This is a literature reference record, not an executable circuit.A reference record, not runnable source. Leona cannot execute it, so it cannot be saved to your Library as a circuit.
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References
- A Threshold for Quantum Advantage in Derivative Pricing
Shouvanik Chakrabarti, Rajiv Krishnakumar, Guglielmo Mazzola, Nikitas Stamatopoulos, Stefan Woerner, William J. Zeng · 2020
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.