Algorithms · Amplitude estimation
Quantum amplitude loading for rainbow options pricing
Price rainbow options — a type of path-independent multi-asset derivative — on a quantum computer.
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 implementationrainbow_options
- Reported costNot stated by the sources read
- Papers1
Price rainbow options — a type of path-independent multi-asset derivative — on a quantum computer. Cibrario, Samimi Golan, Ranieri, Dri, Ippoliti, Cohen, Mattia, Montrucchio, Naveh and Corbelletto introduce what the abstract calls a novel approach to pricing rainbow options — a type of path-independent multi-asset derivative — with quantum computers. Leveraging the Iterative Quantum Amplitude Estimation method, they present an end-to-end quantum circuit implementation, and say they emphasize efficiency by delaying the transition to price space. They also analyze two different amplitude-loading techniques for handling exponential functions. The authors validate their quantum pricing model with experiments on the IBM QASM simulator, which the abstract frames as a contribution to the evolving field of quantum finance. The abstract does not describe the circuit's cost or the two amplitude-loading techniques beyond naming them, and it does not state the size of the simulated instances or the accuracy the validation achieved.
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 →
Cibrario, Samimi Golan, Ranieri, Dri, Ippoliti, Cohen, Mattia, Montrucchio, Naveh and Corbelletto introduce what the abstract calls a novel approach to pricing rainbow options — a type of path-independent multi-asset derivative — with quantum computers. Leveraging the Iterative Quantum Amplitude Estimation method, they present an end-to-end quantum circuit implementation, and say they emphasize efficiency by delaying the transition to price space. They also analyze two different amplitude-loading techniques for handling exponential functions. The authors validate their quantum pricing model with experiments on the IBM QASM simulator, which the abstract frames as a contribution to the evolving field of quantum finance. The abstract does not describe the circuit's cost or the two amplitude-loading techniques beyond naming them, and it does not state the size of the simulated instances or the accuracy the validation achieved. The sources read state no complexity bound for this record (The abstract of arXiv:2402.05574, the only source read for this record, states no complexity bound: no big-O expression, no qubit or gate count, and no run time. What it states is a method and a validation. The method: "Leveraging the Iterative Quantum Amplitude Estimation method, we present an end-to-end quantum circuit implementation, emphasizing efficiency by delaying the transition to price space." and "Moreover, we analyze two different amplitude loading techniques for handling exponential functions." The validation: "Experiments on the IBM QASM simulator validate our quantum pricing model, contributing to the evolving field of quantum finance." The demonstration this record covers states no complexity bound of its own. The field is therefore left empty on purpose rather than filled with a bound written from memory.).
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
- rainbow_options
- Reported cost
- Not stated by the sources read
- Complexity basis
- The abstract of arXiv:2402.05574, the only source read for this record, states no complexity bound: no big-O expression, no qubit or gate count, and no run time. What it states is a method and a validation. The method: "Leveraging the Iterative Quantum Amplitude Estimation method, we present an end-to-end quantum circuit implementation, emphasizing efficiency by delaying the transition to price space." and "Moreover, we analyze two different amplitude loading techniques for handling exponential functions." The validation: "Experiments on the IBM QASM simulator validate our quantum pricing model, contributing to the evolving field of quantum finance." The demonstration this record covers states no complexity bound of its own. The field is therefore left empty on purpose rather than filled with a bound written from memory.
- 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: Quantum amplitude loading for rainbow options pricing
PROBLEM: Price rainbow options — a type of path-independent multi-asset derivative — on a quantum computer.
IDEA: Cibrario, Samimi Golan, Ranieri, Dri, Ippoliti, Cohen, Mattia, Montrucchio, Naveh and Corbelletto introduce what the abstract calls a novel approach to pricing rainbow options — a type of path-independent multi-asset derivative — with quantum computers. Leveraging the Iterative Quantum Amplitude Estimation method, they present an end-to-end quantum circuit implementation, and say they emphasize efficiency by delaying the transition to price space. They also analyze two different amplitude-loading techniques for handling exponential functions. The authors validate their quantum pricing model with experiments on the IBM QASM simulator, which the abstract frames as a contribution to the evolving field of quantum finance. The abstract does not describe the circuit's cost or the two amplitude-loading techniques beyond naming them, and it does not state the size of the simulated instances or the accuracy the validation achieved.
REPORTED COST: Not stated by the sources read
BASIS: The abstract of arXiv:2402.05574, the only source read for this record, states no complexity bound: no big-O expression, no qubit or gate count, and no run time. What it states is a method and a validation. The method: "Leveraging the Iterative Quantum Amplitude Estimation method, we present an end-to-end quantum circuit implementation, emphasizing efficiency by delaying the transition to price space." and "Moreover, we analyze two different amplitude loading techniques for handling exponential functions." The validation: "Experiments on the IBM QASM simulator validate our quantum pricing model, contributing to the evolving field of quantum finance." The demonstration this record covers states no complexity bound of its own. The field is therefore left empty on purpose rather than filled with a bound written from memory.
PRIMARY SOURCE: Francesca Cibrario, Or Samimi Golan, Giacomo Ranieri, Emanuele Dri, Mattia Ippoliti, Ron Cohen, Christian Mattia, Bartolomeo Montrucchio, Amir Naveh, Davide Corbelletto (2024), Quantum Amplitude Loading for Rainbow Options Pricing — https://arxiv.org/abs/2402.05574
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.
Related entries
- Quantum amplitude estimation
Algorithms
- Option pricing by amplitude estimation
Algorithms
- Iterative phase estimation
Algorithms
- Quantum phase estimation
Algorithms
References
- Quantum Amplitude Loading for Rainbow Options Pricing
Francesca Cibrario, Or Samimi Golan, Giacomo Ranieri, Emanuele Dri, Mattia Ippoliti, Ron Cohen, Christian Mattia, Bartolomeo Montrucchio, Amir Naveh, Davide Corbelletto · 2024
Primary source: it introduces the amplitude-loading approach to pricing rainbow options, describes the end-to-end quantum circuit built on Iterative Quantum Amplitude Estimation, names the two amplitude-loading techniques for exponential functions it analyzes, and reports validating the model with experiments on the IBM QASM simulator. Consult it for the circuit's cost, for how the two amplitude-loading techniques compare, and for the size and precision of the simulated instances, none of which the abstract states.