Iterative phase estimation

O'Loan, Caleb J

doi:10.1088/1751-8113/43/1/015301

Cited by 12 publications

(10 citation statements)

References 25 publications

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“…This quantum algorithm allows a quadratic speed-up compared to traditional Monte Carlo simulations, but will most likely require a universal faulttolerant quantum computer [51]. However, research to improve the algorithms is ongoing [52][53][54]. Here we have used a new algorithm [22] that retains the AE speed-up but that uses less gates to measure the price of an option.…”

Section: Resultsmentioning

confidence: 99%

Option Pricing using Quantum Computers

Stamatopoulos

Egger

Sun

et al. 2020

Quantum

202

207

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We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

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Section: Resultsmentioning

confidence: 99%

Option Pricing using Quantum Computers

Stamatopoulos

Egger

Sun

et al. 2020

Quantum

202

207

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“…We determine the control phase at the m-th click measurement as m = m−1 + π/2 (21) and use the same updating formula for the b's as (17). Furthermore, the individual steps of this scheme are similar to those of the adaptive one, except for the following steps:…”

Section: B Nonadaptive Schemementioning

confidence: 99%

Nanoscale magnetometry using a single-spin system in diamond

2011

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We propose a protocol to estimate magnetic fields using a single nitrogen-vacancy (N-V) center in diamond, where the estimate precision scales inversely with time, δB ∼ 1/T , rather than the square-root of time, δB ∼ 1/ √ T . The method is based on converting the task of magnetometry into phase estimation, performing quantum phase estimation on a single N-V nuclear spin using either adaptive or nonadaptive feedback control, and the recently demonstrated capability to perform single-shot readout within the N-V [P. Neumann et al., Science 329, 542 (2010)]. We present numerical simulations to show that our method provides an estimate whose precision scales close to ∼1/T (T ∼ the total estimation time), and moreover will give an unambiguous estimate of the static magnetic field experienced by the N-V. By combining this protocol with recent proposals for scanning magnetometry using an N-V, our protocol will provide a significant decrease in signal acquisition time while providing an unambiguous spatial map of the magnetic field.

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“…In order to perform the calculation of VaR for the two asset portfolio on real quantum hardware it is likely that qubit coherence times will have to be increased by several orders of magnitude and that cross-talk will have to be further suppressed. However, approximating, parallelizing, and decomposing quantum phase estimation is ongoing research and we expect significant improvements in this area not only through hardware, but also algorithms [41][42][43]. This can also help to shorten the required circuit depths, and thus, to reduce the requirements on the hardware to achieve a quantum advantage.…”

Section: Discussionmentioning

confidence: 99%

Quantum risk analysis

2019

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We present a quantum algorithm that analyzes risk more efficiently than Monte Carlo simulations traditionally used on classical computers. We employ quantum amplitude estimation to evaluate risk measures such as Value at Risk and Conditional Value at Risk on a gate-based quantum computer. Additionally, we show how to implement this algorithm and how to trade off the convergence rate of the algorithm and the circuit depth. The shortest possible circuit depth -growing polynomially in the number of qubits representing the uncertainty -leads to a convergence rate of O(M −2/3 ). This is already faster than classical Monte Carlo simulations which converge at a rate of O(M −1/2 ). If we allow the circuit depth to grow faster, but still polynomially, the convergence rate quickly approaches the optimum of O(M −1 ). Thus, for slowly increasing circuit depths our algorithm provides a near quadratic speed-up compared to Monte Carlo methods. We demonstrate our algorithm using two toy models. In the first model we use real hardware, such as the IBM Q Experience, to measure the financial risk in a Treasury-bill (T-bill) faced by a possible interest rate increase. In the second model, we simulate our algorithm to illustrate how a quantum computer can determine financial risk for a two-asset portfolio made up of Government debt with different maturity dates. Both models confirm the improved convergence rate over Monte Carlo methods. Using simulations, we also evaluate the impact of cross-talk and energy relaxation errors.I.

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Iterative phase estimation

Cited by 12 publications

References 25 publications

Option Pricing using Quantum Computers

Option Pricing using Quantum Computers

Nanoscale magnetometry using a single-spin system in diamond

Quantum risk analysis

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