Related papers: Simulating the non-Hermitian dynamics of financial…
We develop a quantum algorithm to price discretely monitored lookback options in the Black-Scholes framework using imaginary time evolution. By rewriting the pricing PDE as a Schrodinger-type equation, the problem becomes the imaginary time…
Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest…
We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation…
We introduce a constructive method for mapping non-unitary dynamics to a weighted set of unitary operations. We utilize this construction to derive a new correspondence between real and imaginary time, which we term Imaginary Time Quantum…
The quantum imaginary time evolution (QITE) methodology was developed to overcome a critical issue as regards non-unitarity in the implementation of imaginary time evolution on a quantum computer. QITE has since been used to approximate…
Quantum simulators were originally proposed for simulating one partial differential equation (PDE) in particular - Schrodinger's equation. Can quantum simulators also efficiently simulate other PDEs? While most computational methods for…
Many computationally hard problems can be encoded in quantum Hamiltonians. The solution to these problems is given by the ground states of these Hamiltonians. A state-of-the-art algorithm for finding the ground state of a Hamiltonian is the…
Quantum Imaginary-Time Evolution (QITE) is a powerful method for preparing ground states on quantum hardware. However, executing QITE has costly measurement budgets for general Hamiltonians. Both fidelity and computational cost are strongly…
An interacting Black-Scholes model for option pricing, where the usual constant interest rate r is replaced by a stochastic time dependent rate r(t) of the form r(t)=r+f(t) dW/dt, accounting for market imperfections and prices…
The quantum imaginary time evolution (QITE) algorithm is a direct implementation of the classical imaginary time evolution algorithm on quantum computer. We implement the QITE algorithm for the case of nuclear Hartree-Fock equations in a…
We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neural ordinary and partial differential equations into quantum…
As a valid tool for solving ground state problems, imaginary time evolution (ITE) is widely used in physical and chemical simulations. Different ITE-based algorithms in their quantum counterpart have recently been proposed and applied to…
Non-Hermitian quantum systems exhibit unique properties and hold significant promise for diverse applications, yet their dynamical simulation poses a particular challenge due to intrinsic openness and non-unitary evolution. Here, we…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
Quantum dynamics, typically expressed in the form of a time-dependent Schr\"odinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission…
In this paper, we construct quantum circuits for the Black-Scholes equations, a cornerstone of financial modeling, based on a quantum algorithm that overcome the cure of high dimensionality. Our approach leverages the Schr\"odingerisation…
This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary…
In this paper we reformulate the problem of pricing options in a quantum setting. Our proposed algorithm involves preparing an initial state, representing the option price, and then evolving it using existing imaginary time simulation…
Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity.…
Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for…