اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA variational quantum algorithm for the Feynman-Kac formula
245
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the correspondence between the Feynman-Kac partial differential equation (PDE) and the Wick-rotated Schr{o}dinger equation for this purpose. The results for a $(2+1)$ dimensional Feynman-Kac system, obtained through the variational quantum algorithm are then compared against classical ODE solvers and Monte Carlo simulation. We see a remarkable agreement between the classical methods and the quantum variational method for an illustrative example on six qubits. In the non-trivial case of PDEs which are preserving probability distributions -- rather than preserving the $ell_2$-norm -- we introduce a proxy norm which is efficient in keeping the solution approximately normalized throughout the evolution. The algorithmic complexity and costs associated to this methodology, in particular for the extraction of properties of the solution, are investigated. Future research topics in the areas of quantitative finance and other types of PDEs are also discussed.
قيم البحث
اقرأ أيضاً
Preparation of Gibbs distributions is an important task for quantum computation. It is a necessary first step in some types of quantum simulations and further is essential for quantum algorithms such as quantum Boltzmann training. Despite this, most
methods for preparing thermal states are impractical to implement on near-term quantum computers because of the memory overheads required. Here we present a variational approach to preparing Gibbs states that is based on minimizing the free energy of a quantum system. The key insight that makes this practical is the use of Fourier series approximations to the logarithm that allows the entropy component of the free-energy to be estimated through a sequence of simpler measurements that can be combined together using classical post processing. We further show that this approach is efficient for generating high-temperature Gibbs states, within constant error, if the initial guess for the variational parameters for the programmable quantum circuit are sufficiently close to a global optima. Finally, we examine the procedure numerically and show the viability of our approach for five-qubit Hamiltonians using Trotterized adiabatic state preparation as an ansatz.
The optimization of circuit parameters of variational quantum algorithms such as the variational quantum eigensolver (VQE) or the quantum approximate optimization algorithm (QAOA) is a key challenge for the practical deployment of near-term quantum c
omputing algorithms. Here, we develop a hybrid quantum/classical optimization procedure inspired by the Jacobi diagonalization algorithm for classical eigendecomposition, and combined with Anderson acceleration. In the first stage, analytical tomography fittings are performed for a local cluster of circuit parameters via sampling of the observable objective function at quadrature points in the circuit angles. Classical optimization is used to determine the optimal circuit parameters within the cluster, with the other circuit parameters frozen. Different clusters of circuit parameters are then optimized in sweeps, leading to a monotonically-convergent fixed-point procedure. In the second stage, the iterative history of the fixed-point Jacobi procedure is used to accelerate the convergence by applying Anderson acceleration/Pulays direct inversion of the iterative subspace (DIIS). This Jacobi+Anderson method is numerically tested using a quantum circuit simulator (without noise) for a representative test case from the multistate, contracted variant of the variational quantum eigensolver (MC-VQE), and is found to be competitive with and often faster than Powells method and L-BFGS.
We propose a neural-network variational quantum algorithm to simulate the time evolution of quantum many-body systems. Based on a modified restricted Boltzmann machine (RBM) wavefunction ansatz, the proposed algorithm can be efficiently implemented i
n near-term quantum computers with low measurement cost. Using a qubit recycling strategy, only one ancilla qubit is required to represent all the hidden spins in an RBM architecture. The variational algorithm is extended to open quantum systems by employing a stochastic Schrodinger equation approach. Numerical simulations of spin-lattice models demonstrate that our algorithm is capable of capturing the dynamics of closed and open quantum many-body systems with high accuracy without suffering from the vanishing gradient (or barren plateau) issue for the considered system sizes.
Rapid developments of quantum information technology show promising opportunities for simulating quantum field theory in near-term quantum devices. In this work, we formulate the theory of (time-dependent) variational quantum simulation, explicitly d
esigned for quantum simulation of quantum field theory. We develop hybrid quantum-classical algorithms for crucial ingredients in particle scattering experiments, including encoding, state preparation, and time evolution, with several numerical simulations to demonstrate our algorithms in the 1+1 dimensional $lambda phi^4$ quantum field theory. These algorithms could be understood as near-term analogs of the Jordan-Lee-Preskill algorithm, the basic algorithm for simulating quantum field theory using universal quantum devices. Our contribution also includes a bosonic version of the Unitary Coupled Cluster ansatz with physical interpretation in quantum field theory, a discussion about the subspace fidelity, a comparison among different bases in the 1+1 dimensional $lambda phi^4$ theory, and the spectral crowding in the quantum field theory simulation.
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining multi-dimensional en
ergy surfaces for small molecules and a spin model. Our method solves related variational problems in parallel by exploiting the global nature of Bayesian optimisation and sharing information between different optimisers. Parallelisation makes our method ideally suited to next generation of variational problems with many physical degrees of freedom. This addresses a key challenge in scaling-up quantum algorithms towards demonstrating quantum advantage for problems of real-world interest.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
