Related papers: A probabilistic imaginary-time evolution quantum a…
Variational Quantum Imaginary Time Evolution (VQITE) is a leading technique for ground state preparation on quantum computers. A significant computational challenge of VQITE is the determination of the quantum geometric tensor. We show that…
A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. A direct unitary block encoding of the explicit time-marching operator is constructed, resulting in the intrinsic…
Quantum phase estimation (QPE) plays a pivotal role in many quantum algorithms, offering provable speedups in applications such as Shor's factoring algorithm. While fault-tolerant quantum algorithms for combinatorial and Hamiltonian…
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through…
We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient flow on the special unitary group. This…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
We propose a quantum algorithm for the linear advection-diffusion equation (ADE) Lattice-Boltzmann method (LBM) that leverages dynamic circuits. Dynamic quantum circuits allow for an optimized collision-operator quantum algorithm,…
We propose a nonvariational scheme for geometry optimization of molecules for the first-quantized eigensolver, a recently proposed framework for quantum chemistry using the probabilistic imaginary-time evolution (PITE) on a quantum…
We propose a hybrid quantum-classical algorithm for solving QUBO problems using an Imaginary Time Evolution-Mimicking Circuit (ITEMC). The circuit parameters are optimized to closely mimic imaginary time evolution, using only single- and…
We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium…
Imaginary time evolution is a powerful tool applied in quantum physics, while existing classical algorithms for simulating imaginary time evolution suffer high computational complexity as the quantum systems become larger and more complex.…
The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional quantum lattice systems in the thermodynamic limit.…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
The variational quantum imaginary time evolution algorithm is efficient in finding the ground state of a quantum Hamiltonian. This algorithm involves solving a system of linear equations in a classical computer and the solution is then used…
Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems, and the heart of a number of numerical methods that have been used with great success in quantum chemistry, condensed matter and…
Computational modeling of cellular systems, where reactants are governed by biochemical equations and physical representations, requires extensive classical computing resources. These limitations significantly constrain the system size and…
We develop a hybrid classical-quantum algorithm to solve a type of linear reaction-diffusion equation, the neutron diffusion (generalized) k-eigenvalue problem that establishes nuclear criticality. The algorithm handles an equation with…
This article introduces a novel framework for developing quantum algorithms for the Lattice Boltzmann Method (LBM) applied to the advection-diffusion equation. We formulate the collision-streaming evolution of the LBM as a compact…