Related papers: Preconditioned Multivariate Quantum Solution Extra…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
Quantum state preparation is an important class of quantum algorithms that is employed as a black-box subroutine in many algorithms, or used by itself to generate arbitrary probability distributions. We present a novel state preparation…
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone…
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting…
We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
Quantum chemistry is among the most promising applications of quantum computing, offering the potential to solve complex electronic structure problems more efficiently than classical approaches. A critical component of any quantum algorithm…
Quantum Max Cut (QMC), also known as the quantum anti-ferromagnetic Heisenberg model, is a QMA-complete problem relevant to quantum many-body physics and computer science. Semidefinite programming relaxations have been fruitful in designing…
Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…
We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifolds (PLoM). It involves solving the spectral problem of the high-dimensional Fokker-Planck (FKP) operator,…
Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…
Quantum computing hardware is advancing at a rapid pace, yet the lack of high-level programming abstractions remains a serious bottleneck in the development of new applications. Widely used frameworks still rely on gate-level circuit…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results…
Quantum error correction (QEC) is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these…