Related papers: Quantum Hamiltonian Descent
Quantum algorithms on the noisy intermediate-scale quantum (NISQ) devices are expected to simulate quantum systems that are classically intractable to demonstrate quantum advantages. However, the non-negligible gate error on the NISQ…
A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
Transport phenomena play a key role in a variety of application domains, and efficient simulation of these dynamics remains an outstanding challenge. While quantum computers offer potential for significant speedups, existing algorithms…
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal…
The local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even…
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine…
Logistic regression (LR) is an important machine learning model for classification, with wide applications in text classification, image analysis and medicine diagnosis, etc. However, training LR generally entails an iterative gradient…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
Quantum annealing is typically regarded as a tool for combinatorial optimization, but its coherent dynamics also offer potential for machine learning. We present a model that encodes classical data into an Ising Hamiltonian, evolves it on a…
Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to implement fault-tolerant quantum algorithms for…
Quantum annealing has emerged as a promising approach for solving NP-hard optimization problems, leveraging quantum phenomena such as quantum tunneling to navigate complex energy landscapes. However, the extent to which quantum tunneling…
Achieving a provable exponential quantum speedup for an important machine learning task has been a central research goal since the seminal HHL quantum algorithm for solving linear systems and the subsequent quantum recommender systems…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
Quantum computing promises to solve problems beyond the reach of classical computers, but today's quantum hardware is error-prone and much slower than classical hardware. Every quantum operation is costly, making it crucial to minimize…
Quantum machine learning and optimization are exciting new areas that have been brought forward by the breakthrough quantum algorithm of Harrow, Hassidim and Lloyd for solving systems of linear equations. The utility of {classical} linear…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
The demand for classical-quantum hybrid algorithms to solve large-scale combinatorial optimization problems using quantum annealing (QA) has increased. One approach involves obtaining an approximate solution using classical algorithms and…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…