Related papers: Understanding Quantum Imaginary Time Evolution and…
Simulation of quantum systems is notoriously challenging for classical computers, while quantum hardware is naturally well-suited for this task. However, the imperfections of contemporary quantum systems poses a considerable challenge in…
This paper presents a hybrid quantum-classical approach to prime factorization. The proposed algorithm is based on the Variational Quantum Eigensolver (VQE), which employs a classical optimizer to find the ground state of a given…
Optimization problems in finance, physics and computer science are typically very hard to tackle in classical computing and quantum computing could help speed up computations and provide efficient methods for tackling large problems.…
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…
For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution…
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…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
We introduce evolved quantum Boltzmann machines as a variational ansatz for quantum optimization and learning tasks. Given two parameterized Hamiltonians $G(\theta)$ and $H(\phi)$, an evolved quantum Boltzmann machine consists of preparing…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
Many optimally scaling quantum simulation algorithms employ controlled time evolution of the Hamiltonian, which is typically the major bottleneck for their efficient implementation. This work establishes a compression protocol for encoding…
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…
In this paper we develop a quantum algorithm to realize finite temperature simulation on a quantum computer. As quantum computers use real-time evolution we did not use the imaginary time methods popular on classical algorithms. Instead, we…
The study of quantum systems evolving from initial states to distinguishable, orthogonal final states is important for information processing applications such as quantum computing and quantum metrology. However, for most unitary evolutions…
Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which…
The imaginary-time evolution method is widely known to be efficient for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of…
Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit…