Related papers: Hamiltonian simulation for hyperbolic partial diff…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…
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…
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
Simple constructions and protocols are demonstrated to allow the implementation of universal quantum computation on an arbitrarily large quantum system by controlling a fixed number of spins, vastly reducing the engineering requirements in…
Implementing variational quantum algorithms with noisy intermediate-scale quantum machines of up to a hundred qubits is nowadays considered as one of the most promising routes towards achieving a quantum practical advantage. In multiqubit…
Variational quantum eigensolver~(VQE) typically optimizes variational parameters in a quantum circuit to prepare eigenstates for a quantum system. Its applications to many problems may involve a group of Hamiltonians, e.g., Hamiltonian of a…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
Quantum phase estimation combined with Hamiltonian simulation is the most promising algorithmic framework to computing ground state energies on quantum computers. Its main computational overhead derives from the Hamiltonian simulation…
Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work, ultra-cold fermionic atoms have been proposed for these purposes by showing…
Digital quantum simulation on quantum systems require algorithms that can be implemented using finite quantum resources. Recent studies have demonstrated digital quantum simulation of open quantum systems on Noisy Intermediate-Scale Quantum…
We develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing…
Until high-fidelity quantum computers with a large number of qubits become widely available, classical simulation remains a vital tool for algorithm design, tuning, and validation. We present a simulator for the Quantum Approximate…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It…
From weather to neural networks, modeling is not only useful for understanding various phenomena, but also has a wide range of potential applications. Although nonlinear differential equations are extremely useful tools in modeling, their…