Related papers: Parallel Quantum Algorithm for Hamiltonian Simulat…
Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian…
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to…
Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing…
Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…
We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in…
Hamiltonian simulation is a key workload in quantum computing, enabling the study of complex quantum systems and serving as a critical tool for classical verification of quantum devices. However, it is computationally challenging because…
We propose a Quantum Machine Learning (QML) framework that leverages quantum parallelism to process entire training datasets in a single quantum operation, addressing the computational bottleneck of sequential data processing in both…
Analog quantum simulation offers a hardware-specific approach to studying quantum dynamics, but mapping a model Hamiltonian onto the available device parameters requires matching the hardware dynamics. We introduce a paradigm for quantum…
Quantum simulation is a popular application of quantum computing, but its practical realization is hindered by the technical limitations of current devices. In this work, we focus on preprocessing Hamiltonians before Trotterization to…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
Classical simulation of real-space quantum dynamics is challenging due to the exponential scaling of computational cost with system dimensions. Quantum computer offers the potential to simulate quantum dynamics with polynomial complexity;…
A Quantum Computer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantum computer threatens the security of public key encryption systems because these systems rely on the fact that…
We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation…
In this tutorial, which contains some original results, we bridge the fields of quantum computing algorithms, conservation laws, and many-body quantum systems by examining three algorithms for searching an unordered database of size $N$…
It is shown that a quantum controlled-NOT gate simultaneously performs the logical functions of three distinct conditional local operations. Each of these local operations can be verified by measuring a corresponding truth table of four…
We present a novel application of the HHL (Harrow-Hassidim-Lloyd) algorithm -- a quantum algorithm solving systems of linear equations -- in solving an open problem about quantum random walks, namely computing hitting (or absorption)…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
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…
Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including…