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Experimentally realizable quantum computers are rapidly approaching the threshold of quantum supremacy. Quantum Hamiltonian simulation promises to be one of the first practical applications for which such a device could demonstrate an…
Quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen…
Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…
Computing the electronic structure of molecules with high precision is a central challenge in the field of quantum chemistry. Despite the enormous success of approximate methods, tackling this problem exactly with conventional computers is…
A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we…
Due to the wide range of technical applications of actinide elements, a thorough understanding of their electronic structure could complement technological improvements in many different areas. Quantum computing could greatly aid in this…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
Quantum machine learning algorithms, the extensions of machine learning to quantum regimes, are believed to be more powerful as they leverage the power of quantum properties. Quantum machine learning methods have been employed to solve…
Quantum computing has recently exhibited great potentials in predicting chemical properties for various applications in drug discovery, material design, and catalyst optimization. Progress has been made in simulating small molecules, such…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Quantum computing holds promise for revolutionizing computational chemistry simulations, particularly in drug discovery. However, current quantum hardware is limited by noise and scale, necessitating bridging technologies. This study…
Quantum computing is a hotspot technology for its potential to accelerate specific applications by exploiting quantum parallelism. However, current physical quantum computers are limited to a relatively small scale, simulators based on…
A key objective of computational solid state physics is to predict electronic properties of periodic materials. However, electronic structure simulations based on density functional theory fail to predict experimental results if…
Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE)…
Many applications of quantum simulation require to prepare and then characterize quantum states by performing an efficient partial tomography to estimate observables corresponding to $k$-body reduced density matrices ($k$-RDMs). For…
Simulating quantum systems using classical computing equipment has been a significant research focus. This work demonstrates that circuits as large and complex as the random circuit sampling (RCS) circuits published as a part of Google's…
We present a classical algorithm for simulating universal quantum circuits composed of "free" nearest-neighbour matchgates or equivalently fermionic-linear-optical (FLO) gates, and "resourceful" non-Gaussian gates. We achieve the promotion…
Efficient methods for the simulation of quantum circuits on classic computers are crucial for their analysis due to the exponential growth of the problem size with the number of qubits. Here we study lumping methods based on bisimulation,…
As research on building scalable quantum computers advances, it is important to be able to certify their correctness. Due to the exponential hardness of classically simulating quantum computation, straight-forward verification through…
One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems…