Related papers: Exponentially More Precise Quantum Simulation of F…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
Quantum chemistry provides a target for quantum simulation of considerable scientific interest and industrial importance. The majority of algorithms to date have been based on a second-quantized representation of the electronic structure…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
Compact representations of fermionic Hamiltonians are necessary to perform calculations on quantum computers that lack error-correction. A fermionic system is typically defined within a subspace of fixed particle number and spin while…
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…
We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
We present a quantum algorithm for simulating quantum chemistry with gate complexity $\tilde{O}(N^{1/3} \eta^{8/3})$ where $\eta$ is the number of electrons and $N$ is the number of plane wave orbitals. In comparison, the most efficient…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
In this work, we present a quantum algorithm for direct first-principles simulation of electron-nuclear dynamics on a first-quantized real-space grid. Our algorithm achieves best-in-class efficiency for block-encoding the…
Performing large-scale, accurate quantum simulations of many-fermion systems is a central challenge in quantum science, with applications in chemistry, materials, and high-energy physics. Despite significant progress, realizing generic…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
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…
We investigate the quantum algorithm of Babbush et al. (arXiv:2303.13012v3) for simulating coupled harmonic oscillators, which promises exponential speedups over classical methods. Focusing on linearly connected oscillator chains, we bridge…
We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$-sparse Hamiltonian $H$…