Related papers: Average-case Speedup for Product Formulas
This article proposes a formalism which unifies Hamiltonian simulation techniques from different fields. This formalism leads to a competitive method to construct the Hamiltonian simulation with a comprehensible, simple-to-implement circuit…
We recently introduced a method to approximate functions of Hermitian Matrix Product Operators or Tensor Trains that are of the form $\mathsf{Tr} f(A)$. Functions of this type occur in several applications, most notably in quantum physics.…
The simulation of adiabatic evolution has deep connections with Adiabatic Quantum Computation, the Quantum Approximate Optimization Algorithm and adiabatic state preparation. Here we address the error analysis problem in quantum simulation…
Quantum computers offer the potential to efficiently simulate the dynamics of quantum systems, a task whose difficulty scales exponentially with system size on classical devices. To assess the potential for near-term quantum computers to…
A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography.…
Digital quantum simulators provide a diversified tool for solving the evolution of quantum systems with complicated Hamiltonians and hold great potential for a wide range of applications. Although much attention is paid to the unitary…
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…
Quantum computation with Trotter product formulae is straightforward and requires little overhead in terms of logical qubits. The choice of the orbital basis significantly affects circuit depth, with localised orbitals yielding lowest…
Despite its simplicity and strong theoretical guarantees, adiabatic state preparation has received considerably less interest than variational approaches for the preparation of low-energy electronic structure states. Two major reasons for…
Accurate simulations of vibrational molecular spectra are expensive on conventional computers. Compared to the electronic structure problem, the vibrational structure problem with quantum computers is less investigated. In this work we…
A primary objective of quantum computation is to efficiently simulate quantum physics. Scientifically and technologically important quantum Hamiltonians include those with spin-$s$, vibrational, photonic, and other bosonic degrees of…
Randomized compilation protocols have recently attracted attention as alternatives to traditional deterministic Trotter-Suzuki methods, potentially reducing circuit depth and resource overhead. These protocols determine gate application…
A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schr\"odinger's quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in…
We derive higher-order error bounds with small prefactors for a general Trotter product formula, generalizing a result of Childs et al. [Phys. Rev. X 11, 011020 (2021)]. We then apply these bounds to the real-time quantum time evolution…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
Classical simulations of time-dependent quantum systems are widely used in quantum control research. In particular, these simulations are commonly used to host iterative optimal control algorithms. This is convenient for algorithms that are…
We simulate the time evolution of collective neutrino oscillations in two-flavor settings on a quantum computer. We explore the generalization of Trotter-Suzuki approximation to time-dependent Hamiltonian dynamics. The trotterization steps…
The most efficient known quantum circuits for preparing unitary coupled cluster states and applying Trotter steps of the arbitrary basis electronic structure Hamiltonian involve interleaved sequences of fermionic Gaussian circuits and Ising…
Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required…
We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors…