Related papers: Trotterization in Quantum Theory
Quantum simulations of strongly interacting fermionic systems, such as those described by the Hubbard model, are promising candidates for useful early fault-tolerant quantum computing applications. This paper presents Tile Trotterization, a…
The product formula, commonly known as Trotter decomposition, is a central tool for digital quantum simulation, whose performance depends critically on how the Hamiltonian is partitioned into tractable blocks. Standard decompositions…
A fundamental challenge in digital quantum simulation (DQS) is the control of inherent errors. These appear when discretizing the time evolution generated by the Hamiltonian of a quantum many-body system as a sequence of quantum gates,…
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…
The transactional interpretation of quantum mechanics, which uses retarded and advanced solutions of the Schrodinger equation and its complex conjugate, offers an original way to visualize and understand quantum processes. After a brief…
Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We…
Trotterization is a standard approach for simulating quantum time evolution on quantum computers, where the Hamiltonian is split into local terms and each term is applied in sequence. The order of these terms affects the fidelity of the…
Fault-tolerant quantum computing is a promising tool for simulating molecules and materials, but frequently-considered applications require substantial resources, and the gap between hardware capabilities and requirements remains…
The simulation of molecules is a widely anticipated application of quantum computers. However, recent studies \cite{WBCH13a,HWBT14a} have cast a shadow on this hope by revealing that the complexity in gate count of such simulations…
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.…
We address a learning-based quantum error mitigation method, which utilizes deep neural network applied at the postprocessing stage, and study its performance in presence of different types of quantum noises. We concentrate on the…
We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from…
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…
The descripition of in a Hermitian setting seemingly nonlocal and nonperturbative phenomena like confinement or superconductivity is most conveniently performed by generalizing quantum theory to a non-Hermitian regime where these phenomena…
The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $\mathcal{O}(N^4)$ gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes…
Trotterization is a technique that allows one to approximate a time evolution of a Hamiltonian by repeatedly evolving the individual terms of the Hamiltonian one-at-a-time for small time durations. Bounds on the error of this approximation…
We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations by a factor of up to…
We give a detailed exposition of the "vectorized" notation for dealing with quantum operations. This notation is used to highlight the relationships between representations of completely-positive dynamics. Vectorization considerably…
We consider a Trotter-type-product formula for approximating the solution of a linear abstract Cauchy problem (given by a strongly continuous semigroup), where the underlying Banach space is a product of two spaces. In contrast to the…
The potential of employing higher orders of the Trotter-Suzuki decomposition of the evolution operator for more effective simulations of quantum systems on a noisy quantum computer is explored. By examining the transverse-field Ising model…