Related papers: Trotterization is substantially efficient for low-…
Trotter decomposition provides a simple approach to simulating open quantum systems by decomposing the Lindbladian into a sum of individual terms. While it is established that Trotter errors in Hamiltonian simulation depend on nested…
Product formulas are one of the main approaches for quantum simulation of the Hamiltonian dynamics of a quantum system. Their implementation cost is computed based on error bounds which are often pessimistic, resulting in overestimating the…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
In quantum computing, Trotter estimates are critical for enabling efficient simulation of quantum systems and quantum dynamics, help implement complex quantum algorithms, and provide a systematic way to control approximate errors. In this…
The thermodynamic cost of resetting an arbitrary initial state to a particular desired state is lower bounded by Landauer's bound. However, here we demonstrate that this lower bound is necessarily unachievable for nearly every initial…
Adiabatic quantum computing is a general framework for preparing eigenstates of Hamiltonians on quantum devices. However, its digital implementation requires an efficient Hamiltonian simulation subroutine, which may introduce extra…
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…
This paper improves and demonstrates the usefulness of the first quantized plane-wave algorithms for the quantum simulation of electronic structure, developed by Babbush et al. and Su et al. We describe the first quantum algorithm for first…
As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the…
In quantum computing, the efficient optimization of Pauli string decompositions is a crucial aspect for the compilation of quantum circuits for many applications, such as chemistry simulations and quantum machine learning. In this paper, we…
A multi-product formula (MPF) is a promising approach for Hamiltonian simulation efficiently both in the system size $N$ and the inverse allowable error $1/\varepsilon$ by combining Trotterization and the linear combination of unitaries…
Trotter product formulas are a natural and powerful approach to perform quantum simulation. However, the error analysis of product formulas is challenging, and their cost is often overestimated. It is established that Trotter error can be…
Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost…
Deep-circuit quantum computation, like Shor's algorithm, is undermined by error accumulation, and near-future quantum techniques are far from adequate for full-fledged quantum error correction. Instead of resorting to shallow-circuit…
Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum…
The aim of this work is to study the physical properties of a one-way quantum computer in an effective low-energy cluster state. We calculate the optimal working conditions as a function of the temperature and of the system parameters. The…
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)…
Simulation of quantum many-body systems is a promising application of quantum computers. However, implementing the time-evolution operator as a quantum circuit efficiently on near-term devices with limited resources is challenging. Standard…
The study of real time dynamics of nuclear systems is of great importance to provide theoretical predictions of cross sections relevant for both terrestrial experiments as well as applications in astrophysics. First principles simulations…
We propose an analysis of the Quantum Phase Estimation (QPE) algorithm applied to many-electron systems by investigating its free parameters such as the time step, number of phase qubits, initial state preparation, number of measurement…