Related papers: Optimal Trotterization in universal quantum simula…
Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics, and numerical simulations. However, the Trotter error's dependency on the input state and its application to unbounded…
Hamiltonian simulation is one of the most promising applications of quantum computers, and the product formula is one of the most important methods for this purpose. Previous related work has mainly focused on the worst$-$case or…
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…
We present an empirical analysis of the scaling of the minimal quantum circuit depth required for a variational quantum simulation (VQS) method to obtain a solution to the time evolution of a quantum system within a predefined error…
As first proposed for the adiabatic quantum information processing by Wu, Byrd and Lidar [ Phys. Rev. Lett. 89, 057904 (2002)], the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the…
One of the most promising applications of near-term quantum computing is the simulation of quantum systems, a classically intractable task. Quantum simulation requires computationally expensive matrix exponentiation; Trotter-Suzuki…
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…
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…
The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum…
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…
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as…
When simulating the time evolution of quantum many-body systems on a digital quantum computer, one faces the challenges of quantum noise and of the Trotter error due to time discretization. The Trotter error in integrable spin chains can be…
Variational quantum algorithms have become the de facto model for current quantum computations. A prominent example of such algorithms -- the quantum approximate optimization algorithm (QAOA) -- was originally designed for combinatorial…
The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation…
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…
Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for…
Understanding the intricate quantum spin dynamics of radical pair reactions is crucial for unraveling the underlying nature of chemical processes across diverse scientific domains. In this work, we leverage Trotterization to map coherent…
Digital quantum simulations offer exciting perspectives for the study of fermionic systems such as molecules or lattice models. However, with quantum error correction still being out of reach with present-day technology, a non-vanishing…
Quantum computers open the possibility of performing real-time calculations for quantum field theory scattering processes. We propose to use an index averaging the absolute value of the difference between the accurately calculated Trotter…