Related papers: Taming Trotter Errors with Quantum Resources
Operator scrambling, which governs the spread of quantum information in many-body systems, is a central concept in both condensed matter and high-energy physics. Accurately capturing the emergent properties of these systems remains a…
We establish tight connections between entanglement entropy and the approximation error in Trotter-Suzuki product formulas for Hamiltonian simulation. Product formulas remain the workhorse of quantum simulation on near-term devices, yet…
As noisy intermediate-scale quantum (NISQ) processors increase in size and complexity, their use as general purpose quantum simulators will rely on algorithms based on the Trotter-Suzuki expansion. We run quantum simulations on a small,…
Although the simulation of quantum chemistry is one of the most anticipated applications of quantum computing, the scaling of known upper bounds on the complexity of these algorithms is daunting. Prior work has bounded errors due to…
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…
Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…
Magic quantum states (non-stabilizer states) play a pivotal role in fault-tolerant quantum computation. Simultaneously, random resources have emerged as a key element in various randomized techniques within contemporary quantum science. In…
Identifying the boundary between classical and quantum computation is a central challenge in quantum information. In multi-qubit systems, entanglement and magic are the key resources underlying genuinely quantum behaviour. While…
Quantum simulation is a promising application of future quantum computers. Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. For an accurate product formula approximation,…
Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to 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…
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…
When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum…
A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general…
Recent studies have shown that Trotter errors are highly initial-state dependent and that standard upper bounds often substantially overestimate them. However, the mechanism underlying anomalously small Trotter errors and a systematic route…
Quantum computers can efficiently simulate many-body systems. As a widely used Hamiltonian simulation tool, the Trotter-Suzuki scheme splits the evolution into the number of Trotter steps $N$ and approximates the evolution of each step by a…
Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we…
Trotterization is the most common and convenient approximation method for Hamiltonian simulations on digital quantum computers, but estimating its error accurately is computationally difficult for large quantum systems. Here, we develop a…
The study of entanglement and magic properties in topologically frustrated systems suggests that, in the thermodynamic limit, these quantities decompose into two distinct contributions. One is determined by the specific nature of the model…
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…