Related papers: Lindbladian Simulation with Commutator Bounds
Quantum simulation has shown great potential in many fields due to its powerful computational capabilities. However, the limited fidelity can lead to a severe limitation on the number of gate operations, which requires us to find optimized…
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…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
We demonstrate that the dynamics of an open quantum system can be calculated efficiently and with predefined error, provided a basis exists in which the system-environment interactions are local and hence obey the Lieb-Robinson bound. We…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
We make progress on an interesting problem on the boundedness of maximal modulations of the Hilbert transform along the parabola. Namely, if we consider the multiplier arising from it and restrict it to lines, we prove uniform $L^p$ bounds…
Estimating transition rates in open quantum systems is hampered by computing-resource demands that grow rapidly with system size. We present a quantum-simulation framework that enables efficient estimation by recasting the transition rate,…
We examine the effectiveness of Lindblad master equation in capturing the short-time dynamics of entanglement and purity in open quantum systems. Focusing on two interacting two-level systems interacting with a larger environment, we…
The Lindblad equation, as one approach to open quantum systems, describes the density matrix of a particle or a chain of interacting particles, which are in contact with a thermal bath. Still, it is not fully understood yet, how arbitrary…
A higher-order Suzuki-Trotter decomposition or Trotterization can be exploited to mitigate the Trotter error in digital quantum simulation. This work revisits the second-order symmetric Trotterization in terms of the Trotter error, where…
Efficient simulation of the semiclassical Schr\"odinger equation has garnered significant attention in the numerical analysis community. While controlling the error in the unitary evolution or the wavefunction typically requires the time…
The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation…
The Lindblad master equation is a foundational tool for modeling the dynamics of open quantum systems. As its use has extended far beyond its original domain, the boundaries of its validity have grown opaque. In particular, the rise of new…
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…
Hamiltonian simulation represents an important module in a large class of quantum algorithms and simulations such as quantum machine learning, quantum linear algebra methods, and modeling for physics, material science and chemistry. One of…
Recent work has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian $H$ for a given simulation problem into subsets $A$ and $B$ such that $H=A+B$, where the terms in $A$ are simulated with a…
An important class of physical systems that are of interest in practice are input-output open quantum systems that can be described by quantum stochastic differential equations and defined on an infinite-dimensional underlying Hilbert…
We present a novel, computationally efficient approach to accelerate quantum optimal control calculations of large multi-qubit systems used in a variety of quantum computing applications. By leveraging the intrinsic symmetry of finite…
We develop a new method for the construction of one-dimensional integrable Lindblad systems, which describe quantum many body models in contact with a Markovian environment. We find several new models with interesting features, such as…
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…