Related papers: A Generalized Circuit for the Hamiltonian Dynamics…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
As established in the seminal work by Berry et al.[1], expanding the time evolution operator using truncated Taylor series (up to some order $K$) makes a good candidate for simulating Hamiltonian dynamics. Here, we adapt the method but…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
In this paper a storage method and a context-aware circuit simulation idea are presented for the sum of block diagonal matrices. Using the design technique for a generalized circuit for the Hamiltonian dynamics through the truncated series,…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
Simulating the dynamics of complex quantum systems is a central application of quantum devices. Here, we propose leveraging the power of measurements to simulate short-time quantum dynamics of physically prepared quantum states in classical…
We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system…
We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture,…
We present a quantum computational framework using Hamiltonian Truncation (HT) for simulating real-time scattering processes in $(1+1)$-dimensional scalar $\phi^4$ theory. Unlike traditional lattice discretisation methods, HT approximates…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…
We describe a simple method for simulating time-independent Hamiltonian $H$ that could be decomposed as $H = \sum_{i=1}^m H_i$ where each $H_i$ can be efficiently simulated. Approaches relying on product formula generally work by splitting…
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…
Quantum computers can efficiently simulate highly entangled quantum systems, offering a solution to challenges facing classical simulation of Quantum Field Theories (QFTs). This paper presents an alternative to traditional methods for…
We develop circuit implementations for digital-level quantum Hamiltonian dynamics simulation algorithms suitable for implementation on a reconfigurable quantum computer, such as trapped ions. Our focus is on the co-design of a problem, its…
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian…