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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,…
We consider simulating an $n$-qubit Hamiltonian with nearest-neighbor interactions evolving for time $t$ on a quantum computer. We show that this simulation has gate complexity $(nt)^{1+o(1)}$ using product formulas, a straightforward…
The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of…
We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary time dynamics for infinite one-dimensional quantum lattice systems. This…
We consider a Trotter-type-product formula for approximating the solution of a linear abstract Cauchy problem (given by a strongly continuous semigroup), where the underlying Banach space is a product of two spaces. In contrast to the…
A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.
Universal quantum simulation may provide insights into those many-body systems that cannot be described classically, and that cannot be efficiently simulated with current technology. The Trotter formula, which decomposes a desired unitary…
The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly…
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…
Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We…
We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the method is illustrated in a variety of examples. Our main…
In analog and digital simulations of practically relevant quantum systems, the target dynamics can only be implemented approximately. The Trotter product formula is the most common approximation scheme as it is a generic method which allows…
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
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…
Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…
We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm…
We give a new method for proving the homomorphic property of a quantum stochastic ow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter…
Simulating the dynamic evolutions of physical and molecular systems in a quantum computer is of fundamental interest in many applications. Its implementation requires efficient quantum simulation algorithms. The Lie-Trotter-Suzuki…
Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models of High Energy Physics whose experimental realizations are either complicated or inaccessible with current technology.…
The product formula, commonly known as Trotter decomposition, is a central tool for digital quantum simulation, whose performance depends critically on how the Hamiltonian is partitioned into tractable blocks. Standard decompositions…