Related papers: Efficient geometric integrators for nonadiabatic q…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of a transport equation with additional growth and non-local…
We present a systematic perturbative construction of the most general metric operator (and positive-definite inner product) for quasi-Hermitian Hamiltonians of the standard form, H= p^2/2 + v(x), in one dimension. We show that this problem…
The numerical integration of the Benjamin and Benjamin--Ono equations are considered. They are non-local partial differential equations involving the Hilbert transform, and due to this, so far quite few structure-preserving integrators have…
Digitized adiabatic quantum factorization is a hybrid algorithm that exploits the advantage of digitized quantum computers to implement efficient adiabatic algorithms for factorization through gate decompositions of analog evolutions. In…
Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
Quantum annealing has recently been used to determine the Ramsey numbers R(m,2) for 3 < m < 9 and R(3,3) [Bian et al. (2013) PRL 111, 130505]. This was greatly celebrated as the largest experimental implementation of an adiabatic evolution…
We introduce high-order dynamical decoupling strategies for open system adiabatic quantum computation. Our numerical results demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding…
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…
Combinatorial optimization problems are crucial for widespread applications but remain difficult to solve on a large scale with conventional hardware. Novel optical platforms, known as coherent or photonic Ising machines, are attracting…
While it is well-known that every nearly-periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy…
We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. This strengthens the superpolynomial separation recently proved by…
Nonadiabatic holonomic quantum computation (NHQC) is implemented by fast evolution processes in a geometric way to withstand local noises. However, recent works of implementing NHQC are sensitive to the systematic noise and error. Here, we…
We introduce the prodiabatic elimination, a powerful approximation technique that systematically extends the adiabatic elimination of fast degrees of freedom in light-matter coupled systems. Through a controlled expansion of operators, the…
Adiabatic elimination is a perturbative model reduction technique based on timescale separation and often used to simplify the description of composite quantum systems. We here analyze a quantum experiment where the perturbative expansion…
We consider the geometric numerical integration of Hamiltonian systems subject to both equality and "hard" inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. We…
We review techniques for simulating fully quantum nonadiabatic dynamics using the frozen-width moving Gaussian basis functions to represent the nuclear wavefunction. A choice of these basis functions is primarily motivated by the idea of…
We propose a high order numerical decomposition of exponentials of hermitean operators in terms of a product of exponentials of simple terms, following an idea which has been pioneered by M. Suzuki, however implementing it for complex…
Efficient control schemes that enable fast, high-fidelity operations are essential for any practical quantum computation. However, current optimization protocols are intractable due to stringent requirements imposed by the microscopic…