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Product formula methods, particularly the second-order Suzuki decomposition, are an important tool for simulating quantum dynamics on quantum computers due to their simplicity and unitarity preservation. While higher-order schemes have been…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational algorithm for solving combinatorial optimization problems on near-term devices. However, as the number of layers in a QAOA circuit increases, which is…
In the Markov decision process model, policies are usually evaluated by expected cumulative rewards. As this decision criterion is not always suitable, we propose in this paper an algorithm for computing a policy optimal for the quantile…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising variational quantum algorithm for addressing NP hard combinatorial optimization problems. However, a significant limitation lies in optimizing its classical…
Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on…
The derivation of combined prefactored compact schemes for first and second order derivatives is described here, relying on the Fourier analysis of the original prefactored compact schemes. By this approach, the order of accuracy of the…
Qualitative numerical planning is classical planning extended with non-negative real variables that can be increased or decreased "qualitatively", i.e., by positive indeterminate amounts. While deterministic planning with numerical…
We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the Principle of Minimal Sensitivity can be…
Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments,…
Perturbative QCD results in the MSbar scheme can be dramatically improved by switching to a scheme that accounts for the dominant power law dependence on the factorization scale in the operator product expansion. We introduce the ``MSR…
The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the…
We describe a new scheme for optimizing many-electron trial wave functions by minimizing the unreweighted variance of the energy using stochastic integration and correlated-sampling techniques. The scheme is restricted to parameters that…
The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools together with key applications. For this,…
Perturbative gadgets are general techniques for reducing many-body spin interactions to two-body ones using perturbation theory. This allows for potential realization of effective many-body interactions using more physically viable two-body…
If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We…
The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth quantum circuit to produce a parameter dependent state. For a given combinatorial optimization problem instance, the quantum expectation of the associated cost…
Quantum computers promise to solve important problems faster than conventional computers. However, unleashing this power has been challenging. In particular, design automation runs into (1) the probabilistic nature of quantum computation…
The factorization theorems of quantum chromodynamics (QCD) apply equally well to most simple quantum field theories that require renormalization but where direct calculations are much more straightforward. Working with these simpler…