Related papers: Scalable semidefinite programming approach to vari…
We present a symmetry-adapted extension of sample-based quantum diagonalization (SQD) that rigorously embeds space-group symmetry into the many-body subspace sampled by quantum hardware. The method is benchmarked on the two-leg ladder…
We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data varies polynomially with time. We show that under a strict…
We present an efficient approach to simulate real-time quantum dynamics using Projected Variational Quantum Dynamics (PVQD), where the computational cost is reduced by strategically optimizing only a subset of the variational parameters at…
Applying the method of moments to the chemical master equation (CME) appearing in stochastic chemical kinetics often leads to the so-called closure problem. Recently, several authors showed that this problem can be partially overcome using…
In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding…
Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…
Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules,…
Brand\~ao and Svore very recently gave quantum algorithms for approximately solving semidefinite programs, which in some regimes are faster than the best-possible classical algorithms in terms of the dimension $n$ of the problem and the…
We study the ternary quadratic problem (TQP), a quadratic optimization problem with linear constraints where the variables take values in $\{0, \pm 1\}$. While semidefinite programming (SDP) techniques are well established for $\{0,1\}$-…
This work is concerned with the issue of applications of the semi-definite programming (SDP) in the field of quantum information science. Our results of the analysis of certain quantum information protocols using this optimization technique…
We present a novel multi-scale embedding scheme that links conventional QM/MM embedding and bootstrap embedding (BE) to allow simulations of large chemical systems on limited quantum devices. We also propose a mixed-basis BE scheme that…
Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021]…
One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
HDSDP is a numerical software solving the semidefinite programming problems. The main framework of HDSDP resembles the dual-scaling interior point solver DSDP [BY2008] and several new features, including a dual method based on the…
Power flow feasibility assessment is computationally challenging for unbalanced three-phase distribution networks. This paper develops a vectorized semidefinite program (SDP) based on the bus injection model (BIM) and reformulates its dual…
A quantitative description of the excited electronic states of point defects and impurities is crucial for understanding materials properties, and possible applications of defects in quantum technologies. This is a considerable challenge…
Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often…
The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge…
In this paper, we present a stabilized sequential quadratic semidefinite programming (SQSDP) method for nonlinear semidefinite programming (NSDP) problems and prove its local convergence. The stabilized SQSDP method is originally developed…