相关论文: Projective purification of correlated reduced dens…

Classical shadow tomography offers a scalable route to estimating properties of quantum states, but the resulting reduced density matrices (RDMs) often violate constraints that ensure they represent $N$-electron states -- known as…

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schr\"odinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based…

The N-representability problem for reduced density matrices remains a fundamental challenge in electronic structure theory. Following our previous work that employs a unitary-evolution algorithm based on an adaptive derivative-assembled…

We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…

Reduced density matrices are central to describing observables in many-body quantum systems. In electronic structure theory, the two-particle reduced density matrix (2-RDM) suffices to determine the energy and other key properties. Recent…

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body…

The reduced density matrix (RDM) is crucial in quantum many-body systems for understanding physical properties, including all local physical quantity information. This study aims to minimize various error constraints that causes challenges…

The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a…

Embedding calculations that find approximate solutions to the Schr\"{o}dinger equation for large molecules and realistic solids are performed commonly in a three step procedure involving (i) construction of a model system with effective…

We propose and analyze a method for improving quantum chemical energy calculations on a quantum computer impaired by decoherence and shot noise. The error mitigation approach relies on the fact that the one- and two-particle reduced density…

Machine learning is actively being explored for its potential to design, validate, and even hybridize with near-term quantum devices. A central question is whether neural networks can provide a tractable representation of a given quantum…

In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly…

An implicit purification scheme is proposed for calculation of the temperature-dependent, grand canonical single-particle density matrix, given as a Fermi operator expansion in terms of the Hamiltonian. The computational complexity is shown…

Fermionic reduced density matrices summarize the key observables in fermionic systems. In electronic systems, the two-particle reduced density matrix (2-RDM) is sufficient to determine the energy and most physical observables of interest.…

We present a family of algorithms for the numerical approximation of the Schr\"odinger equation with potential concentrated at a finite set of points. Our methods belong to the so-called fast and oblivious convolution quadrature algorithms.…

It is virtually impossible to directly solve the Schr\"odinger equation for a many-electron wave function due to the exponential growth in degrees of freedom with increasing particle number. The two-body reduced density matrix (2-RDM)…

Many-body wavefunctions usually lie in high-dimensional Hilbert spaces. However, physically relevant states, i.e, the eigenstates of the Schr\"odinger equation are rare. For many-body systems involving only pairwise interactions, these…

Reduced density matrices (RDMs) are fundamental in quantum information processing, allowing the computation of local observables, such as energy and correlation functions, without the exponential complexity of fully characterizing quantum…

We present a constructive solution to the N-representability problem---a full characterization of the conditions for constraining the two-electron reduced density matrix (2-RDM) to represent an N-electron density matrix. Previously known…

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…