Related papers: Determining the N-representability of a reduced de…
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…
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…
Here we present a many-body theory based on a solution of the $N$-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an…
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…
Classical shadow tomography provides a randomized scheme for approximating the quantum state and its properties at reduced computational cost with applications in quantum computing. In this Letter we present an algorithm for realizing fewer…
In the search for accurate approximate solutions of the many-body Schr\"odinger equation, reduced density matrices play an important role, as they allow to formulate approximate methods with polynomial scaling in the number of particles.…
The $N$-representability problem places fundamental constraints on reduced density matrices (RDMs) that originate from physical many-fermion quantum states. Motivated by recent developments in functional theories, we introduce a hierarchy…
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…
The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges…
This work discusses the main analogies and differences between the deterministic approach underlying most cosmological N-body simulations and the probabilistic interpretation of the problem that is often considered in mathematics and…
It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While…
A previous study of diatomic molecules revealed that variational second-order density matrix theory has serious problems in the dissociation limit when the N-representability is imposed at the level of the usual two-index (P, Q, G) or even…
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)…
Representability determines when a two-particle reduced density matrix (2-RDM) corresponds to a physical quantum state, enabling many-particle quantum calculations with 2-RDMs rather than the wave function. In this Letter, we present a…
Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence,connectivity and gate…
We recently presented a constructive solution to the N-representability problem of the two-electron reduced density matrix (2-RDM)---a systematic approach to constructing complete conditions to ensure that the 2-RDM represents a realistic…
The quantum many-body problem can be rephrased as a variational determination of the two-body reduced density matrix, subject to a set of N-representability constraints. The mathematical problem has the form of a semidefinite program. We…
Variational calculation of the ground state energy and its properties using the second-order reduced density matrix (2-RDM) is a promising approach for quantum chemistry. A major obstacle with this approach is that the $N$-representability…
We describe a new method (HOP) for identifying groups of particles in N-body simulations. Having assigned to every particle an estimate of its local density, we associate each particle with the densest of the N_hop particles nearest to it.…
Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most…