Linus Pauling contributions span structural biology, chemistry in its broadest definition, quantum mechanical theory, valence bond theory, and even nuclear physics. A principal tool developed and used by Pauling is Xray, and electron, diffraction. One possible extension of the Pauling oeuvre could be the marriage of crystallography and quantum mechanics. Such an effort dates back to the sixties and has now flourished into an entire subfield termed quantum crystallography. Quantum crystallography could be achieved through the application of Clinton equations to yield N-representable density matrices consistent with experimental data. The implementation of the Clinton equations is qualitatively different for small and for large systems. For a small system, quantum mechanics is extracted from Xray data while for a large system, the quantum mechanics is injected into the system. In both cases, Nrepresentability is imposed by the use of the Clinton equations.
Consider a projector matrix P, representing the first order reduced density matrix in a basis of orthonormal atom-centric basis functions. A mathematical question arises, and that is, how to break P into its natural component kernel projector matrices, while preserving N-representability of P. The answer relies upon 2- projector triple products, P'jPP'j. The triple product solutions, applicable within the quantum crystallography of large molecules, are determined by a new form of the Clinton equations, which - in their original form - have long been used to ensure N-representability of density…
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 errors required for their experimental realization. Here we propose a class of quantum-classical hybrid algorithms that compute the energy from a two-electron reduced density matrix (2-RDM). The 2-RDM is constrained by $N$-representability conditions, conditions for representing an $N$-electron wavefunction, that mitigates noise from the quantum circuit. We com…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given state. The operational tangibility of the framework assures that the resultant general relations admit natural operational interpretations and characterisations, and thereby perhaps most importantly, their experimental verifiability. In view of the universal formulation, Heisenberg's original philosophy of the uncertainty principle, most typically exemplified in …
Classical optimisation of reduced density matrix estimations with classical shadows using N-representability conditions under shot noise considerations
A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational tangibility of the framework, the resultant general relations admit natural operational interpretations and characterisations, and are thus also experimentally verifiable. In view of the universal formulation, Heisenberg's philosophy of the uncertainty principle is also revisited; it is reformulated and restated as a refined no-go theorem, albeit perhaps in…
Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch's theorem precludes the straightforward application of the often indispensable energy band theory to study model Hamiltonians on hyperbolic lattices. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized b…
The classical map hypernetted-chain (CHNC) method for interacting electrons uses a kinetic energy functional in the form of a classical-fluid temperature. Here we show that the CHNC generated two-body densities and pair-distribution functions (PDFs) correspond to $N$-representable densities. Comparisons of results from CHNC with quantum Monte Carlo (QMC) and Path Integral Monte Carlo (PIMC) are used to validate the CHNC results. Since the PDFs are sufficient to obtain the equation of state or linear-response properties of electron-ion systems, we apply the CHNC method for fully classical calcu…
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 straightforward approach to this algorithmic step estimates each component of the marginal independently without making use of the algebraic and geometric structure of the marginals. Within the field of quantum chemistry, this structure is termed the fermionic $n$-representability conditions, and is supported by a vast amount of literature on both theoretical and pra…
Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography scheme which relies on approximating the probability distribution over the outcomes of an informationally complete measurement in a variational manifold represented by a convolutional neural network. We show an excellent representability of prototypical ground- and steady states with this ansatz using a number of variational parameters that scales polynomia…
Quantum electrodynamics of equilibrium systems: A rigorous Maxwell-regularized functional-theoretic formulation
Ludwig-Maximilians-Universität München（慕尼黑大学）；Oslo Metropolitan University（奥斯陆都市大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构与动力学研究所）；Center for Free-Electron Laser Science（自由电子激光科学中心）；The Flatiron Institute, Simons Foundation（西蒙斯基金会平顿研究所）
The simulation of strongly correlated many-electron systems is one of the most promising applications for near-term quantum devices. Here we use a class of eigenvalue solvers (presented in Phys. Rev. Lett. 126, 070504 (2021)) in which a contraction of the Schrödinger equation is solved for the two-electron reduced density matrix (2-RDM) to resolve the energy splittings of ortho-, meta-, and para-isomers of benzyne ${\textrm C_6} {\textrm H_4}$. In contrast to the traditional variational quantum eigensolver, the contracted quantum eigensolver solves an integration (or contraction) of the many-e…
