Many-Body Excited States with a Contracted Quantum Eigensolver.

Calculating ground and excited states is an exciting prospect for near-term quantum computing applications, and accurate and efficient algorithms are needed to assess viable directions. We develop an excited-state approach based on the contracted quantum eigensolver (ES-CQE), which iteratively attempts to find a solution to a contraction of the Schrödinger equation projected onto a subspace and does not require a priori information on the system. We focus on the anti-Hermitian portion of the equation, leading to a two-body unitary ansatz. We investigate the role of symmetries, initial states, constraints, and overall performance within the context of the model strongly correlated rectangular H4 system. We show that the ES-CQE achieves near-exact accuracy across the majority of states, covering regions of strong and weak electron correlation, while also elucidating challenging instances for two-body unitary ansatz.

Cavity-Mediated Molecular Entanglement and Generation of Non-classical States of Light.

The generation and control of entanglement in a quantum mechanical system are critical elements of nearly all quantum applications. Molecular systems are promising candidates, with numerous degrees of freedom able to be targeted. However, knowledge of intersystem entanglement mechanisms in such systems is limited. In this work, we demonstrate the generation of entanglement between vibrational degrees of freedom in molecules via strong coupling to a cavity mode driven by a weak coherent field. In a bimolecular system, we show that entanglement can be generated not only between the cavity and molecular system but also between molecules. This process also results in the generation of nonclassical states of light, providing potential pathways for harnessing entanglement in molecular systems.

Qubit Condensation for Assessing Efficacy of Molecular Simulation on Quantum Computers.

Quantum computers may demonstrate significant advantages over classical devices, as they are able to exploit a purely quantum-mechanical phenomenon known as entanglement in which a single quantum state simultaneously populates two-or-more classical configurations. However, due to environmental noise and device errors, elaborate quantum entanglement can be difficult to prepare on modern quantum computers. In this paper, we introduce a metric based on the condensation of qubits to assess the ability of a quantum device to simulate many-electron systems. Qubit condensation occurs when the qubits on a quantum computer condense into a single, highly correlated particle-hole state. While conventional metrics like gate errors and quantum volume do not directly target entanglement, the qubit-condensation metric measures the quantum computer's ability to generate an entangled state that achieves nonclassical long-range order across the device. To demonstrate, we prepare qubit condensations on various quantum devices and probe the degree to which qubit condensation is realized via postmeasurement analysis. We show that the predicted ranking of the quantum devices is consistent with the errors obtained from molecular simulations of H2 using a contracted quantum eigensolver.

Accelerated Convergence of Contracted Quantum Eigensolvers through a Quasi-Second-Order, Locally Parameterized Optimization.

A contracted quantum eigensolver (CQE) finds a solution to the many-electron Schrödinger equation by solving its integration (or contraction) to the two-electron space─a contracted Schrödinger equation (CSE)─on a quantum computer. When applied to the anti-Hermitian part of the CSE (ACSE), the CQE iterations optimize the wave function, with respect to a general product ansatz of two-body exponential unitary transformations that can exactly solve the Schrödinger equation. In this work, we accelerate the convergence of the CQE and its wave function ansatz via tools from classical optimization theory. By treating the CQE algorithm as an optimization in a local parameter space, we can apply quasi-second-order optimization techniques, such as quasi-Newton approaches or nonlinear conjugate gradient approaches. Practically, these algorithms result in superlinear convergence of the wave function to a solution of the ACSE. Convergence acceleration is important because it can both minimize the accumulation of noise on near-term intermediate-scale quantum (NISQ) computers and achieve highly accurate solutions on future fault-tolerant quantum devices. We demonstrate the algorithm, as well as some heuristic implementations relevant for cost-reduction considerations, comparisons with other common methods such as variational quantum eigensolvers, and a Fermionic-encoding-free form of the CQE.

Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices.

The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or nontrivial high-dimensional classical optimization. Here, we introduce a quantum solver of contracted eigenvalue equations, the quantum analog of classical methods for the energies and reduced density matrices of ground and excited states. The solver does not require deep circuits or difficult classical optimization and achieves an exponential speed-up over its classical counterpart. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.

Quantum-classical hybrid algorithm for the simulation of all-electron correlation.

While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation-the static correlation-on the quantum computer and the non-exponentially scaling part-the dynamic correlation-on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating the statically correlated 2-RDM. We obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby demonstrate the ability of the developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.

Stabilization of cationic aluminum hydroxide clusters in high pH environments with a CaCl2/l-arginine matrix.

We present a way of stabilizing cationic partially hydrolyzed aluminum clusters in a non-acidic environment, through Ca2+ and l-Arginine doping. The Keggin Al13-mer (ε-AlO4Al12(OH)24(H2O)127+) aluminum cluster can be stabilized with CaCl2 and l-arginine in a way to preserve the metal clusters. We use size-exclusion chromatography (SEC) and 27Al nuclear magnetic resonance (NMR) spectroscopy to demonstrate that positively-charged Keggin structures are preserved and that the conversion to Al(OH)3 materials is halted even at alkaline pH. The system serves to stabilize acidic Al clusters in alkaline or neutral conditions, while preserving their inherent cationic behavior.

Using reduced density matrix techniques to capture static and dynamic correlation in the energy landscape for the decomposition of the CH2CH2ONO radical and support a non-IRC pathway.

The unexpected abundance of HNO in the photodecomposition of the radical 2-nitrosooxy ethyl (CH2CH2ONO) is investigated through calculations of the potential energy surface by the anti-Hermitian contracted Schrödinger equation (ACSE) method, which directly generates the 2-electron reduced density matrix. The ACSE, which is able to balance single-reference (dynamic) and multi-reference (static) correlation effects, reveals some subtle correlation effects along the intrinsic reaction coordinate (IRC) en route to NO + oxirane, an IRC which offers a potential bifurcation to the HNO + vinoxy product channel. These effects were not fully captured by either single-reference techniques, such as coupled cluster, or multi-reference techniques, such as second-order multi-reference perturbation theory. These correlation effects reveal small to moderate energy changes in key transition states, which have implications for the reaction mechanism as related to the production of HNO.

Isomerization of Keggin Al13 Ions Followed by Diffusion Rates.

The solution chemistry of aluminum has long interested scientists due to its relevance to materials chemistry and geochemistry. The dynamic behavior of large aluminum-oxo-hydroxo clusters, specifically [Al13 O4 (OH)24 (H2 O)12 ]7+ (Al13 ), is the focus of this paper. 27 Al NMR, 1 H NMR, and 1 H DOSY techniques were used to follow the isomerization of the ϵ-Al13 in the presence of glycine and Ca2+ at 90 °C. Although the conversion of ϵ-Al13 to new clusters and/or Baker-Figgis-Keggin isomers has been studied previously, new 1 H NMR and 1 H DOSY analyses provided information about the role of glycine, the ligated intermediates, and the mechanism of isomerization. New 1 H NMR data suggest that glycine plays a critical role in the isomerization. Surprisingly, glycine does not bind to Al30 clusters, which were previously proposed as an intermediate in the isomerization. Additionally, a highly symmetric tetrahedral signal (δ=72 ppm) appeared during the isomerization process, which evidence suggests corresponds to the long-sought α-Al13 isomer in solution.

Ultrathin hybrid films of polyoxohydroxy clusters and proteins: layer-by-layer assembly and their optical and mechanical properties.

The hierarchical assembly of inorganic and organic building blocks is an efficient strategy to produce high-performance materials which has been demonstrated in various biomaterials. Here, we report a layer-by-layer (LBL) assembly method to fabricate ultrathin hybrid films from nanometer-scale ionic clusters and proteins. Two types of cationic clusters (hydrolyzed aluminum clusters and zirconium-glycine clusters) were assembled with negatively charged bovine serum albumin (BSA) protein to form high-quality hybrid films, due to their strong electrostatic interactions and hydrogen bonding. The obtained hybrid films were characterized by scanning electron microscope (SEM), UV-vis, Raman spectroscopy, Fourier transform infrared spectroscopy (FTIR), X-ray fluorescence (XRF), and X-ray diffraction (XRD). The results demonstrated that the cluster-protein hybrid films exhibited structural homogeneity, relative transparency, and bright blue fluorescence. More importantly, these hybrid films displayed up to a 70% increase in hardness and up to a 100% increase in reduced Young's modulus compared to the pure BSA film. These hybrid cluster-protein films could be potentially used as biomedical coatings in the future because of their good transparency and excellent mechanical properties.

Controlled step-wise isomerization of the Keggin-type Al(13) and determination of the γ-Al(13) structure.

Partial hydrolysis of AlCl3 with Ca(OH)2 and the amino acid glycine enables the selective transformation of the Al13 Keggin structures, outlining the ε → δ → γ isomerization process. Through this, a new γ-Al13 Keggin structure was able to be isolated and characterized through (27)Al NMR and single-crystal XRD.