Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme.

The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH) 3 and (FH) 2 -H 2 O systems with the STO-3G basis set. VQE-UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH) 2 -H 2 O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7-7.7 for 18 qubit systems.

Range-separated density functional theory using multiresolution analysis and quantum computing.

Quantum computers are expected to outperform classical computers for specific problems in quantum chemistry. Such calculations remain expensive, but costs can be lowered through the partition of the molecular system. In the present study, partition was achieved with range-separated density functional theory (RS-DFT). The use of RS-DFT reduces both the basis set size and the active space size dependence of the ground state energy in comparison with the use of wave function theory (WFT) alone. The utilization of pair natural orbitals (PNOs) in place of canonical molecular orbitals (MOs) results in more compact qubit Hamiltonians. To test this strategy, a basis-set independent framework, known as multiresolution analysis (MRA), was employed to generate PNOs. Tests were conducted with the variational quantum eigensolver for a number of molecules. The results show that the proposed approach reduces the number of qubits needed to reach a target energy accuracy.

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule.

Quantum computers are reaching one crucial milestone after another. Motivated by their progress in quantum chemistry, we performed an extensive series of simulations of quantum-computer runs that were aimed at inspecting the best-practice aspects of these calculations. In order to compare the performance of different setups, the ground-state energy of the hydrogen molecule was chosen as a benchmark for which the exact solution exists in the literature. Applying the variational quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi-Kitaev transformation, we analyzed the impact of various computational technicalities. These included (i) the choice of the optimization methods, (ii) the architecture of the quantum circuits, as well as (iii) the different types of noise when simulating real quantum processors. On these, we eventually performed a series of experimental runs as a complement to our simulations. The simultaneous perturbation stochastic approximation (SPSA) and constrained optimization by linear approximation (COBYLA) optimization methods clearly outperformed the Nelder-Mead and Powell methods. The results obtained when using the Ry variational form were better than those obtained when the RyRz form was used. The choice of an optimum entangling layer was sensitively interlinked with the choice of the optimization method. The circular entangling layer was found to worsen the performance of the COBYLA method, while the full-entangling layer improved it. All four optimization methods sometimes led to an energy that corresponded to an excited state rather than the ground state. We also show that a similarity analysis of measured probabilities can provide a useful insight.

Variational Quantum Algorithm Applied to Collision Avoidance of Unmanned Aerial Vehicles.

Mission planning for multiple unmanned aerial vehicles (UAVs) is a complex problem that is expected to be solved by quantum computing. With the increasing application of UAVs, the demand for efficient conflict management strategies to ensure airspace safety continues to increase. In the era of noisy intermediate-scale quantum (NISQ) devices, variational quantum algorithms (VQA) for optimizing parameterized quantum circuits with the help of classical optimizers are currently one of the most promising strategies to gain quantum advantage. In this paper, we propose a mathematical model for the UAV collision avoidance problem that maps the collision avoidance problem to a quadratic unconstrained binary optimization (QUBO) problem. The problem is formulated as an Ising Hamiltonian, then the ground state is solved using two kinds of VQAs: the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We select conditional value-at-risk (CVaR) to further promote the performance of our model. Four examples are given to validate that with our method the probability of obtaining a feasible solution can exceed 90% based on appropriate parameters, and our method can enhance the efficiency of a UAVs' collision avoidance model.

Parallel Generalized Real Symmetric-Definite Eigenvalue Problem.

A computationally fast Fortran 90+ quadruple precision portable parallel GRSDEP (generalized real symmetric-definite eigenvalue problem) package suitable for large (80,000 x 80,000 or greater) dense matrices is discussed in this paper.

SIESTA-SIPs: Massively parallel spectrum-slicing eigensolver for an ab initio molecular dynamics package.

Integration of Shift-and-Invert Parallel Spectral Transformation (SIPs) eigensolver (as implemented in the SLEPc library) into an ab initio molecular dynamics package, SIESTA, is described. The effectiveness of the code is demonstrated on applications to polyethylene chains, boron nitride sheets, and bulk water clusters. For problems with the same number of orbitals, the performance of the SLEPc eigensolver depends on the sparsity of the matrices involved, favoring reduced dimensional systems such as polyethylene or boron nitride sheets in comparison to bulk systems like water clusters. For all problems investigated, performance of SIESTA-SIPs exceeds the performance of SIESTA with default solver (ScaLAPACK) at the larger number of cores and the larger number of orbitals. A method that improves the load-balance with each iteration in the self-consistency cycle by exploiting the emerging knowledge of the eigenvalue spectrum is demonstrated. © 2018 Wiley Periodicals, Inc.

Quantum synergy in peptide folding: A comparative study of CVaR-variational quantum eigensolver and molecular dynamics simulation.

One of the technological fields that is developing the fastest is quantum computing in biology. One of the main problems is protein folding, which calls for precise, effective algorithms with fast computing times. Mapping the least energy conformation state of proteins with disordered areas requires enormous computing resources. The current study uses quantum algorithms, such as the Variational Quantum Eigensolver (VQE), to estimate the lowest energy value of 50 peptides, each consisting of seven amino acids. To determine the ground state energy value, Variational Quantum Optimisation (VQE) is first utilised to generate the energy values along with Conditional Value at Risk (CVaR) as an aggregation function is applied over 100 iterations of 500,000 shots each. This is contrasted with 50 millisecond molecular dynamics-based simulations to determine the energy levels and folding pattern. In comparison to MD-based simulations, the results point to CvaR-VQE producing more effective folding outcomes with respect to sampling and global optimization. Protein folding can be solved to get deep insights into biological processes and drug formulation with improving quantum technology and algorithms.

Co-designing ab initio electronic structure methods on a RISC-V vector architecture.

Ab initio electronic structure applications are among the most widely used in High-Performance Computing (HPC), and the eigenvalue problem is often their main computational bottleneck. This article presents our initial efforts in porting these codes to a RISC-V prototype platform leveraging a wide Vector Processing Unit (VPU). Our software tester is based on a mini-app extracted from the ELPA eigensolver library. The user-space emulator Vehave and a RISC-V vector architecture implemented on an FPGA were tested. Metrics from both systems and different vectorisation strategies were extracted, ranging from the simplest and most portable one (using autovectorisation and assisting this by fusing loops in the code) to the more complex one (using intrinsics). We observed a progressive reduction in the number of vectorised instructions, executed instructions and computing cycles with the different methodologies, which will lead to a substantial speed-up in the calculations. The obtained outcomes are crucial in advancing the porting of computational materials and molecular science codes to (post)-exascale architectures using RISC-V-based technologies fully developed within the EU. Our evaluation also provides valuable feedback for hardware designers, engineers and compiler developers, making this use case pivotal for co-design efforts.

The NOMAD mini-apps: A suite of kernels from ab initio electronic structure codes enabling co-design in high-performance computing.

This article introduces a suite of mini-applications (mini-apps) designed to optimise computational kernels in ab initio electronic structure codes. The suite is developed from flagship applications participating in the NOMAD Center of Excellence, such as the ELPA eigensolver library and the GW implementations of the exciting, Abinit, and FHI-aims codes. The mini-apps were identified by targeting functions that significantly contribute to the total execution time in the parent applications. This strategic selection allows for concentrated optimisation efforts. The suite is designed for easy deployment on various High-Performance Computing (HPC) systems, supported by an integrated CMake build system for straightforward compilation and execution. The aim is to harness the capabilities of emerging (post)exascale systems, which necessitate concurrent hardware and software development - a concept known as co-design. The mini-app suite serves as a tool for profiling and benchmarking, providing insights that can guide both software optimisation and hardware design. Ultimately, these developments will enable more accurate and efficient simulations of novel materials, leveraging the full potential of exascale computing in material science research.

Quantum neuronal sensing of quantum many-body states on a 61-qubit programmable superconducting processor.

Classifying many-body quantum states with distinct properties and phases of matter is one of the most fundamental tasks in quantum many-body physics. However, due to the exponential complexity that emerges from the enormous numbers of interacting particles, classifying large-scale quantum states has been extremely challenging for classical approaches. Here, we propose a new approach called quantum neuronal sensing. Utilizing a 61-qubit superconducting quantum processor, we show that our scheme can efficiently classify two different types of many-body phenomena: namely the ergodic and localized phases of matter. Our quantum neuronal sensing process allows us to extract the necessary information coming from the statistical characteristics of the eigenspectrum to distinguish these phases of matter by measuring only one qubit and offers better phase resolution than conventional methods, such as measuring the imbalance. Our work demonstrates the feasibility and scalability of quantum neuronal sensing for near-term quantum processors and opens new avenues for exploring quantum many-body phenomena in larger-scale systems.

The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry.

New approaches into computational quantum chemistry can be developed through the use of quantum computing. While universal, fault-tolerant quantum computers are still not available, and we want to utilize today's noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE)-an algorithm for calculating the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, and physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal method of running the hybrid classical-quantum optimization is to: (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but ensure a high final readout precision; (ii) emphasize efficient problem encoding and ansatz parametrization; and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently, it is quite difficult to perform trustworthy calculations of molecular energies.

Variational algorithms for linear algebra.

Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices. We show that the solutions of linear systems of equations and matrix-vector multiplications can be translated as the ground states of the constructed Hamiltonians. Based on the variational quantum algorithms, we introduce Hamiltonian morphing together with an adaptive ansätz for efficiently finding the ground state, and show the solution verification. Our algorithms are especially suitable for linear algebra problems with sparse matrices, and have wide applications in machine learning and optimisation problems. The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation. We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations. We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.