We develop a high-performance simulator for variational quantum eigensolver (VQE), the major innovations include: (1) A differentiable matrix product state (MPS) based VQE simulator that seamlessly integrates MPS into the automatic differentiation framework, which overcomes the exponential memory growth of state-vector simulator and can efficiently calculate gradients with a cost independent of the number of parameters; (2) A dynamic scheme to distribute the gradient calculations to achieve good load balance; (3) A parallel adaptive VQE which integrates our differentiable MPS simulator to further enhance the simulation performance; (4) Study of real chemical systems with convergence to chemical accuracy using our simulator, achieving nearly linearly strong and weak scaling for chemical systems with up to 100 qubits. Our simulator provides an ideal test ground for VQE and paves the way of benchmarking large-scale VQE experiments on near-term quantum computers.
We develop a high-performance simulator for variational quantum eigensolver (VQE), the major innovations include: (1) A differentiable matrix product state (MPS) based VQE simulator that seamlessly integrates MPS into the automatic differentiation framework, which overcomes the exponential memory growth of state-vector simulator and can efficiently calculate gradients with a cost independent of the number of parameters; (2) A dynamic scheme to distribute the gradient calculations to achieve good load balance; (3) A parallel adaptive VQE which integrates our differentiable MPS simulator to further enhance the simulation performance; (4) Study of real chemical systems with convergence to chemical accuracy using our simulator, achieving nearly linearly strong and weak scaling for chemical systems with up to 100 qubits. Our simulator provides an ideal test ground for VQE and paves the way of benchmarking large-scale VQE experiments on near-term quantum computers.
Quantum computational chemistry (QCC) is the use of quantum computers to solve problems in computational quantum chemistry. We develop a high performance variational quantum eigensolver (VQE) simulator for simulating quantum computational chemistry problems on a new Sunway supercomputer. The major innovations include: (1) a Matrix Product State (MPS) based VQE simulator to reduce the amount of memory needed and increase the simulation efficiency; (2) a combination of the Density Matrix Embedding Theory with the MPS-based VQE simulator to further extend the simulation range; (3) A three-level parallelization scheme to scale up to 20 million cores; (4) Usage of the Julia script language as the main programming language, which both makes the programming easier and enables cutting edge performance as native C or Fortran; (5) Study of real chemistry systems based on the VQE simulator, achieving nearly linearly strong and weak scaling. Our simulation demonstrates the power of VQE for large quantum chemistry systems, thus paves the way for large-scale VQE experiments on near-term quantum computers.
Quantum Computing is believed to be the ultimate solution for quantum chemistry problems. Before the advent of large-scale, fully fault-tolerant quantum computers, the variational quantum eigensolver (VQE) is a promising heuristic quantum algorithm to solve real world quantum chemistry problems on near-term noisy quantum computers. Here we propose a highly parallelizable classical simulator for VQE based on the matrix product state representation of quantum state, which significantly extend the simulation range of the existing simulators. Our simulator seamlessly integrates the quantum circuit evolution into the classical auto-differentiation framework, thus the gradients could be computed efficiently similar to the classical deep neural network, with a scaling that is independent of the number of variational parameters. As applications, we use our simulator to study commonly used small molecules such as HF, HCl, LiH and H 2 O, as well as larger molecules CO 2 , BeH 2 and H 4 with up to 40 qubits. The favorable scaling of our simulator against the number of qubits and the number of parameters could make it an ideal testing ground for near-term quantum algorithms and a perfect benchmarking baseline for oncoming large scale VQE experiments on noisy quantum computers.
Quantum chemistry is one of the most promising applications of quantum computers in the near future. For noisy intermediate-scale quantum devices, the quantum-classical hybrid framework based on the variational quantum eigensolver (VQE) has become the method of choice. In the literature, there are many different variants of VQE, but it is not known which one is optimal for a given molecule. For this purpose, we perform a thorough benchmarking on more than ten different kinds of VQE ansatzes (in systems up to 30 qubits), based on their performance on the energy accuracy, runtime until convergence, and number of parameters. Our results show that the ADAPT ansatz can be used to obtain more accurate energy for small systems (below 14 qubits), but it costs much more computational resources. For larger molecules, UCCSD0 has better performance. However, all the tested ansatzes can hardly reach chemical accuracy at stretched bond lengths. Our results were obtained using MindSpore Quantum, where the codes and the benchmarking toolkit are publicly available at Gitee.
Quantum computing is moving beyond its early stage and seeking for commercial applications in chemical and biomedical sciences. In the current noisy intermediate-scale quantum computing era, the quantum resource is too scarce to support these explorations. Therefore, it is valuable to emulate quantum computing on classical computers for developing quantum algorithms and validating quantum hardware. However, existing simulators mostly suffer from the memory bottleneck so developing the approaches for large-scale quantum chemistry calculations remains challenging. Here we demonstrate a high-performance and massively parallel variational quantum eigensolver (VQE) simulator based on matrix product states, combined with embedding theory for solving large-scale quantum computing emulation for quantum chemistry on HPC platforms. We apply this method to study the torsional barrier of ethane and the quantification of the protein-ligand interactions. Our largest simulation reaches 1000 qubits, and a performance of 216.9 PFLOP/s is achieved on a new Sunway supercomputer, which sets the state-of-the-art for quantum computing emulation for quantum chemistry.
The Variational Quantum Eigensolver (VQE) is widely regarded as a promising algorithm for calculating ground states of quantum systems that are intractable for classical computers. This promise is typically motivated by the hope of mitigating the exponential growth of Hilbert space with system size. Here we scrutinize how the computational cost of adaptive VQE scales with the size of the target system. We demonstrate that the Rényi entropy derived from classical simulations predicts the required number of adaptive iterations of VQE with high accuracy (R2≈0.99). We validate this on a benchmarking set of more than 20 different molecules with active spaces ranging from four to ten orbitals. For these molecules, we find an exponential scaling of the number of adaptive iterations, and in turn, of the circuit depth with the system size. We therefore conclude that it is unlikely that VQE in its current form is able to simulate large molecular systems with high fidelity without exponential resource requirements.
The advancements in classical computational components such as CPUs and GPUs have had a reverberating impact on the democratization of computational power available, with the field of computational chemistry reaping significant benefits from the propulsion of the limits of systems studied. The accurate prediction of chemical properties and reaction dynamics through computational simulation is now a centerpiece of modern chemical research, significantly accelerating discoveries research areas of materials science and drug development, as well as industrially relevant processes such as the emission of aldehydes from soft foams, flame retardants and pyrolysis and the carbonylation of epoxides. These achievements of computational chemistry still are overshadowed in the face of fundamental bottlenecks where classical methods remain constrained by the exponential scaling when treating large and/or strongly correlated quantum many-body systems. This innate computational complexity often constitutes chemically accurate calculations based on first principles impractical, or plain impossible, for systems beyond modest sizes. Quantum computing offers a potential pathway around these limitations, originally formally formulated by David Deutsch as a tool for simulating quantum systems, with the first quantum algorithms indicating speed-ups compared to classical counterparts arising from Peter Shor and Lov Grover for the prime factorization of an integer number and unstructured search respectively. Relying on fundamental theorems by Claude Shannon, it has been demonstrated that through the use of error-correcting codes fault-tolerant quantum computers are able to safeguard information against noise and decoherence, strongly indicating towards exponential speedups in solving central computational chemistry problems, such as determining ground state energies or reaction pathways of chemical systems. Substantial strides in experimental quantum computing over the past decade, including proof-of-principle demonstrations of quantum error correction, mean to bring full-scale fault-tolerant quantum computing within the grasp of humanity. The breakthroughs needed to attain scalable, error-corrected quantum computation with capabilities exceeding those of classical methods in real-world scenarios is likely still some years away. While striving to address the engineering challenges standing in the way of achieving fault tolerant quantum computing, substantial effort has been focused toward developing and benchmarking hybrid algorithms tailored for the Noisy Intermediate- Scale Quantum (NISQ) devices, available now to researchers. These hybrid quantum-classical algorithms, with the most notable being the Variational Quantum Eigensolver (VQE), allow the probing of quantum computing’s utility in computational chemistry even in the face of significant hardware noise and limited coherence times. The work presented in this thesis introduces several key additions the VQE framework, geared especially towards to NISQ hardware, where the mindful use of available resources is imperative. First, the implementation of the Conjugate Model Search optimizer is described, an optimization method that integrates simple models that are surrogate to the original function, combined with conjugate gradient optimization to navigate effectively parameter landscapes typical of variational algorithms, prone to noise. Second, this thesis contains the proposal and extensive study of a hyperparameter tuning procedure employing genetic algorithms, allowing for comprehensive simulation benchmarks that augment the robustness and efficiency of VQE implementations with respect to convergence time through real wall-time models of quantum processors. Continuing, a bridge is presented between quantum simulation and quantum chemistry, through qubit-to-fermion mappings of existing quantum gates, further enabling the direct and accurate modeling of chemical systems on trapped atom quantum hardware with the added arsenal provided by techniques designed for qubit architectures. Additionally, experimental data contained in this thesis include detailed benchmarking data collected from state-of-the-art trapped ion quantum processors available at the Johannes Gutenberg Universität Mainz, demonstrating the actual viability and performance of various methodologies for extracting results. Lastly, the state of VQE is examined, as it served as a springboard for a plethora of advancements in the development of quantum computing hardware, as well as the direction the field of simulation of computational quantum chemistry via quantum devices is headed towards in the coming years.