1000 Quantum Bits! Chinese scientists achieve the largest scale chemical simulation

Quantum computing is moving beyond its early stages and seeking commercial applications in the chemical and biomedical sciences. In the current era of noisy mesoscale quantum computing, quantum resources are too scarce to support these explorations. Therefore, simulating quantum computation on classical computers is of great value for developing quantum algorithms and verifying quantum hardware. However, most of the existing simulators have memory bottlenecks, so it remains challenging to develop methods for large-scale quantum chemical computation.

 

Recently, a joint team from the Institute of Computing Technology, Chinese Academy of Sciences, University of Science and Technology of China, and Shandong University has demonstrated a high-performance and massively parallel matrix product state-based variational quantum instanton solver (VQE) simulator that combines embedding theory to solve large-scale quantum computing simulations of quantum chemistry on an HPC platform.

 

 

Ultimately, the team's largest simulation reached 1000 quantum bits, achieving 216.9 PFLOP/s on the new Shenwei-TaihuLight supercomputer - setting the state-of-the-art for quantum computing simulations of quantum chemistry. level.

 

Simulating quantum computing on classical computers is difficult due to exponential runtime and memory requirements.

 

The quantum advantage in random circuit sampling (RCS) problems has been demonstrated on noisy mesoscale quantum (NISQ) computers. In practical applications, scientists have used quantum Monte Carlo (QMC) methods to estimate the ground state energy of diamond using 16 quantum bits and 65 circuit depths - the largest quantum chemical calculation ever performed using a quantum computer.

 

The Variational Quantum Feature Solver (VQE) used in this experiment is an attractive candidate for solving quantum chemistry problems on NISQ devices, offering great flexibility in selecting quantum circuits and reducing errors.

 

 

Typical simulations of chemical and material systems are performed using a classical simulator. A comparison of atomic number (Na), quantum bit number (Nq) and estimated CNOT gate number (NCNOT) is listed

 

Compared to RCS and QMC experiments, VQE simulations with tens of quantum bits are significantly more challenging for quantum hardware because:

 

1) the rapid expansion of the circuit depth as the number of quantum bits increases;

 

2) the nonlinear optimization of a large number of parameters significantly increases the computational cost.

 

As a result, the largest VQE experiments performed on quantum computers have used only 12 quantum bits, and most current VQE simulations with classical simulators are also limited to relatively small molecules of 10-20 quantum bits.

 

In this experiment, the scientists demonstrated a high-performance and massively parallel VQE simulator using the matrix product state (MPS) representation of quantum states.

 

 

Framework of the quantum computing chemistry simulator. a) Conceptual illustration of quantum computing simulation of quantum chemistry; b) Matrix product state (MPS) representation of the quantum states of each fragment in the VQE simulator using DMET. c) DMET calculation procedure for real chemical systems.

 

The team's simulator maximizes the power of tensor network methods and supercomputers in order to overcome exponential memory bottlenecks and achieve maximal classical simulations of quantum computational chemistry.

 

The MPS-VQE algorithm is the main computational bottleneck on HPC; experimentally, the team overcomes this bottleneck with optimized SVD and tensor operation algorithms. For matrix sizes from 100 to 500, the team's one-sided Jacobi SVD is on average more than 60 times faster than the non-optimized version. As a result, the maximum simulation using the MPS-VQE simulator (Simulator) scales up to 1000 quantum bits for one-time energy evaluation, up to 92 quantum bits for fully fused VQE simulations, and up to 10^5 double quantum bit gates.

 

Combined with DMET, the team's simulator is used to study practical quantum chemical systems containing 103 atoms and achieves an accuracy comparable to state-of-the-art computational methods.

 

The team uses hydrogen chains to evaluate the scalability and performance of the DMET-MPS-VQE simulator; and discusses the application of the MPS-VQE and DMET-MPS-VQE simulators to the study of real chemical systems. It is finally concluded that the correlation between simulation and experiment is quite good.

 

Potential energy curves (PEC) of hydrogen molecules calculated using the MPS-VQE simulator.

 

 

Experimental results. a) Comparison of the performance of tensor contraction with matrix size. . b) Performance comparison of SVD versus matrix size, which was evaluated on a CG containing 1 MPE and 64 CPEs; c) Computation time of hydrogen chains versus MPS-VQE simulator; d) Performance (PFLOP/s) and robust scalability of MPS-VQE simulator integrated with DMET on the next generation Shenwei supercomputer.

 

As a heuristic quantum algorithm, the accuracy and performance of VQE should be verified in real applications.

 

In this work, the MPS-VQE simulator scales up to 1000 quantum bits in a single energy evaluation and up to 92 quantum bits in convergent VQE simulations, in addition, the DMET-MPS-VQE simulator scales up to 39 million cores (cores) on the Shenwei supercomputer. It is worth mentioning that we can use VQE to obtain desired realistic applications, which are comparable to experimental observations.

 

The development of quantum computers requires the interweaving and contribution of classical supercomputers, which allows us to benefit from more mature classical computing.

 

The scale of the simulations achieved in this work far exceeds those in the existing literature, both in terms of the number of quantum bits and in terms of circuit depth, and the capabilities of existing quantum computers. This simulator will be an excellent benchmark and verification tool for developing the next generation of quantum computers, and a flexible platform for quantum researchers to explore industrially relevant applications with tens of quantum bits.

 

Link to original article:

https://www.nature.com/articles/s41534-023-00696-7