In this work, we present a new large-scale quantum circuit simulator. It is based on the tensor network contraction technique to represent quantum circuits. We propose a novel parallelization algorithm based on step-dependent slicing . In this paper, we push the requirement on the size of a quantum computer that will be needed to demonstrate the advantage of quantum computation with Quantum Approximate Optimization Algorithm (QAOA). We computed a single amplitude of QAOA ansatz state on 210 qubits. The simulation involved 1,785 gates on 1,024 nodes of the Cray XC 40 supercomputer Theta. To the best of our knowledge, this constitutes the largest simulation of QAOA ansatz simulations reported to this date.
In this work, we present a new large-scale quantum circuit simulator. It is based on the tensor network contraction technique to represent quantum circuits. We propose a novel parallelization algorithm based on step-dependent slicing . In this paper, we push the requirement on the size of a quantum computer that will be needed to demonstrate the advantage of quantum computation with Quantum Approximate Optimization Algorithm (QAOA). We computed a single amplitude of QAOA ansatz state on 210 qubits. The simulation involved 1,785 gates on 1,024 nodes of the Cray XC 40 supercomputer Theta. To the best of our knowledge, this constitutes the largest simulation of QAOA ansatz simulations reported to this date.
Simulation of quantum computing on supercomputers is a significant research topic, which plays a vital role in quantum algorithm verification, error-tolerant verification, and other applications. Tensor-network contraction based on density matrix is an important single-amplitude simulation strategy, but it is hard to execute on the distributed computing systems. In this paper, we studied the problem in detail, and propose a scheme based on cutting edges of undirected graphs. This scheme cuts edges of undirected graphs with large tree width to obtain many undirected subgraphs with small tree width, and these subgraphs contracted on different computing cores. The contraction results of slave cores are summarized in the master node, which is consistent with the original tensor-network contraction. Thus, we can simulate the larger scale quantum circuit than single core. Moreover, it is an NP-hard problem to find the global optimum cutting edges, and we propose a search strategy based on a heuristic algorithm to approach it. In order to verify the effectiveness of our scheme, we conduct tests based on the quantum approximation optimization algorithm (QAOA) and Shor's algorithm, and it can simulate a 120-qubit three-regular QAOA algorithm on a 4096-core supercomputer, which greatly exceeds the simulation scale on a single core of 100 qubits.
Tensors are a natural generalization of matrices, and tensor networks are a natural generalization of matrix products. Despite the simple definition of tensor networks, they are versatile enough to represent many different kinds of "products" that arise in various theoretical and practical problems. In particular, the powerful computational model of quantum computation can be defined almost entirely in terms of matrix products and tensor products, both of which are special cases of tensor networks. As such, (classical) algorithms for evaluating tensor networks have profound importance in the study of quantum computation. In this thesis, we design and implement a parallel algorithm for tensor network contraction. In addition to finding efficient contraction orders for a tensor network, we also dynamically slice it into multiple sub-tasks with lower space and time costs, in order to evaluate the tensor network in parallel. We refer to such an evaluation strategy as a contraction scheme for the tensor network. In addition, we introduce a local optimization procedure that improves the efficiency of the contraction schemes we find. We also investigate the applications of our parallel tensor network contraction algorithm in quantum computation. The most ready application is the simulation of random quantum supremacy circuits, where we benchmark our algorithm to demonstrate its advantage over other similar tensor network based simulators. Other applications we found include evaluating the energy function of a Quantum Approximate Optimization Algorithm (QAOA), and simulating surface codes under a realistic error model with crosstalk.
Abstract Quantum computing holds significant promise for solving complex problems, but simulating quantum circuits on classical computers remains essential due to the current limitations of quantum hardware. Efficient simulation is crucial for the development and validation of quantum algorithms and quantum computers. This paper explores and compares various strategies to leverage different levels of parallelism to accelerate the contraction of tensor networks representing large quantum circuits. We propose a new parallel multistage algorithm based on communities. The original tensor network is partitioned into several communities, which are then contracted in parallel. The pairs of tensors of the resulting network can be contracted in parallel using a GPU. We use the Girvan–Newman algorithm to obtain the communities and the contraction plans. We compare the new algorithm with two other parallelisation strategies: one based on contracting all the pairs of tensors in the GPU and another one that uses slicing to cut some indexes of the tensor network and then MPI processes to contract the resulting slices in parallel. The new parallel algorithm gets the best results with different well-known quantum circuits with a high degree of entanglement, including random quantum circuits. In conclusion, the results show that the main factor that limits the simulation is the space cost. However, the parallel multistage algorithm manages to reduce the cost of sequential simulation for circuits with a high number of qubits and allows simulating larger circuits.
Classical simulation of quantum computation is necessary for studying the numerical behavior of quantum algorithms, as there does not yet exist a large viable quantum computer on which to perform numerical tests. Tensor network (TN) contraction is an algorithmic method that can efficiently simulate some quantum circuits, often greatly reducing the computational cost over methods that simulate the full Hilbert space. In this study we implement a tensor network contraction program for simulating quantum circuits using multi-core compute nodes. We show simulation results for the Max-Cut problem on 3- through 7-regular graphs using the quantum approximate optimization algorithm (QAOA), successfully simulating up to 100 qubits. We test two different methods for generating the ordering of tensor index contractions: one is based on the tree decomposition of the line graph, while the other generates ordering using a straight-forward stochastic scheme. Through studying instances of QAOA circuits, we show the expected result that as the treewidth of the quantum circuit's line graph decreases, TN contraction becomes significantly more efficient than simulating the whole Hilbert space. The results in this work suggest that tensor contraction methods are superior only when simulating Max-Cut/QAOA with graphs of regularities approximately five and below. Insight into this point of equal computational cost helps one determine which simulation method will be more efficient for a given quantum circuit. The stochastic contraction method outperforms the line graph based method only when the time to calculate a reasonable tree decomposition is prohibitively expensive. Finally, we release our software package, qTorch (Quantum TensOR Contraction Handler), intended for general quantum circuit simulation. For a nontrivial subset of these quantum circuits, 50 to 100 qubits can easily be simulated on a single compute node.
Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient quantum computation on limited quantum resources. Modern exascale high-performance computing platforms offer significant potential for advancing tensor network quantum circuit simulation capabilities. We implement TN-Sim, a tensor network simulator backend within the NWQ-Sim software package that utilizes the Tensor Algebra for Many-body Methods (TAMM) framework to support both distributed HPC-scale computations and local simulations with ITensor. To optimize the scale up in computation across multiple nodes we implement a task based parallelization scheme to demonstrate parallelized gate contraction for wide quantum circuits with many gates per layer. Through the integration of the TAMM framework with Matrix Product State (MPS) tensor network approaches, we deliver a simulation environment that can scale from local systems to HPC clusters. We demonstrate an MPS tensor network simulator running on the state-of-the-art Perlmutter (NVIDIA) supercomputer and discuss the potential portability of this software to HPC clusters such as Frontier (AMD) and Aurora (Intel). We also discuss future improvements including support for different tensor network topologies and enhanced computational efficiency.
Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However, the massive parallelization of the algorithm makes it vulnerable to computer node failures. In this work, we apply coded computing to a practical parallel tensor network contraction algorithm. To the best of our knowledge, this is the first attempt to code tensor network contractions. Inspired by matrix multiplication codes, we provide two coding schemes: 2-node code for practicality in quantum simulation and hyperedge code for generality. Our 2-node code successfully achieves significant gain for f-resilient number compared to naive replication, proportional to both the number of node failures and the dimension product of sliced indices. Our hyperedge code can cover tensor networks out of the scope of quantum, with degraded gain in the exchange of its generality.