qTorch: The quantum tensor contraction handler

Abstract

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.

Improving Variational Quantum Optimization using CVaR

“…5, to obtain the same accuracy as the expected value we would need to increase the number of samples by a factor 1 α . Results in this paper suggest choosing α ∈ [0.1, 0.25] as a good empirical choice, implying that the number of samples should be increased by a factor [4,10] to attain the same accuracy. However, our empirical evaluation uses the same, fixed number of samples across all α, and still shows significant benefits of CVaR optimization.…”

“…It is widely be-Stefan Woerner: wor@zurich.ibm.com lieved that quantum computers cannot solve such problems in polynomial time (i.e., NP ⊆ BQP [5]), but there is significant effort toward designing quantum algorithms that could be practically useful by quickly finding near-optimal solutions to these hard problems. Among these algorithms, two candidates are more likely to be efficiently implementable on noisy quantum computers: the Variational Quantum Eigensolver (VQE) [10,16], and the Quantum Approximate Optimization Algorithm (QAOA) [6,7,9]. Both VQE and QAOA use a parametrized quantum circuit U (θ) (also called variational form) to generate trial wave functions |ψ(θ) = U (θ) |0 , guided by a classical optimization algorithm that aims to solve:…”

OpenFermion: the electronic structure package for quantum computers

“…Besides Hamiltonian generation, OpenFermion also includes methods for outputting Trotter-Suzuki decompositions of arbitrary operators, providing the corresponding quantum circuit in QASM format [87]. These methods were included in order to simplify porting the resulting quantum circuits to other simulation packages, such as LIQUi| > [75], qTorch [79], Project-Q [70], and qHipster [88]. For instance, the function pauli exp to qasm takes a list of QubitOperators and an optional evolution time as input, and outputs the QASM specification as a string.…”

“…Moreover, to maximize usefulness within the field, every effort has been made to design OpenFermion as a modular library which is agnostic with respect to quantum programming language frameworks. Through its plugin system, OpenFermion is able to interface with, and benefit from, any of the frameworks being developed for both more abstract quantum software and hardware specific compilation [70][71][72][73][74][75][76][77][78][79][80].…”

QuEST and High Performance Simulation of Quantum Computers

“…The number of single compute node generic [8][9][10] and specialised [11][12][13][14] simulators is rapidly growing. However despite many reported distributed simulators [2,3,[15][16][17][18][19][20] and proposals for GPU accelerated simulators [18,[21][22][23][24], QuEST is the first open source simulator available to offer both facilities, and the only simulator to offer support on all hardware plaforms commonly used in the classical simulation of quantum computation II.…”