# Alibaba Cloud Quantum Development Platform: Applications to Quantum Algorithm Design

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Abstract:

We report our work on the Alibaba Cloud Quantum Development Platform (AC-QDP). The capability of AC-QDP's computational engine was already reported in \cite{CZH+18, ZHN+19}.In this follow-up article, we demonstrate with figures how AC-QDP helps in testing large-scale quantum algorithms (currently within the QAOA framework). We give new ...More

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Introduction

- In the past two years significant efforts have been made towards building intermediate-scale quantum devices (NISQs).
- Optimal QAOA sequences for small-cycle free graphs; 2.
- The QAOA consists of two phases; in the first phase, optimal angle sequences (γ, β) are obtained; in the second phase, these parameters are used to generate a certain number of copies of the state |γ, β via a quantum circuit.

Highlights

- In the past two years significant efforts have been made towards building intermediate-scale quantum devices (NISQs)
- The capability of Alibaba Cloud Quantum Development Platform (AC-QDP)’s computational engine was already reported in [8, 20]. In this follow-up article, we focus on showing how AC-QDP helps in testing of large-scale quantum algorithms, currently within the Quantum Approximate Optimization Algorithm (QAOA) framework
- The QAOA consists of two phases; in the first phase, optimal angle sequences (γ, β) are obtained; in the second phase, these parameters are used to generate a certain number of copies of the state |γ, β via a quantum circuit
- To compare our QAOA simulator with existing quantum simulation package equipped with QAOA functionalities, we choose MAX-CUT problems on a random regular graph and compare the time spent for a single energy function query
- Cirq and Qiskit use the state-vector evolution, whereas qTorch is based on tensor-network simulation with a featured QAOA implementation
- Each software is given the same random instance of a regular graph, and is asked to perform 5 times the energy query to obtain an average time for a single query

Results

- In the case that only the QAOA energy function value is needed, tensor-network based approach allows them to handle much bigger instances than the authors could ever hope for with the state-vector approach.
- Cirq and Qiskit use the state-vector evolution, whereas qTorch is based on tensor-network simulation with a featured QAOA implementation.
- Fig. 1 shows the performance of AC-QDP compared to other softwares, for degree 3 cases: Figure 1: Benchmarking results for random 3-regular graphs.
- The authors apply our QAOA software on a family of instances called small-cycle-free regular graphs.
- All kregular graphs with the same number of vertices and a girth at least 2p + 2 yeild identical QAOA energy functions Fp, and the simulation of QAOA on such instances can be readily reduced to the single lightcone on the unique tree-like subgraph, parametrized by the degree d and the depth p.
- In [11], 1-level QAOA is compared with classical one-step local algorithm on triangle-free regular graphs.
- This suggests that the optimal angle sequences for the tree-like case is usually a good starting point for the QAOA when dealing with large regular graphs.
- It is proposed in [16] that the angle sequences for small-cycle-free instances be used directly to completely get rid of the optimization phase, which could be chanllenging on noisy quantum devices.
- Thanks to the tensor-network-based implementation, the software is able to efficiently query small-cycle-free instances of large degree d and number of layers p, albeit the number of vertices involved in the tree-like subgraphs might be large.

Conclusion

- Even when the conjecture holds, it is not sufficient to put the graph isomorphism problem in quantum polynomial time, since the difference between the energy values can be exponentially small.
- The authors have extensively tested the QAOA-based algorithm described above with the Alibaba Cloud Quantum Development Platform, and the authors could separate all non-isomorphic three regular graphs up-to size 18, all strongly regular graphs up-to size 26 and Miyazaki graphs of size 20.
- The depth one QAOA values for 3-regular graphs with respect to the CUT energy function is solely the function of the degree sequence, the number of nodes and the number of triangles of the graph.

Summary

- In the past two years significant efforts have been made towards building intermediate-scale quantum devices (NISQs).
- Optimal QAOA sequences for small-cycle free graphs; 2.
- The QAOA consists of two phases; in the first phase, optimal angle sequences (γ, β) are obtained; in the second phase, these parameters are used to generate a certain number of copies of the state |γ, β via a quantum circuit.
- In the case that only the QAOA energy function value is needed, tensor-network based approach allows them to handle much bigger instances than the authors could ever hope for with the state-vector approach.
- Cirq and Qiskit use the state-vector evolution, whereas qTorch is based on tensor-network simulation with a featured QAOA implementation.
- Fig. 1 shows the performance of AC-QDP compared to other softwares, for degree 3 cases: Figure 1: Benchmarking results for random 3-regular graphs.
- The authors apply our QAOA software on a family of instances called small-cycle-free regular graphs.
- All kregular graphs with the same number of vertices and a girth at least 2p + 2 yeild identical QAOA energy functions Fp, and the simulation of QAOA on such instances can be readily reduced to the single lightcone on the unique tree-like subgraph, parametrized by the degree d and the depth p.
- In [11], 1-level QAOA is compared with classical one-step local algorithm on triangle-free regular graphs.
- This suggests that the optimal angle sequences for the tree-like case is usually a good starting point for the QAOA when dealing with large regular graphs.
- It is proposed in [16] that the angle sequences for small-cycle-free instances be used directly to completely get rid of the optimization phase, which could be chanllenging on noisy quantum devices.
- Thanks to the tensor-network-based implementation, the software is able to efficiently query small-cycle-free instances of large degree d and number of layers p, albeit the number of vertices involved in the tree-like subgraphs might be large.
- Even when the conjecture holds, it is not sufficient to put the graph isomorphism problem in quantum polynomial time, since the difference between the energy values can be exponentially small.
- The authors have extensively tested the QAOA-based algorithm described above with the Alibaba Cloud Quantum Development Platform, and the authors could separate all non-isomorphic three regular graphs up-to size 18, all strongly regular graphs up-to size 26 and Miyazaki graphs of size 20.
- The depth one QAOA values for 3-regular graphs with respect to the CUT energy function is solely the function of the degree sequence, the number of nodes and the number of triangles of the graph.

- Table1: Time for a single query in seconds, for regular graphs with n = 1000 vertices
- Table2: Comparison of different optimizers on small-cycle-free regular graphs, together with the best values obtained. Cases where the experiment was infeasible is indicated by ‘-’. Best function values found are highlighted. The number of vertices and the averaged time per query in ACQDP are also listed
- Table3: Best angle sequences found by classical optimizers in AC-QDP

Funding

- We would like to thank our colleagues from various teams in Alibaba Cloud Intelligence supporting us in the numerical experiments presented in this paper

Study subjects and analysis

cases: 3

The regular graphs are chosen randomly, running through 10, 20, 30, 50, 100 and 1000 vertices with degree 3, 4 and 5. Fig. 1 shows the performance of AC-QDP compared to other softwares, for degree 3 cases: Figure 1: Benchmarking results for random 3-regular graphs. For each number of vertices, 5 random instances are drawn, and QAOA of depth 1 through 4 are simulated

Reference

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