Fast Simulation of High-Depth QAOA Circuits

Until high-fidelity quantum computers with a large number of qubits become widely available, classical simulation remains a vital tool for algorithm design, tuning, and validation. We present a simulator for the Quantum Approximate Optimization Algorithm (QAOA). Our simulator is designed with the goal of reducing the computational cost of QAOA parameter optimization and supports both CPU and GPU execution. Our central observation is that the computational cost of both simulating the QAOA state and computing the QAOA objective to be optimized can be reduced by precomputing the diagonal Hamiltonian encoding the problem. We reduce the time for a typical QAOA parameter optimization by eleven times for $n = 26$ qubits compared to a state-of-the-art GPU quantum circuit simulator based on cuQuantum. Our simulator is available on GitHub: https://github.com/jpmorganchase/QOKitComment: Additional references added in v

Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm

In this work, we compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers such as Gurobi and MQLib to solve the combinatorial optimization problem MaxCut on 3-regular graphs. The goal is to identify under which conditions QAOA can achieve "quantum advantage" over classical algorithms, in terms of both solution quality and time to solution. One might be able to achieve quantum advantage on hundreds of qubits and moderate depth $p$ by sampling the QAOA state at a frequency of order 10 kHz. We observe, however, that classical heuristic solvers are capable of producing high-quality approximate solutions in linear time complexity. In order to match this quality for $\textit{large}$ graph sizes $N$, a quantum device must support depth $p>11$. Otherwise, we demonstrate that the number of required samples grows exponentially with $N$, hindering the scalability of QAOA with $p\leq11$. These results put challenging bounds on achieving quantum advantage for QAOA MaxCut on 3-regular graphs. Other problems, such as different graphs, weighted MaxCut, maximum independent set, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices

Embedding Learning in Hybrid Quantum-Classical Neural Networks

Quantum embedding learning is an important step in the application of quantum machine learning to classical data. In this paper we propose a quantum few-shot embedding learning paradigm, which learns embeddings useful for training downstream quantum machine learning tasks. Crucially, we identify the circuit bypass problem in hybrid neural networks, where learned classical parameters do not utilize the Hilbert space efficiently. We observe that the few-shot learned embeddings generalize to unseen classes and suffer less from the circuit bypass problem compared with other approaches.Comment: 8 pages, 11 figures, submitted to QCE22 (2022 IEEE International Conference on Quantum Computing & Engineering (QCE)

Similarity-Based Parameter Transferability in the Quantum Approximate Optimization Algorithm

The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization problem is achieved by preparing a quantum state through the optimization of quantum circuit parameters. Optimal QAOA parameter concentration effects for special MaxCut problem instances have been observed, but a rigorous study of the subject is still lacking. In this work we show clustering of optimal QAOA parameters around specific values; consequently, successful transferability of parameters between different QAOA instances can be explained and predicted based on local properties of the graphs, including the type of subgraphs (lightcones) from which graphs are composed as well as the overall degree of nodes in the graph (parity). We apply this approach to several instances of random graphs with a varying number of nodes as well as parity and show that one can use optimal donor graph QAOA parameters as near-optimal parameters for larger acceptor graphs with comparable approximation ratios. This work presents a pathway to identifying classes of combinatorial optimization instances for which variational quantum algorithms such as QAOA can be substantially accelerated.Comment: 22 pages, 21 figures, 3 tables, 1 algorithm. arXiv admin note: substantial text overlap with arXiv:2106.0753

Large-Scale Tensor Network Quantum Algorithm Simulator

As quantum computing field is starting to reach the realm of advantage over classical algorithms, simulating quantum circuits becomes increasingly challenging as we design and evaluate more complex quantum algorithms. In this context, tensor networks, which have become a standard method for simulations in various areas of physics, from many-body quantum physics to quantum gravity, offer a natural approach. Despite the availability of efficient tools for physics simulations, simulating quantum circuits presents unique challenges, which I address in this work, specifically using the Quantum Approximate Optimization Algorithm as an example. The main results of this work span several steps of the problem. For the step of creating a tensor network, I demonstrate that applying the diagonal representation of quantum gates leads to a complexity reduction in tensor network contraction by one to four orders of magnitude. For large-scale contraction of tensor networks, I propose a step-dependent parallelization approach which performs slicing of partially contracted tensor network. Finally, I study tensor network contractions on GPU and propose an algorithm of contraction which uses both CPU and GPU to reduce GPU overhead. In our benchmarks, this algorithm reduces time to solution from 6 seconds to 1.5-2 seconds

Large-Scale Classical Simulations for Development of Quantum Optimization Algorithms

As quantum computing field is starting to reach the realm of advantage over classical algorithms, simulating quantum circuits becomes increasingly challenging as we design and evaluate more complex quantum algorithms. In this context, tensor networks, which have become a standard method for simulations in various areas of physics, from many-body quantum physics to quantum gravity, offer a natural approach. Despite the availability of efficient tools for physics simulations, simulating quantum circuits presents unique challenges, which I address in this work, specifically using the Quantum Approximate Optimization Algorithm as an example. For large-scale contraction of tensor networks, I propose a step-dependent parallelization approach which performs slicing of partially contracted tensor networks. I also study tensor network contractions on GPU and propose an algorithm of contraction which uses both CPU and GPU to reduce GPU overhead. In our benchmarks, this algorithm reduces time to solution from 6 seconds to 1.5-2 seconds. These improvements allow to predict the performance of Quantum Approximate Optimization Algorithm (QAOA) on MaxCut problem without running the quantum optimization. This predicted QAOA performance is then used to systematically compare to the classical MaxCut solvers. It turns out that one needs to simulate a deep quantum circuit in order to compete with classical solvers. In search for provable speedups, I then turn to a different combinatorial optimization problem, Low-Autocorrelation Binary Sequences (LABS). This study involves simulating ground state overlap for deep circuits. This task is more suited for a state vector simulation, which requires advanced distributed algorithms when done at scale