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Classical and quantum annealing are two heuristic optimization methods that search for an optimal solution by slowly decreasing thermal or quantum fluctuations. Optimizing annealing schedules is important both for performance and fair comparisons between classical annealing, quantum annealing, and other algorithms. Here we present a heuristic approach for the optimization of annealing schedules for quantum annealing and apply it to 3D Ising spin glass problems. We find that if both classical and quantum annealing schedules are similarly optimized, classical annealing outperforms quantum annealing for these problems when considering the residual energy obtained in slow annealing. However, when performing many repetitions of fast annealing, simulated quantum annealing is seen to outperform classical annealing for our benchmark problems.
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New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a higher order (smaller) excitation probability. We verify these results by solving numerically the time-dependent Schrodinger equation for small size systems
Quantum annealing is a practical approach to execute the native instruction set of the adiabatic quantum computation model. The key of running adiabatic algorithms is to maintain a high success probability of evolving the system into the ground state of a problem-encoded Hamiltonian at the end of an annealing schedule. This is typically done by executing the adiabatic algorithm slowly to enforce adiabacity. However, properly optimized annealing schedule can accelerate the computational process. Inspired by the recent success of DeepMinds AlphaZero algorithm that can efficiently explore and find a good winning strategy from a large combinatorial search with a neural-network-assisted Monte Carlo Tree Search (MCTS), we adopt MCTS and propose a neural-network-enabled version, termed QuantumZero (QZero), to automate the design of an optimal annealing schedule in a hybrid quantum-classical framework. The flexibility of having neural networks allows us to apply transfer-learning technique to boost QZeros performance. We find both MCTS and QZero to perform very well in finding excellent annealing schedules even when the annealing time is short in the 3-SAT examples we consider in this study. We also find MCTS and QZero to be more efficient than many other leading reinforcement leanring algorithms for the task of desining annealing schedules. In particular, if there is a need to solve a large set of similar problems using a quantum annealer, QZero is the method of choice when the neural networks are first pre-trained with examples solved in the past.
In a typical quantum annealing protocol, the system starts with a transverse field Hamiltonian which is gradually turned off and replaced by a longitudinal Ising Hamiltonian. The ground state of the Ising Hamiltonian encodes the solution to the computational problem of interest, and the state overlap with this ground state gives the success probability of the annealing protocol. The form of the annealing schedule can have a significant impact on the ground state overlap at the end of the anneal, so precise control over these annealing schedules can be a powerful tool for increasing success probabilities of annealing protocols. Here we show how superconducting circuits, in particular capacitively shunted flux qubits (CSFQs), can be used to construct quantum annealing systems by providing tools for mapping circuit flux biases to Pauli coefficients. We use this mapping to find customized annealing schedules: appropriate circuit control biases that yield a desired annealing schedule, while accounting for the physical limitations of the circuitry. We then provide examples and proposals that utilize this capability to improve quantum annealing performance.
We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function and then transforming the k-bit coupling ($kgeq 3$) terms to quadratic terms using ancillary variables. The method is efficient and uses $mathcal{O}(text{log}^2(N))$ binary variables (qubits) for finding the factors of integer $N$. The method was tested using the D-Wave 2000Q for finding an embedding and determining the prime factors for a given composite number. As examples, we present quantum annealing results for factoring 15, 143, 59989, and 376289 using 4, 12, 59, and 94 logical qubits respectively. The method is general and could be used to factor larger numbers
Recent advances in quantum technology have led to the development and the manufacturing of programmable quantum annealers that promise to solve certain combinatorial optimization problems faster than their classical counterparts. Semi-supervised learning is a machine learning technique that makes use of both labeled and unlabeled data for training, which enables a good classifier with only a small amount of labeled data. In this paper, we propose and theoretically analyze a graph-based semi-supervised learning method with the aid of the quantum annealing technique, which efficiently utilize the quantum resources while maintaining a good accuracy. We illustrate two classification examples, suggesting the feasibility of this method even with a small portion (20%) of labeled data is involved.
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