The objective of this short letter is to study the optimal partitioning of value stream networks into two classes so that the number of connections between them is maximized. Such kind of problems are frequently found...
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The objective of this short letter is to study the optimal partitioning of value stream networks into two classes so that the number of connections between them is maximized. Such kind of problems are frequently found in the design of different systems such as communication network configuration, and industrial applications in which certain topological characteristics enhance value-stream network resilience. The main interest is to improve the Max-Cut algorithm proposed in the quantumapproximateoptimization approach (QAOA), looking to promote a more efficient implementation than those already published. A discussion regarding linked problems as well as further research questions are also reviewed.
As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize ...
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As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of the quantum circuit output. One of these algorithms, the quantum approximate optimization algorithm stands out as a promising approach to tackling combinatorial problems. However, finding the appropriate parameters is a difficult task. Although QAOA exhibits concentration properties, they can depend on instances characteristics that may not be easy to identify, but may nonetheless offer useful information to find good parameters. In this work, we study unsupervised Machine Learning approaches for setting these parameters without optimization. We perform clustering with the angle values but also instances encodings (using instance features or the output of a variational graph autoencoder), and compare different approaches. These angle-finding strategies can be used to reduce calls to quantum circuits when leveraging QAOA as a subroutine. We showcase them within Recursive-QAOA up to depth 3 where the number of QAOA parameters used per iteration is limited to 3, achieving a median approximation ratio of 0.94 for MaxCut over 200 Erdos-Renyi graphs. We obtain similar performances to the case where we extensively optimize the angles, hence saving numerous circuit calls.
Smart logistics and supply chain play can determine the success or failure of any business. The cost, time, and carbon footprint are critical elements to be considered. Smart logistics solely consume 53% of the compan...
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Smart logistics and supply chain play can determine the success or failure of any business. The cost, time, and carbon footprint are critical elements to be considered. Smart logistics solely consume 53% of the company's income and produce up to 10% of its carbon footprint. Moreover, the time consumed in transportation and supply chains from the resource acquisition to the client contributes to the business profit. Enhancing smart logistics systems by selecting the optimal route is a hard problem even for today's supercomputers. On the other hand, quantum-based processing and quantumalgorithms are proved to solve convoluted computation to attain a heuristic system swiftly compared with classical processing methods. Notably, quantum approximate optimization algorithm (QAOA), as a variational quantumalgorithm for approximately solving discrete combinatorial optimization problems can be deployed into the smart logistics dilemma to improve the scalability of the system, decrease the time, thus reducing the carbon footprint and smart manufacturing system cost. Moreover, blockchain, as a secure distributed ledger, is capable of bringing the desired security to the smart logistic system. To this end, we propose an improved QAOA based on blockchain technology to improve the scalability and reduce the cost of smart logistics.
The quantum approximate optimization algorithm (QAOA) is a method of approximately solving combinatorial optimization problems. While QAOA is developed to solve a broad class of combinatorial optimization problems, it...
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The quantum approximate optimization algorithm (QAOA) is a method of approximately solving combinatorial optimization problems. While QAOA is developed to solve a broad class of combinatorial optimization problems, it is not clear which classes of problems are best suited for it. One factor in demonstrating quantum advantage is the relationship between a problem instance and the circuit depth required to implement the QAOA method. As errors in noisy intermediate-scale quantum (NISQ) devices increase exponentially with circuit depth, identifying lower bounds on circuit depth can provide insights into when quantum advantage could be feasible. Here, we identify how the structure of problem instances can be used to identify lower bounds for circuit depth for each iteration of QAOA and examine the relationship between problem structure and the circuit depth for a variety of combinatorial optimization problems including MaxCut and MaxIndSet. Specifically, we show how to derive a graph, G, that describes a general combinatorial optimization problem and show that the depth of circuit is at least the chromatic index of G. By looking at the scaling of circuit depth, we argue that MaxCut, MaxIndSet, and some instances of vertex covering and Boolean satisfiability problems are suitable for QAOA approaches while knapsack and traveling salesperson problems are not.
We study the relationship between the quantum approximate optimization algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum s...
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We study the relationship between the quantum approximate optimization algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of the QAOA dynamics and the group of classical symmetries of the objective function. The connection is general and includes but is not limited to problems defined on graphs. We show a series of results exploring the connection and highlight examples of hard problem classes where a nontrivial symmetry subgroup can be obtained efficiently. In particular, we show how classical objective function symmetries lead to invariant measurement outcome probabilities across states connected by such symmetries, independent of the choice of algorithm parameters or number of layers. To illustrate the power of the developed connection, we apply machine learning techniques toward predicting QAOA performance based on symmetry considerations. We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically important setting where QAOA parameter schedules are constrained to be linear and hence easier to optimize.
The quantum approximate optimization algorithm (QAOA), as a hybrid quantum/classical algorithm, has received much interest recently. QAOA can also be viewed as a variational ansatz for quantum control. However, its di...
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The quantum approximate optimization algorithm (QAOA), as a hybrid quantum/classical algorithm, has received much interest recently. QAOA can also be viewed as a variational ansatz for quantum control. However, its direct application to emergent quantum technology encounters additional physical constraints: (i) the states of the quantum system are not observable;(ii) obtaining the derivatives of the objective function can be computationally expensive or even inaccessible in experiments, and (iii) the values of the objective function may be sensitive to various sources of uncertainty, as is the case for noisy intermediate-scale quantum (NISQ) devices. Taking such constraints into account, we show that policy-gradient-based reinforcement learning (RL) algorithms are well suited for optimizing the variational parameters of QAOA in a noise-robust fashion, opening up the way for developing RL techniques for continuous quantum control. This is advantageous to help mitigate and monitor the potentially unknown sources of errors in modern quantum simulators. We analyze the performance of the algorithm for quantum state transfer problems in single- and multi-qubit systems, subject to various sources of noise such as error terms in the Hamiltonian, or quantum uncertainty in the measurement process. We show that, in noisy setups, it is capable of outperforming state-of-the-art existing optimizationalgorithms.
quantum approximate optimization algorithm (QAOA) is one of the most promising quantumalgorithms for the Noisy Intermediate-Scale quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of ...
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ISBN:
(纸本)9781728154169
quantum approximate optimization algorithm (QAOA) is one of the most promising quantumalgorithms for the Noisy Intermediate-Scale quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of utmost importance. We perform a large-scale numerical study of the approximation ratios attainable by QAOA is the low-to medium-depth regime. To find good QAOA parameters we perform 990 million 10-qubit QAOA circuit evaluations. We find that the approximation ratio increases only marginally as the depth is increased, and the gains are offset by the increasing complexity of optimizing variational parameters. We observe a high variation in approximation ratios attained by QAOA, including high variations within the same class of problem instances. We observe that the difference in approximation ratios between problem instances increases as the similarity between instances decreases. We find that optimal QAOA parameters concentrate for instances in out benchmark, confirming the previous findings for a different class of problems.
The Traveling Salesman Problem (TSP) is one of the most often-used NP-Hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also being used heav...
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ISBN:
(纸本)9798350311990
The Traveling Salesman Problem (TSP) is one of the most often-used NP-Hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also being used heavily as a vehicle to study the feasibility of the quantum computing paradigm for this class of problems. In this work, we formulate the symmetric TSP as an optimization problem, which we solve using the quantum approximate optimization algorithm (QAOA) approach. By adopting an improved qubit encoding strategy and a layerwise learning optimization protocol, we obtain numerical results on the gate-based digital quantum simulator for the 3-, 4-, and 5city TSPs. Specifically, we focus on three QAOA mixer designs to evaluate their performances in terms of numerical accuracy and optimization cost. Based on our results, we propose that a well-balanced QAOA mixer design is more prominent on gatebased simulators or realistic quantum devices in the near future. In addition, we study the sensitivity of TSP graph properties such as graph skewness and penalty weight in the TSP-QAOA simulation. Overall, our results prove digital quantum simulation is a powerful candidate for obtaining the optimal solution to the TSP.
The searching efficiency of the quantum approximate optimization algorithm is dependent on both the classical and quantum sides of the algorithm. Recently, a quantumapproximate Bayesian optimizationalgorithm (QABOA)...
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The searching efficiency of the quantum approximate optimization algorithm is dependent on both the classical and quantum sides of the algorithm. Recently, a quantumapproximate Bayesian optimizationalgorithm (QABOA) that includes two mixers was developed, where surrogate-based Bayesian optimization is applied to improve the sampling efficiency of the classical optimizer. A continuous-time quantum walk mixer is used to enhance exploration, and the generalized Grover mixer is also applied to improve exploitation. In this article, an extension of the QABOA is proposed to further improve its searching efficiency. The searching efficiency is enhanced through two aspects. First, two mixers, including one for exploration and the other for exploitation, are applied in an alternating fashion. Second, uncertainty of the quantum circuit is quantified with a new quantum Mat & eacute;rn kernel based on the kurtosis of the basis state distribution, which increases the chance of obtaining the optimum. The proposed new two-mixer QABOA's with and without uncertainty quantification are compared with three single-mixer QABOA's on five discrete and four mixed-integer problems. The results show that the proposed two-mixer QABOA with uncertainty quantification has the best performance in efficiency and consistency for five out of the nine tested problems. The results also show that QABOA with the generalized Grover mixer performs the best among the single-mixer algorithms, thereby demonstrating the benefit of exploitation and the importance of dynamic exploration-exploitation balance in improving searching efficiency.
quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the...
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quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate optimization algorithm (QAOA), which can be used to solve certain quantum control problems, state preparation problems, and combinatorial optimization problems. We demonstrate that the error of QAOA simulation can be significantly reduced by robust control optimization techniques, specifically, by sequential convex programming (SCP), to ensure error suppression in situations where the source of the error is known but not necessarily its magnitude. We show that robust optimization improves both the objective landscape of QAOA as well as overall circuit fidelity in the presence of coherent errors and errors in initial state preparation. Copyright (C) 2020 The Authors.
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