Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unre-alized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum algorithmic modeling. One such recent development is Quan-tumCircuitOpt (QCOpt), an open-source software framework that leverages state-of-the-art optimization-based solvers to find provably optimal compact circuit decompositions, which are exact up to global phase and machine precision. The quantum circuit design problem can be modeled using non-linear, non-convex constraints. However, QCOpt reformulates these non-linear constraints using well-known linearization techniques such that the resulting design problem is solved as a mixed-integer linear programming model. In this work, we instead explore whether the QCOpt's model could also be effective with a continuous Non-Linear Programming (NLP) model obtained via relaxation of the integer variables in the non-linear constraints. We are able to present not only multiple significant enhancements to QCOpt, with up to 11.3x speed up in run times on an average, but also opportunities for more generally exploring the behavior of gradient-based NLP solvers.
Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unre-alized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum algorithmic modeling. One such recent development is Quan-tumCircuitOpt (QCOpt), an open-source software framework that leverages state-of-the-art optimization-based solvers to find provably optimal compact circuit decompositions, which are exact up to global phase and machine precision. The quantum circuit design problem can be modeled using non-linear, non-convex constraints. However, QCOpt reformulates these non-linear constraints using well-known linearization techniques such that the resulting design problem is solved as a mixed-integer linear programming model. In this work, we instead explore whether the QCOpt's model could also be effective with a continuous Non-Linear Programming (NLP) model obtained via relaxation of the integer variables in the non-linear constraints. We are able to present not only multiple significant enhancements to QCOpt, with up to 11.3x speed up in run times on an average, but also opportunities for more generally exploring the behavior of gradient-based NLP solvers.
In recent years, the quantum computing community has seen an explosion of novel methods to implement non-trivial quantum computations on near-term hardware. An important direction of research has been to decompose an arbitrary entangled state, represented as a unitary, into a quantum circuit, that is, a sequence of gates supported by a quantum processor. It has been well known that circuits with longer decompositions and more entangling multi-qubit gates are error-prone for the current noisy, intermediate-scale quantum devices. To this end, there has been a significant interest to develop heuristic-based methods to discover compact circuits. We contribute to this effort by proposing QuantumCircuitOpt (QCOpt), a novel open-source framework which implements mathematical optimization formulations and algorithms for decomposing arbitrary unitary gates into a sequence of hardware-native gates. A core innovation of QCOpt is that it provides optimality guarantees on the quantum circuits that it produces. In particular, we show that QCOpt can find up to 57% reduction in the number of necessary gates on circuits with up to four qubits, and in run times less than a few minutes on commodity computing hardware. We also validate the efficacy of QCOpt as a tool for quantum circuit design in comparison with a naive brute-force enumeration algorithm. We also show how the QCOpt package can be adapted to various built-in types of native gate sets, based on different hardware platforms like those produced by IBM, Rigetti and Google. We hope this package will facilitate further algorithmic exploration for quantum processor designers, as well as quantum physicists.
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to solve unconstrained binary programming problems, while mixed-integer linear programming is of most interest in practice. We attempt to bridge the gap between the capability of quantum computing and real-world applications by developing a new approach for mixed-integer programming. The approach applies Benders decomposition to decompose the mixed-integer programming into binary programming and linear programming sub-problems, which are solved by a noisy intermediate-scale quantum processor and conventional processor, respectively. The algorithm is provably able to reach the optimal solution of the original mixed-integer programming problem. The algorithm is tested on a D-Wave 2000Q quantum processing unit and is shown to be effective for small-scaled test cases. We also test the algorithm on a mixed-integer programming inspired by power system applications. Many insights are drawn from the numerical results for both the capabilities and limitations of the proposed algorithm.
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer programming. State-of-the-art integer programming algorithms can compute strong relaxation bounds even for hard instances, but may have to enumerate a large number of subproblems for determining an optimum solution. If the potential of quantum computing is realized, it can be expected that in particular finding high-quality solutions for hard problems can be done fast. Still, near-future quantum hardware considerably limits the size of treatable problems. In this work, we go one step into integrating the potentials of quantum and classical techniques for combinatorial optimization. We propose a hybrid heuristic for the weighted maximum-cut problem and for quadratic unconstrained binary optimization. The heuristic employs a linear programming relaxation, rendering it well-suited for integration into exact branch-and-cut algorithms. For large instances, we reduce the problem size according to a linear relaxation such that the reduced problem can be handled by quantum machines of limited size. Moreover, we improve the applicability of depth-1 QAOA, a parameterized quantum algorithm, by deriving a parameter estimate for arbitrary instances. We present numerous computational results from real quantum hardware.
Quantum computing (QC) is emerging as a new computing resource that could be superior to conventional computing (CC) for certain classes of optimization problems. However, in principle QC can only solve unconstrained binary programming problems, while mixed-integer linear programming (MIP) is of most interest in practice. We attempt to bridge the gap between the capability of QC and real-world applications by developing a new approach for MIP. The idea is decomposing the MIP into binary programming and linear programming (LP) problems, which are respectively solved by QC and conventional computing. We formalize a decomposition approach that ensures that with a sufficient number of back and forth iterations, the algorithm can reach the optimal solution of the original MIP problem. The algorithm is tested on a 2000Q D-Wave quantum processing units (QPU) and is shown to be effective for small-scaled test cases.
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks for power system applications. The main issue of these formulations is the computational complexity of the solution algorithms, as they are considered NP-Hard problems. Quantum computing can give a direct solution to this problem, as it has been experimentally shown that it can provide significant speedups in solving MILPs. In this work, we present a general framework for solving power system optimization problems with a Quantum Computer (QC), which leverages mathematical tools and QCs' sampling ability to provide accelerated solutions. Our guiding applications are the optimal transmission switching and the verification of neural networks trained to solve a DC Optimal Power Flow. Specifically, using an accelerated version of Benders Decomposition , we split a given MILP into an Integer Master Problem and a linear Subproblem and solve it through a hybrid ``quantum-classical'' approach, getting the best of both worlds. We provide 2 use cases, and benchmark the developed framework against other classical and hybrid methodologies, to demonstrate the opportunities and challenges of hybrid quantum-classical algorithms for power system mixed integer optimization problems.
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks for power system applications. The main issue of these formulations is the computational complexity of the solution algorithms, as they are considered NP-Hard problems. Quantum computing has been tested as a potential solution towards reducing the computational burden imposed by these problems, providing promising results, motivating the can be used to speedup the solution of MILPs. In this work, we present a general framework for solving power system optimization problems with a Quantum Computer (QC), which leverages mathematical tools and QCs' sampling ability to provide accelerated solutions. Our guiding applications are the optimal transmission switching and the verification of neural networks trained to solve a DC Optimal Power Flow. Specifically, using an accelerated version of Benders Decomposition , we split a given MILP into an Integer Master Problem and a linear Subproblem and solve it through a hybrid ``quantum-classical'' approach, getting the best of both worlds. We provide 2 use cases, and benchmark the developed framework against other classical and hybrid methodologies, to demonstrate the opportunities and challenges of hybrid quantum-classical algorithms for power system mixed integer optimization problems.