Bryan O'Gorman

A case study in programming a quantum annealer for hard operational planning problems

We report on a case study in programming an early quantum annealer to attack optimization problems related to operational planning. While a number of studies have looked at the performance of quantum annealers on problems native to their architecture, and others have examined performance of select problems stemming from an application area, ours is one of the first studies of a quantum annealer’s performance on parametrized families of hard problems from a practical domain. We explore two different general mappings of planning problems to quadratic unconstrained binary optimization (QUBO) problems, and apply them to two parametrized families of planning problems, navigation-type and scheduling-type. We also examine two more compact, but problem-type specific, mappings to QUBO, one for the navigation-type planning problems and one for the scheduling-type planning problems. We study embedding properties and parameter setting and examine their effect on the efficiency with which the quantum annealer solves these problems. From these results, we derive insights useful for the programming and design of future quantum annealers: problem choice, the mapping used, the properties of the embedding, and the annealing profile all matter, each significantly affecting the performance.

Resource efficient gadgets for compiling adiabatic quantum optimization problems

A resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a -local, optimization Hamiltonian is developed. This result is important because adiabatic quantum algorithms are often most easily formulated using many-body interactions but experimentally available interactions are generally 2-body. In this context, the efficiency of a reduction gadget is measured by the number of ancilla qubits required as well as the amount of control precision needed to implement the resulting Hamiltonian. First, methods of applying these gadgets to obtain 2-local Hamiltonians using the least possible number of ancilla qubits are optimized. Next, a novel reduction gadget which minimizes control precision and a heuristic which uses this gadget to compile 3-local problems with a significant reduction in control precision are shown. Finally, numerics are presented which indicate a substantial decrease in the resources required to implement randomly generated, 3-body optimization Hamiltonians when compared to other methods in the literature.

Construction of Energy Functions for Lattice Heteropolymer Models: Efficient Encodings for Constraint Satisfaction Programming and Quantum Annealing

Optimization problems associated with the interaction of linked particles are at the heart of polymer science, protein folding and other important problems in the physical sciences. In this review we explain how to recast these problems as constraint satisfaction problems such as linear programming, maximum satisability, and pseudo-boolean optimization. By encoding problems this way, one can leverage substantial insight and powerful solvers from the computer science community which studies constraint programming for diverse applications such as logistics, scheduling, articial intelligence, and circuit design. We demonstrate how to constrain and embed lattice heteropolymer problems using several strategies. Each strikes a unique balance between number of constraints, complexity of constraints, and number of variables. In addition, each strategy has distinct advantages and disadvantages depending on problem size and available resources. Finally, we show how to reduce the locality of couplings in these energy functions so they can be realized as Hamiltonians on existing adiabatic quantum annealing machines.

Determination and Correction of Persistent Biases in Quantum Annealers

Calibration of quantum computers is essential to the effective utilisation of their quantum resources. Specifically, the performance of quantum annealers is likely to be significantly impaired by noise in their programmable parameters, effectively misspecification of the computational problem to be solved, often resulting in spurious suboptimal solutions. We developed a strategy to determine and correct persistent, systematic biases between the actual values of the programmable parameters and their user-specified values. We applied the recalibration strategy to two D-Wave Two quantum annealers, one at NASA Ames Research Center in Moffett Field, California, and another at D-Wave Systems in Burnaby, Canada. We show that the recalibration procedure not only reduces the magnitudes of the biases in the programmable parameters but also enhances the performance of the device on a set of random benchmark instances.

A NASA perspective on quantum computing

NASA Perspective on Quantum Computing. In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can provide an advantage, and if so by how much, or how to design quantum algorithms that realize such advantages. Many of the most challenging computational problems arising in the practical world are tackled today by heuristic algorithms that have not been mathematically proven to outperform other approaches but have been shown to be effective empirically. While quantum heuristic algorithms have been proposed, empirical testing becomes possible only as quantum computation hardware is built. The next few years will be exciting as empirical testing of quantum heuristic algorithms becomes more and more feasible. While large-scale universal quantum computers are likely decades away, special-purpose quantum computational hardware has begun to emerge, which will become more powerful over time, as well as small-scale universal quantum computers.

Quantum Approximate Optimization with Hard and Soft Constraints

Challenging computational problems arising in the practical world are frequently tackled by heuristic algorithms. Small universal quantum computers will emerge in the next year or two, enabling a substantial broadening of the types of quantum heuristics that can be investigated beyond quantum annealing. The immediate question is: what experiments should we prioritize that will give us insight into quantum heuristics? One leading candidate is the quantum approximate optimization algorithm (QAOA) metaheuristic. In this work, we provide a framework for designing QAOA circuits for a variety of combinatorial optimization problems with both hard constraints that must be met and soft constraints whose violation we wish to minimize. We work through a number of examples, and discuss design principles.

Comparing planning problem compilation approaches for quantum annealing

One approach to solving planning problems is to compile them to other problems for which powerful off-the-shelf solvers are available; common targets include SAT, CSP, and MILP. Recently, a novel optimization technique has become available: quantum annealing (QA). QA takes as input problem instances of quadratic unconstrained binary optimization (QUBO) problem. Early quantum annealers are now available, though their constraints restrict the types of QUBOs they can take as input. Here, we introduce the planning community to the key steps in compiling planning problems to QA hardware: a hardware-independent step, mapping, and a hardware-dependent step, embedding. After describing two approaches to mapping general planning problems to QUBO, we describe preliminary results from running an early quantum annealer on a parametrized family of hard planning problems. The results show that different mappings can substantially affect performance, even when many features of the resulting instances are similar. We conclude with insights gained from this early study that suggest directions for future work.