Davide Venturelli

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.

Quantum Optimization of Fully Connected Spin Glasses

The Sherrington-Kirkpatrick model with random

Compiling quantum circuits to realistic hardware architectures using temporal planners

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Quantum Annealing via Environment-Mediated Quantum Diffusion

couplings is programmed on the D-Wave Two annealer featuring 509 qubits interacting on a Chimera-type graph. The performance of the optimizer compares and correlates to simulated annealing. When considering the effect of the static noise, which degrades the performance of the annealer, one can estimate an improvement on the comparative scaling of the two methods in favor of the D-Wave machine. The optimal choice of parameters of the embedding on the Chimera graph is shown to be associated to the emergence of the spin-glass critical temperature of the embedded problem.

A NASA perspective on quantum computing

To run quantum algorithms on emerging gate-model quantum hardware, quantum circuits must be compiled to take into account constraints on the hardware. For near-term hardware, with only limited means to mitigate decoherence, it is critical to minimize the duration of the circuit. We investigate the application of temporal planners to the problem of compiling quantum circuits to newly emerging quantum hardware. While our approach is general, we focus on compiling to superconducting hardware architectures with nearest neighbor constraints. Our initial experiments focus on compiling Quantum Alternating Operator Ansatz (QAOA) circuits whose high number of commuting gates allow great flexibility in the order in which the gates can be applied. That freedom makes it more challenging to find optimal compilations but also means there is a greater potential win from more optimized compilation than for less flexible circuits. We map this quantum circuit compilation problem to a temporal planning problem, and generated a test suite of compilation problems for QAOA circuits of various sizes to a realistic hardware architecture. We report compilation results from several state-of-the-art temporal planners on this test set. This early empirical evaluation demonstrates that temporal planning is a viable approach to quantum circuit compilation.

Temporal Planning for Compilation of Quantum Approximate Optimization Circuits

We show that quantum diffusion near a quantum critical point can provide an efficient mechanism of quantum annealing. It is based on the diffusion-mediated recombination of excitations in open systems far from thermal equilibrium. We find that, for an Ising spin chain coupled to a bosonic bath and driven by a monotonically decreasing transverse field, excitation diffusion sharply slows down below the quantum critical region. This leads to spatial correlations and effective freezing of the excitation density. Still, obtaining an approximate solution of an optimization problem via the diffusion-mediated quantum annealing can be faster than via closed-system quantum annealing or Glauber dynamics.

Comparing planning problem compilation approaches for quantum annealing

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 Annealing Implementation of Job-Shop Scheduling

We investigate the application of temporal planners to the problem of compiling quantum circuits to emerging quantum hardware. While our approach is general, we focus our initial experiments on Quantum Approximate Optimization Algorithm (QAOA) circuits that have few ordering constraints and thus allow highly parallel plans. We report on experiments using several temporal planners to compile circuits of various sizes to a realistic hardware architecture. This early empirical evaluation suggests that temporal planning is a viable approach to quantum circuit compilation.

Parametrized families of hard planning problems from phase transitions

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.