Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum controls under uncertainties. In this paper, we consider a stochastic discrete optimization formulation of a discretized binary optimal quantum control problem involving Hamiltonians with predictable uncertainties. We propose a sample-based reformulation that optimizes both risk-neutral and risk-averse measurements of control policies, and solve these with two gradient-based algorithms using sum-up-rounding approaches. Furthermore, we discuss the differentiability of the objective function and prove upper bounds of the gaps between the optimal solutions to binary control problems and their continuous relaxations. We conduct numerical simulations on various sized problem instances based on two applications of quantum pulse optimization; we evaluate different strategies to mitigate the impact of uncertainties in quantum systems. We demonstrate that the controls of our stochastic optimization model achieve significantly higher quality and robustness compared with the controls of a deterministic model. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This work was supported by the US Department of Energy, Advanced Scientific Computing Research [Grants DE-AC02-06CH11357, DE-SC0018018]; Defense Sciences Office, DARPA [Grant IAA-8839-annex-130]; the US National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation [Grant 2041745]; and the US National Aeronautics and Space Administration (NASA) Ames Research Center [Grant 80ARC020D0010]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0560 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0560 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily be run on noisy devices with limited fidelities. Thus, the evaluation of an objective function (e.g., the guiding function in the quantum approximate optimization algorithm (QAOA) or the expectation of the electronic Hamiltonian in variational quantum eigensolver (VQE)) required by a classical optimizer is subject not only to stochastic error from estimating an expected value but also to error resulting from intermittent hardware noise. Model-based derivative-free optimization methods have emerged as popular choices of a classical optimizer in the noisy VQA setting, based on empirical studies. However, these optimization methods were not explicitly designed with the consideration of noise. In this work we adapt recent developments from the “noise-aware numerical optimization” literature to these commonly used derivative-free model-based methods. We introduce the key defining characteristics of these novel noise-aware derivative-free model-based methods that separate them from standard model-based methods. We study an implementation of such noise-aware derivative-free model-based methods and compare its performance on demonstrative VQA simulations to classical solvers packaged in scikit-quant. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers and the Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing program under contract number DE-AC02-06CH11357. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0578 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0578 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical optimization and computing techniques to develop an algorithmic framework that sequentially optimizes the number of control switches and the duration of each control interval on a continuous time horizon. Specifically, we first solve the continuous relaxation of the binary control problem based on time discretization and then use a heuristic to obtain a controller sequence with a penalty on the number of switches. Then, we formulate a switching time optimization model and apply sequential least-squares programming with accelerated time-evolution simulation to solve the model. We demonstrate that our computational framework can obtain binary controls with high-quality performance and also reduce computational time via solving a family of quantum control instances in various quantum physics applications.

In this paper we propose QContext, a new com-piler structure that incorporates context-aware and topology- aware decompositions. Because of circuit equivalence rules and resynthesis, variants of a gate-decomposition template may exist. QContext exploits the circuit information and the hardware topology to select the gate variant that increases circuit optimization opportunities. We study the basis-gate-level context-aware decomposition for Toffoli gates and the native-gate-level context- aware decomposition for CNOT gates. Our experiments show that QContext reduces the number of gates as compared with the state-of-the-art approach, Orchestrated Trios [12].

While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can mitigate the effects of imperfect hardware by optimizing quantum circuits for objectives such as critical path length. Few approaches consider quantum circuits in terms of the set of vendor-calibrated operations (i.e., native gates) available on target hardware. This manuscript expands the analytical and numerical approaches for optimizing quantum circuits at this abstraction level. We present a procedure for combining the strengths of analytical native gate-level optimization with numerical optimization. Although we focus on optimizing Toffoli gates on the IBMQ native gate set, the methods presented are generalizable to any gate and superconducting qubit architecture. Our optimized Toffoli gate implementation demonstrates an 18% reduction in infidelity compared with the canonical implementation as benchmarked on IBM Jakarta with quantum process tomography. Assuming the inclusion of multi-qubit cross-resonance (MCR) gates in the IBMQ native gate set, we produce Toffoli implementations with only six multi-qubit gates, a 25% reduction from the canonical eight multi-qubit implementations for linearly connected qubits.

Finding high-quality parameters is a central obstacle to using the quantum approximate optimization algorithm (QAOA). Previous work partially addresses this issue for QAOA on unweighted MaxCut problems by leveraging similarities in the objective landscape among different problem instances. However, we show that the more general weighted MaxCut problem has significantly modified objective landscapes, with a proliferation of poor local optima. Our main contribution is a simple rescaling scheme that overcomes these deleterious effects of weights. We show that for a given QAOA depth, a single “typical” vector of QAOA parameters can be successfully transferred to weighted MaxCut instances. This transfer leads to a median decrease in the approximation ratio of only 2.0 percentage points relative to a considerably more expensive direct optimization on a dataset of 34,701 instances with up to 20 nodes and multiple weight distributions. This decrease can be reduced to 1.2 percentage points at the cost of only 10 additional QAOA circuit evaluations with parameters sampled from a pretrained metadistribution, or the transferred parameters can be used as a starting point for a single local optimization run to obtain approximation ratios equivalent to those achieved by exhaustive optimization in 96.35% of our cases.

While showing great promise, circuit synthesis techniques that combine numerical optimization with search over circuit structures face scalability challenges due to a large number of parameters, exponential search spaces, and complex objective functions. The LEAP algorithm improves scaling across these dimensions using iterative circuit synthesis, incremental re-optimization, dimensionality reduction, and improved numerical optimization. LEAP draws on the design of the optimal synthesis algorithm QSearch by extending it with an incremental approach to determine constant prefix solutions for a circuit. By narrowing the search space, LEAP improves scalability from four to six qubit circuits. LEAP was evaluated with known quantum circuits such as QFT and physical simulation circuits like the VQE, TFIM, and QITE. LEAP can compile four qubit unitaries up to $59\times$ faster than QSearch and five and six qubit unitaries with up to $1.2\times$ fewer CNOTs compared to the QFAST package. LEAP can reduce the CNOT count by up to $36\times$, or $7\times$ on average, compared to the CQC Tket compiler. Despite its heuristics, LEAP has generated optimal circuits for many test cases with a priori known solutions. The techniques introduced by LEAP are applicable to other numerical-optimization-based synthesis approaches.

Introducing additional tunable parameters to quantum circuits is a powerful way of improving per-formance without increasing hardware requirements. A recently introduced multiangle extension of the quantum approximate optimization algorithm (ma-QAOA) signifi-cantly improves the solution quality compared with QAOA by allowing the parameters for each term in the Hamilto-nian to vary independently. Prior results suggest, however, considerable redundancy in parameters, the removal of which would reduce the cost of parameter optimization. In this work we show numerically the connection between the problem symmetries and the parameter redundancy by demonstrating that symmetries can be used to reduce the number of parameters used by ma-QAOA without decreasing the solution quality. We study Max-Cut on all 7,565 connected, non-isomorphic 8-node graphs with a nontrivial symmetry group and show numerically that in 67.4% of these graphs, symmetry can be used to reduce the number of parameters with no decrease in the objective, with the average ratio of parameters reduced by 28.1%. Moreover, we show that in 35.9% of the graphs this reduction can be achieved by simply using the largest symmetry. For the graphs where reducing the number of parameters leads to a decrease in the objective, the largest symmetry can be used to reduce the parameter count by 37.1% at the cost of only a 6.1% decrease in the objective. We demonstrate the central role of symmetries by showing that a random parameter reduction strategy leads to much worse performance.

VTMOP is a Fortran 2008 software package containing two Fortran modules for solving computationally expensive bound-constrained blackbox multiobjective optimization problems. VTMOP implements the algorithm of [ 32 ], which handles two or more objectives, does not require any derivatives, and produces well-distributed points over the Pareto front. The first module contains a general framework for solving multiobjective optimization problems by combining response surface methodology, trust region methodology, and an adaptive weighting scheme. The second module features a driver subroutine that implements this framework when the objective functions can be wrapped as a Fortran subroutine. Support is provided for both serial and parallel execution paradigms, and VTMOP is demonstrated on several test problems as well as one real-world problem in the area of particle accelerator optimization.

Almost all applications stop scaling at some point; those that don't are seldom performant when considering time to solution on anything but aspirational/unicorn resources. Recognizing these tradeoffs as well as greater user functionality in a near-term exascale computing era, we present libEnsemble, a library aimed at particular scalability- and capability-stretching uses. libEnsemble enables running concurrent instances of an application in dynamically allocated ensembles through an extensible Python library. We highlight the structure, execution, and capabilities of the library on leading pre-exascale environments as well as advanced capabilities for exascale environments and beyond.

Quantum computing (QC) is a new paradigm offering the potential of exponential speedups over classical computing for certain computational problems. Each additional qubit doubles the size of the computational state space available to a QC algorithm. This exponential scaling underlies QC’s power, but today’s Noisy Intermediate-Scale Quantum (NISQ) devices face significant engineering challenges in scalability. The set of quantum circuits that can be reliably run on NISQ devices is limited by their noisy operations and low qubit counts. This paper introduces CutQC, a scalable hybrid computing approach that combines classical computers and quantum computers to enable evaluation of quantum circuits that cannot be run on classical or quantum computers alone. CutQC cuts large quantum circuits into smaller subcircuits, allowing them to be executed on smaller quantum devices. Classical postprocessing can then reconstruct the output of the original circuit. This approach offers significant runtime speedup compared with the only viable current alternative—purely classical simulations—and demonstrates evaluation of quantum circuits that are larger than the limit of QC or classical simulation. Furthermore, in real-system runs, CutQC achieves much higher quantum circuit evaluation fidelity using small prototype quantum computers than the state-of-the-art large NISQ devices achieve. Overall, this hybrid approach allows users to leverage classical and quantum computing resources to evaluate quantum programs far beyond the reach of either one alone.

Heavy-duty vehicles (HDVs) traveling in single file with small intervehicle distances experience reduced aerodynamic drag and, therefore, have improved fuel economy. In this paper, we attempt to maximize the amount of fuel saved by coordinating platoon formation using a distributed network of controllers. These virtual controllers, placed at major intersections in a road network, help coordinate the velocity of approaching vehicles so they arrive at the junction simultaneously and can therefore platoon. This control is initiated only if the cost of forming the platoon is smaller than the savings incurred from platooning. In a large-scale simulation of the German Autobahn network, we observe that savings surpassing 5% when only a few thousand vehicles participate in the system. These results are corroborated by an analysis of real-world HDV data that show significant platooning opportunities currently exist, suggesting that a slightly invasive network of distributed controllers, such as the one proposed in this paper, can yield considerable savings.