arXiv subjects

Sebastian Brandhofer

Publications and source records attributed to Sebastian Brandhofer.

16 recordsLinked to original sources

arXiv2026

Quantum Approximate Optimization via Noise-Directed Adaptive Warm-Starting

Progress towards a quantum advantage using known heuristic methods for combinatorial optimization is impeded by hardware noise and limited qubit count. Here, we propose a noise-aware adaptive approach to quantum approximate optimization, Noise-Directed Adaptive Warm-Starting (ND-AWS), that builds on recent concepts such as Warm-Start QAOA and Noise-Directed Adaptive Remapping. By leveraging bitflip gauge transformations, our algorithm exploits amplitude-damping-like noise components. We experimentally implement high-performance quantum optimization ans\"atze on 100-qubit Ising Hamiltonians, showing that ND-AWS generally improves the performance over a non-gauge-transformed iterative Warm-Starting variant, at no additional circuit cost. This places our results among the highest-quality demonstrations of quantum optimization with similar ans\"atze at this scale. Crucially, the simplicity of the framework opens the door for future enhancements such as adaptive bias schedules, and integration with classical solvers.

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arXiv2026

Setting angles in quantum approximate optimization at utility-scale

The quantum approximate optimization algorithm (QAOA) is a powerful heuristic that seeks to solve combinatorial optimization problems using quantum hardware and classical optimization in tandem. Various methods exist to train the parameterized quantum circuits that serve as an ansatz in QAOA. However, which method works best to identify optimal angles for a given problem instance remains poorly understood, especially at utility-scale, i.e., $100$ qubits or more. In this work, we address this challenge through utility-scale benchmarks from which we distill operational guidance for QAOA practitioners. First, we investigate approximation techniques, such as matrix product states and Pauli propagation, to find optimal angles. Second, we train QAOA on small-scale representative problems and transfer the angles to larger ones. We then validate the results on quantum hardware for utility-scale problem instances that can be meaningfully executed. In this way, we identify insights for QAOA angle setting strategies that work best for problems at the utility scale, including as a function of resource cost for the search. Crucially, the operational implications we draw from our benchmarks will help quantum optimization practitioners execute QAOA end-to-end pipelines efficiently on current and future hardware.

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arXiv2026

Quantum-enhanced Markov Chain Monte Carlo for Combinatorial Optimization

Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales known to be hard for state-of-the-art classical solvers is not yet in reach. In this work, we offer a different way to approach combinatorial optimization with near-term quantum computing. Motivated by the promising results observed in using quantum-enhanced Markov chain Monte Carlo (QeMCMC) for approximating complicated probability distributions, we combine ideas of sampling from the device with QeMCMC together with warm-starting and parallel tempering, in the context of combinatorial optimization. We demonstrate empirically that our algorithm recovers the global optima for instances of the Maximum Independent Set problem (MIS) up to 117 decision variables using 117 qubits on IBM quantum hardware. We show early evidence of a scaling advantage of our algorithm compared to similar classical methods for the chosen instances of MIS. MIS is practically relevant across domains like financial services and molecular biology, and, in some cases, already difficult to solve to optimality classically with only a few hundred decision variables.

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arXiv2025

Approximate quantum circuit compilation for proton-transfer kinetics on quantum processors

Proton transfer reactions are fundamental to many chemical and biological systems, where quantum effects such as tunneling, delocalization, and zero-point motion play key kinetic control roles. However, classical methods capable of accurately capturing these phenomena scale prohibitively with system size. Here, we develop and demonstrate quantum computing algorithms based on the Nuclear-Electronic Orbital framework, treating the transferring proton quantum mechanically. We assess the potential of current quantum devices for simulating proton transfer kinetics with high accuracy. We first construct a deep initial ans\"atze within a truncated orbital space by employing the frozen natural orbital approximation. Then, to balance circuit depth against state fidelity, we implement an adaptive form of approximate quantum compiling. Using resulting circuits at varying compression levels transpiled for the ibm_fez device, we compute barrier heights and delocalised proton densities along the proton transfer pathway using a realistic hardware noise model. We find that, although current quantum hardware introduces significant noise relative to the demanding energy tolerances involved, our approach allows substantial circuit simplification while maintaining energy barrier estimates within 13% of the reference value. Despite present hardware limitations, these results offer a practical means of approximating key circuit segments in near-term devices and early fault-tolerant quantum computing systems.

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arXiv2024

Hardware-Efficient Preparation of Graph States on Near-Term Quantum Computers

Highly entangled quantum states are an ingredient in numerous applications in quantum computing. However, preparing these highly entangled quantum states on currently available quantum computers at high fidelity is limited by ubiquitous errors. Besides improving the underlying technology of a quantum computer, the scale and fidelity of these entangled states in near-term quantum computers can be improved by specialized compilation methods. In this work, the compilation of quantum circuits for the preparation of highly entangled architecture-specific graph states is addressed by defining and solving a formal model. Our model incorporates information about gate cancellations, gate commutations, and accurate gate timing to determine an optimized graph state preparation circuit. Up to now, these aspects have only been considered independently of each other, typically applied to arbitrary quantum circuits. We quantify the quality of a generated state by performing stabilizer measurements and determining its fidelity. We show that our new method reduces the error when preparing a seven-qubit graph state by 3.5x on average compared to the state-of-the-art Qiskit solution. For a linear eight-qubit graph state, the error is reduced by 6.4x on average. The presented results highlight the ability of our approach to prepare higher fidelity or larger-scale graph states on gate-based quantum computing hardware.

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arXiv2024

Benchmarking the performance of quantum computing software

We present Benchpress, a benchmarking suite for evaluating the performance and range of functionality of multiple quantum computing software development kits. This suite consists of a collection of over $1000$ tests measuring key performance metrics for a wide variety of operations on quantum circuits comprised of up to $930$ qubits and $\mathcal{O}(10^{6})$ two-qubit gates, as well as an execution framework for running the tests over multiple quantum software packages in a unified manner. We give a detailed overview of the benchmark suite, its methodology, and generate representative results over seven different quantum software packages. The flexibility of the Benchpress framework allows for benchmarking that not only keeps pace with quantum hardware improvements but can preemptively gauge the quantum circuit processing costs of future device architectures. Being open-source, Benchpress ensures the transparency and verification of performance claims.

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arXiv2023

Optimal Partitioning of Quantum Circuits using Gate Cuts and Wire Cuts

A limited number of qubits, high error rates, and limited qubit connectivity are major challenges for effective near-term quantum computations. Quantum circuit partitioning divides a quantum computation into a set of computations that include smaller-scale quantum (sub)circuits and classical postprocessing steps. These quantum subcircuits require fewer qubits, incur a smaller effort for satisfying qubit connectivity requirements, and typically incur less error. Thus, quantum circuit partitioning has the potential to enable quantum computations that would otherwise only be available on more matured hardware. However, partitioning quantum circuits generally incurs an exponential increase in quantum computing runtime by repeatedly executing quantum subcircuits. Previous work results in non-optimal subcircuit executions hereby limiting the scope of quantum circuit partitioning. In this work, we develop an optimal partitioning method based on recent advances in quantum circuit knitting. By considering wire cuts and gate cuts in conjunction with ancilla qubit insertions and classical communication, the developed method can determine a minimal cost quantum circuit partitioning. Compared to previous work, we demonstrate the developed method to reduce the overhead in quantum computing time by 73% on average for 56% of evaluated quantum circuits. Given a one hour runtime budget on a typical near-term quantum computer, the developed method could reduce the qubit requirement of the evaluated quantum circuits by 40% on average. These results highlight the ability of the developed method to extend the computational reach of near-term quantum computers by reducing the qubit requirement at a lower increase in quantum circuit executions.

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arXiv2023

Optimal Qubit Reuse for Near-Term Quantum Computers

Near-term quantum computations are limited by high error rates, the scarcity of qubits and low qubit connectivity. Increasing support for mid-circuit measurements and qubit reset in near-term quantum computers enables qubit reuse that may yield quantum computations with fewer qubits and lower errors. In this work, we introduce a formal model for qubit reuse optimization that delivers provably optimal solutions with respect to quantum circuit depth, number of qubits, or number of swap gates for the first time. This is in contrast to related work where qubit reuse is used heuristically or optimally but without consideration of the mapping effort. We further investigate reset errors on near-term quantum computers by performing reset error characterization experiments. Using the hereby obtained reset error characterization and calibration data of a near-term quantum computer, we then determine a qubit assignment that is optimal with respect to a given cost function. We define this cost function to include gate errors and decoherence as well as the individual reset error of each qubit. We found the reset fidelity to be state-dependent and to range, depending on the reset qubit, from 67.5% to 100% in a near-term quantum computer. We demonstrate the applicability of the developed method to a number of quantum circuits and show improvements in the number of qubits and swap gate insertions, estimated success probability, and Hellinger fidelity of the investigated quantum circuits.

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arXiv2023

ArsoNISQ: Analyzing Quantum Algorithms on Near-Term Architectures

While scalable, fully error corrected quantum computing is years or even decades away, there is considerable interest in noisy intermediate-scale quantum computing (NISQ). In this paper, we introduce the ArsoNISQ framework that determines the tolerable error rate of a given quantum algorithm computation, i.e. quantum circuits, and the success probability of the computation given a success criterion and a NISQ computer. ArsoNISQ is based on simulations of quantum circuits subject to errors according to the Pauli error model. ArsoNISQ was evaluated on a set of quantum algorithms that can incur a quantum speedup or are otherwise relevant to NISQ computing. Despite optimistic expectations in recent literature, we did not observe quantum algorithms with intrinsic robustness, i.e. algorithms that tolerate one error on average, in this evaluation. The evaluation demonstrated, however, that the quantum circuit size sets an upper bound for its tolerable error rate and quantified the difference in tolerate error rates for quantum circuits of similar sizes. Thus, the framework can assist quantum algorithm developers in improving their implementation and selecting a suitable NISQ computing platform. Extrapolating the results into the quantum advantage regime suggests that the error rate of larger quantum computers must decrease substantially or active quantum error correction will need to be deployed for most of the evaluated algorithms.

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arXiv2023

SAT-Based Quantum Circuit Adaptation

As the nascent field of quantum computing develops, an increasing number of quantum hardware modalities, such as superconducting electronic circuits, semiconducting spins, trapped ions, and neutral atoms, have become available for performing quantum computations. These quantum hardware modalities exhibit varying characteristics and implement different universal quantum gate sets that may e.g. contain several distinct two-qubit quantum gates. Adapting a quantum circuit from a, possibly hardware-agnostic, universal quantum gate set to the quantum gate set of a target hardware modality has a crucial impact on the fidelity and duration of the intended quantum computation. However, current quantum circuit adaptation techniques only apply a specific decomposition or allow only for local improvements to the target quantum circuit potentially resulting in a quantum computation with less fidelity or more qubit idle time than necessary. These issues are further aggravated by the multiple options of hardware-native quantum gates rendering multiple universal quantum gates sets accessible to a hardware modality. In this work, we developed a satisfiability modulo theories model that determines an optimized quantum circuit adaptation given a set of allowed substitutions and decompositions, a target hardware modality and the quantum circuit to be adapted. We further discuss the physics of the semiconducting spins hardware modality, show possible implementations of distinct two-qubit quantum gates, and evaluate the developed model on the semiconducting spins hardware modality. Using the developed quantum circuit adaptation method on a noisy simulator, we show the Hellinger fidelity could be improved by up to 40% and the qubit idle time could be decreased by up to 87% compared to alternative quantum circuit adaptation techniques.

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arXiv2023

Special Session: Noisy Intermediate-Scale Quantum (NISQ) Computers -- How They Work, How They Fail, How to Test Them?

First quantum computers very recently have demonstrated "quantum supremacy" or "quantum advantage": Executing a computation that would have been impossible on a classical machine. Today's quantum computers follow the NISQ paradigm: They exhibit error rates that are much higher than in conventional electronics and have insufficient quantum resources to support powerful error correction protocols. This raises questions which relevant computations are within the reach of NISQ architectures. Several "NISQ-era algorithms" are assumed to match the specifics of such computers; for instance, variational optimisers are based on intertwining relatively short quantum and classical computations, thus maximizing the chances of success. This paper will critically assess the promise and challenge of NISQ computing. What has this field achieved so far, what are we likely to achieve soon, where do we have to be skeptical and wait for the advent of larger-scale fully error-corrected architectures?

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arXiv2023

Multiplexed Pseudo-Deterministic Photon Source with Asymmetric Switching Elements

The reliable, deterministic production of trustworthy high-quality single photons is a critical component of discrete variable, optical quantum technology. For single-photon based fully error-corrected quantum computing systems, it is estimated that photon sources will be required to produce a reliable stream of photons at rates exceeding 1 GHz [1]. Photon multiplexing, where low probability sources are combined with switching networks to route successful production events to an output, are a potential solution but requires extremely fast single photon switching with ultra-low loss rates. In this paper we examine the specific properties of the switching elements and present a new design that exploits the general one-way properties of common switching elements such as thermal pads. By introducing multiple switches to a basic, temporal multiplexing device, we are able to use slow switching elements in a multiplexed source being pumped at much faster rates. We model this design under multiple error channels and show that anticipated performance is now limited by the intrinsic loss rate of the optical waveguides within integrated photonic chipsets.

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arXiv2023

Error Analysis of the Variational Quantum Eigensolver Algorithm

Variational quantum algorithms have been one of the most intensively studied applications for near-term quantum computing applications. The noisy intermediate-scale quantum (NISQ) regime, where small enough algorithms can be run successfully on noisy quantum computers expected during the next 5 years, is driving both a large amount of research work and a significant amount of private sector funding. Therefore, it is important to understand whether variational algorithms are effective at successfully converging to the correct answer in presence of noise. We perform a comprehensive study of the variational quantum eigensolver (VQE) and its individual quantum subroutines. Building on asymptotic bounds, we show through explicit simulation that the VQE algorithm effectively collapses already when single errors occur during a quantum processing call. We discuss the significant implications of this result in the context of being able to run any variational type algorithm without resource expensive error correction protocols.

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arXiv2022

Benchmarking the performance of portfolio optimization with QAOA

We present a detailed study of portfolio optimization using different versions of the quantum approximate optimization algorithm (QAOA). For a given list of assets, the portfolio optimization problem is formulated as quadratic binary optimization constrained on the number of assets contained in the portfolio. QAOA has been suggested as a possible candidate for solving this problem (and similar combinatorial optimization problems) more efficiently than classical computers in the case of a sufficiently large number of assets. However, the practical implementation of this algorithm requires a careful consideration of several technical issues, not all of which are discussed in the present literature. The present article intends to fill this gap and thereby provide the reader with a useful guide for applying QAOA to the portfolio optimization problem (and similar problems). In particular, we will discuss several possible choices of the variational form and of different classical algorithms for finding the corresponding optimized parameters. Viewing at the application of QAOA on error-prone NISQ hardware, we also analyze the influence of statistical sampling errors (due to a finite number of shots) and gate and readout errors (due to imperfect quantum hardware). Finally, we define a criterion for distinguishing between "easy" and "hard" instances of the portfolio optimization problem

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arXiv2022

Calibration-Aware Transpilation for Variational Quantum Optimization

Today's Noisy Intermediate-Scale Quantum (NISQ) computers support only limited sets of available quantum gates and restricted connectivity. Therefore, quantum algorithms must be transpiled in order to become executable on a given NISQ computer; transpilation is a complex and computationally heavy process. Moreover, NISQ computers are affected by noise that changes over time, and periodic calibration provides relevant error rates that should be considered during transpilation. Variational algorithms, which form one main class of computations on NISQ platforms, produce a number of similar yet not identical quantum ``ansatz'' circuits. In this work, we present a transpilation methodology optimized for variational algorithms under potentially changing error rates. We divide transpilation into three steps: (1) noise-unaware and computationally heavy pre-transpilation; (2) fast noise-aware matching; and (3) fast decomposition followed by heuristic optimization. For a complete run of a variational algorithm under constant error rates, only step (3) needs to be executed for each new ansatz circuit. Step (2) is required only if the error rates reported by calibration have changed significantly since the beginning of the computation. The most expensive Step (1) is executed only once for the whole run. This distribution is helpful for incremental, calibration-aware transpilation when the variational algorithm adapts its own execution to changing error rates. Experimental results on IBM's quantum computer show the low latency and robust results obtained by calibration-aware transpilation.

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arXiv2021

Optimal Mapping for Near-Term Quantum Architectures based on Rydberg Atoms

Quantum algorithms promise quadratic or exponential speedups for applications in cryptography, chemistry and material sciences. The topologies of today's quantum computers offer limited connectivity, leading to significant overheads for implementing such quantum algorithms. One-dimensional topology displacements that remedy these limits have been recently demonstrated for architectures based on Rydberg atoms, and they are possible in principle in photonic and ion trap architectures. We present the first optimal quantum circuit-to-architecture mapping algorithm that exploits such one-dimensional topology displacements. We benchmark our method on quantum circuits with up to 15 qubits and investigate the improvements compared with conventional mapping based on inserting swap gates into the quantum circuits. Depending on underlying technology parameters, our approach can decrease the quantum circuit depth by up to 58% and increase the fidelity by up to 29%. We also study runtime and fidelity requirements on one-dimensional displacements and swap gates to derive conditions under which one-dimensional topology displacements provide benefits.

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