arXiv subjects

Adam Glos

Publications and source records attributed to Adam Glos.

At least 19 recordsLinked to original sources

arXiv2026

Scalable quantum circuit generation for iterative ground state approximation using Majorana Propagation

We introduce the Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Majorana Propagation Eigensolver (ADAPT-VMPE), a quantum-inspired classical algorithm that exploits Majorana Propagation (MP) to produce circuits for approximating the ground state of molecular Hamiltonians. Equipped with the theoretical guarantees of MP, which provide controllable bounds on the approximation error, ADAPT-VMPE offers an efficient and scalable approach for iterative ansatz construction. A theoretical analysis of the computational complexity demonstrates that it is polynomial in both the number of qubits and the number of iterations. We present an in-depth analysis of circuit construction strategies, analyzing their impact on convergence and provide practical guidance for efficient ansatz generation. Using ADAPT-VMPE, we construct up to 100-qubit ans\"atze for a strongly correlated photosensitizer currently undergoing human clinical trials for cancer treatment. Our results demonstrate that constant overlap with the ground state across system sizes can be reached in polynomial time with polynomially sized circuits.

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arXiv2025

Simulation of Fermionic circuits using Majorana Propagation

We introduce Majorana Propagation, an algorithmic framework for the classical simulation of Fermionic circuits. Inspired by Pauli Propagation, Majorana Propagation operates by applying successive truncations throughout the Heisenberg evolution of the observable. We identify monomial length as an effective truncation strategy for typical, unstructured circuits by proving that high-length Majorana monomials are exponentially unlikely to contribute to expectation values and the backflow of high-length monomials to lower-length monomials is quadratically suppressed. We provide performance guarantees by proving analytically that approximation errors decrease exponentially with the truncation threshold and that only polynomial resources are required to compute the expectation value of observables up to a fixed error for an ensemble of circuits relevant to quantum chemistry. Majorana Propagation can be used either independently, or in conjunction with quantum hardware, to simulate Fermionic systems relevant to quantum chemistry and condensed matter. We exemplify this by using Majorana Propagation to find circuits that approximate ground states for strongly correlated systems of up to 52 Fermionic modes. Our results indicate that Majorana Propagation is orders of magnitude faster and more accurate than state-of-the-art tensor-network-based circuit simulators.

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arXiv2024

A generic multi-Pauli compilation framework for limited connectivity

Efficient and effective compilation of quantum circuits remains an important aspect of executing quantum programs. In this paper, we propose a generic compilation framework particularly suitable for limited connectivity, that extends many of the known techniques for Pauli network synthesis. Our compilation method, built on the introduced Clifford Executive Representation, stands out by considering the implementation of multiple Pauli operators at once, which are not necessarily commuting. The proposed technique also allows for effective Clifford circuit synthesis. We benchmark our methods against circuits resulting from the Variational Quantum Eigensolver algorithm and the results show that the proposed methods outperform the state-of-the-art.

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arXiv2024

Practical techniques for high-precision measurements on near-term quantum hardware and applications in molecular energy estimation

Achieving high-precision measurements on near-term quantum devices is critical for advancing quantum computing applications. Quantum computers suffer from high readout errors, making quantum simulations with high accuracy requirements particularly challenging. This paper implements practical techniques to reach accuracies essential for quantum chemistry by addressing key overheads and noise sources. Specifically, we leverage locally biased random measurements for reducing shot overhead, repeated settings with parallel quantum detector tomography for reducing circuit overhead and mitigating readout errors, and blended scheduling for mitigating time-dependent noise. We demonstrate these techniques via molecular energy estimation of the BODIPY molecule on a Hartree-Fock state on an IBM Eagle r3, obtaining a reduction in measurement errors by an order of magnitude from 1-5% to 0.16%. These strategies pave the way for more reliable quantum computations, particularly for applications requiring precise molecular energy calculations.

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arXiv2024

Treespilation: Architecture- and State-Optimised Fermion-to-Qubit Mappings

Quantum computers hold great promise for efficiently simulating Fermionic systems, benefiting fields like quantum chemistry and materials science. To achieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping to encode the Fermioinc problem in the qubits of a quantum computer. In this work, we introduce "treespilation," a technique for efficiently mapping Fermionic systems using a large family of favourable tree-based mappings previously introduced by some of the authors. We use this technique to minimise the number of CNOT gates required to simulate chemical groundstates found numerically using the ADAPT-VQE algorithm. We observe significant reductions, up to $74\%$, in CNOT counts on full connectivity and for limited qubit connectivity-type devices such as IBM Eagle and Google Sycamore, we observe similar reductions in CNOT counts. In many instances, the reductions achieved on these limited connectivity devices even surpass the initial full connectivity CNOT count. Additionally, we find our method improves the CNOT and parameter efficiency of QEB- and qubit-ADAPT-VQE, which are, to our knowledge, the most CNOT-efficient VQE protocols for molecular state preparation.

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arXiv2023

Classification and transformations of quantum circuit decompositions for permutation operations

Efficient decomposition of permutation unitaries is vital as they frequently appear in quantum computing. In this paper, we identify the key properties that impact the decomposition process of permutation unitaries. Then, we classify these decompositions based on the identified properties, establishing a comprehensive framework for analysis. We demonstrate the applicability of the presented framework through the widely used multi-controlled Toffoli gate, revealing that the existing decompositions in the literature belong to only three out of ten of the identified classes. Motivated by this finding, we propose transformations that can adapt a given decomposition into a member of another class, enabling resource reduction.

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arXiv2023

Integer Factorization through Func-QAOA

Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research. Although Peter Shor's breakthrough quantum algorithm offers a viable solution, current limitations of noisy intermediate-scale quantum (NISQ) computers hinder its practical implementation. To address this, researchers have explored alternative methods for factorization suitable for NISQ devices. One such method is the Quantum Approximate Optimization Algorithm, which treats factoring as an optimization problem defined over binary bits, resulting in various problematic aspects. In this paper, we explore the Func-QAOA approach for factorization, which premises overcoming some of the limitations of previous approaches and allows the incorporation of more advanced factorization techniques. After reviewing the most promising quantum implementations for integer arithmetics, we present a few illustrative examples to demonstrate the efficacy of the Func-QAOA approach and discuss methods to reduce the search space to speed up the optimization process.

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arXiv2023

Hamiltonian-Oriented Homotopy QAOA

The classical homotopy optimization approach has the potential to deal with highly nonlinear landscape, such as the energy landscape of QAOA problems. Following this motivation, we introduce Hamiltonian-Oriented Homotopy QAOA (HOHo-QAOA), that is a heuristic method for combinatorial optimization using QAOA, based on classical homotopy optimization. The method consists of a homotopy map that produces an optimization problem for each value of interpolating parameter. Therefore, HOHo-QAOA decomposes the optimization of QAOA into several loops, each using a mixture of the mixer and the objective Hamiltonian for cost function evaluation. Furthermore, we conclude that the HOHo-QAOA improves the search for low energy states in the nonlinear energy landscape and outperforms other variants of QAOA.

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arXiv2022

Prog-QAOA: Framework for resource-efficient quantum optimization through classical programs

Current state-of-the-art quantum optimization algorithms require representing the original problem as a binary optimization problem, which is then converted into an equivalent cost Hamiltonian suitable for the quantum device. Implementing each term of the cost Hamiltonian separately often results in high redundancy, significantly increasing the resources required. Instead, we propose to design classical programs for computing the objective function and certifying the constraints, and later compile them to quantum circuits, eliminating the reliance on the binary optimization problem representation. This results in a new variant of the Quantum Approximate Optimization Algorithm (QAOA), which we name the Program-based QAOA (Prog-QAOA). We exploit this idea for optimization tasks like the Travelling Salesman Problem and Max-$K$-Cut and obtain circuits that are near-optimal with respect to all relevant cost measures, e.g., number of qubits, gates, and circuit depth. While we demonstrate the power of Prog-QAOA only for a particular set of paradigmatic problems, our approach is conveniently applicable to generic optimization problems.

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arXiv2022

Adaptive POVM implementations and measurement error mitigation strategies for near-term quantum devices

We present adaptive measurement techniques tailored for variational quantum algorithms on near-term small and noisy devices. In particular, we generalise earlier "learning to measure" strategies in two ways. First, by considering a class of adaptive positive operator valued measures (POVMs) that can be simulated with simple projective measurements without ancillary qubits, we decrease the amount of required qubits and two-qubit gates. Second, by introducing a method based on Quantum Detector Tomography to mitigate the effect of noise, we are able to optimise the POVMs as well as to infer expectation values reliably in the currently available noisy quantum devices. Our numerical simulations clearly indicate that the presented strategies can significantly reduce the number of needed shots to achieve chemical accuracy in variational quantum eigensolvers, thus helping to solve one of the bottlenecks of near-term quantum computing.

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arXiv2022

Quantum network medicine: rethinking medicine with network science and quantum algorithms

Scientific and technological advances in medicine and systems biology have unequivocally shown that health and disease must be viewed in the context of the interplay among multiple molecular and environmental factors. Understanding the effects of cellular interconnection on disease progression may lead to the identification of novel disease genes and pathways, and hence influence precision diagnostics and therapeutics. To accomplish this goal, the emerging field of network medicine applies network science approaches to investigate disease pathogenesis, integrating information from relevant Omics databases, including protein-protein interaction, correlation-based, gene regulatory, and Bayesian networks. However, this requires analysing and computing large amounts of data. Moreover, if we are to efficiently search for new drugs and new drug combinations, there is a pressing need for computational methods that could allow us to access the immense chemical compound space until now largely unexplored. Finally, at the microscopic level, drug-target chemistry simulation is ultimately a quantum problem, and hence it requires a quantum solution. As we will discuss, quantum computing may be a key ingredient in enabling the full potential of network medicine. We propose to combine network medicine and quantum algorithms in a novel research field, quantum network medicine, to lay the foundations of a new era of disease prevention and drug design.

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arXiv2022

Optimizing the Production of Test Vehicles using Hybrid Constrained Quantum Annealing

Optimization of pre-production vehicle configurations is one of the challenges in the automotive industry. Given a list of tests requiring cars with certain features, it is desirable to find the minimum number of cars that cover the tests and obey the configuration rules. In this paper, we model the problem in the framework of satisfiability and solve it by utilizing the newly introduced hybrid constrained quadratic model (CQM) solver provided by D-Wave. The problem definition is based on the "Optimizing the Production of Test Vehicles" use case given in the BMW Quantum Computing Challenge. We formulate a constrained quadratic model for the problem and use a greedy algorithm to configure the cars. We benchmark the results obtained from the CQM solver with the results from the classical solvers like CBC (Coin-or branch and cut) and Gurobi. We conclude that the performance of the CQM solver is comparable to classical solvers in optimizing the number of test vehicles. As an extension to the problem, we describe how the scheduling of the tests can be incorporated into the model.

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arXiv2021

Application of graph theory in quantum computer science

In this dissertation we demonstrate that the continuous-time quantum walk models remain powerful for nontrivial graph structures. We consider two aspects of this problem. First, it is known that the standard Continuous-Time Quantum Walk (CTQW), proposed by Childs and Goldstone, can propagate quickly on the infinite path graph. However, the Schr\"odinger equation requires the Hamiltonian to be symmetric, and thus only undirected graphs can be implemented. In this thesis, we address the question, whether it is possible to construct a continuous-time quantum walk on general directed graphs, preserving its propagation properties. Secondly, the quantum spatial search defined through CTQW has been proven to work well on various undirected graphs. However, most of these graphs have very simple structures. The most advanced results concerned the Erd\H{o}s-R\'enyi model of random graphs, which is the most popular but not realistic random graph model, and Barab\'asi-Albert random graphs, for which full quadratic speed-up was not confirmed. In the scope of this aspect we analyze, whether quantum speed-up is observed for complicated graph structures as well.

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arXiv2021

Error mitigation for variational quantum algorithms through mid-circuit measurements

Noisy Intermediate-Scale Quantum (NISQ) algorithms require novel paradigms of error mitigation. To obtain noise-robust quantum computers, each logical qubit is equipped with hundreds or thousands of physical qubits. However, it is not possible to use memory-consuming techniques for current quantum devices having at most hundreds or at best thousands of physical qubits on their own. For specific problems, valid quantum states have a unique structure as in the case of Fock states and W-states where the Hamming weight is fixed, and the evolution takes place in a smaller subspace of the full Hilbert space. With this pre-knowledge, some errors can be detected in the course of the evolution of the circuit, by filtering the states not obeying the pattern through post-selection. In this paper, we present mid-circuit post-selection schemes for frequently used encodings such as one-hot, binary, gray, and domain-wall encoding. For the particular subspace of one-hot states, we propose a method that works by compressing the full Hilbert space to a smaller subspace, allowing projecting to the desired subspace without using any ancilla qubits. We demonstrate the effectiveness of the approach for the Quantum Alternating Operator Ansatz algorithm. Our method is particularly suitable for the currently available hardware, where measuring and resetting is possible, but classical control conditional operators are not.

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arXiv2021

Unconstrained Binary Models of the Travelling Salesman Problem Variants for Quantum Optimization

Quantum computing is offering a novel perspective for solving combinatorial optimization problems. To fully explore the possibilities offered by quantum computers, the problems need to be formulated as unconstrained binary models, taking into account limitation and advantages of quantum devices. In this work, we provide a detailed analysis of the Travelling Salesman Problem with Time Windows (TSPTW) in the context of solving it on a quantum computer. We introduce quadratic unconstrained binary optimization and higher order binary optimization formulations of this problem. We demonstrate the advantages of edge-based and node-based formulations of the TSPTW problem. Additionally, we investigate the experimental realization of the presented methods on a quantum annealing device. The provided results pave the path for utilizing quantum computer for a variety of real-world task which can be cast in the form of Travelling Salesman Problem with Time Windows problem.

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arXiv2021

Quantum speedups for dynamic programming on $n$-dimensional lattice graphs

Motivated by the quantum speedup for dynamic programming on the Boolean hypercube by Ambainis et al. (2019), we investigate which graphs admit a similar quantum advantage. In this paper, we examine a generalization of the Boolean hypercube graph, the $n$-dimensional lattice graph $Q(D,n)$ with vertices in $\{0,1,\ldots,D\}^n$. We study the complexity of the following problem: given a subgraph $G$ of $Q(D,n)$ via query access to the edges, determine whether there is a path from $0^n$ to $D^n$. While the classical query complexity is $\widetilde{\Theta}((D+1)^n)$, we show a quantum algorithm with complexity $\widetilde O(T_D^n)$, where $T_D < D+1$. The first few values of $T_D$ are $T_1 \approx 1.817$, $T_2 \approx 2.660$, $T_3 \approx 3.529$, $T_4 \approx 4.421$, $T_5 \approx 5.332$. We also prove that $T_D \geq \frac{D+1}{\mathrm e}$, thus for general $D$, this algorithm does not provide, for example, a speedup, polynomial in the size of the lattice. While the presented quantum algorithm is a natural generalization of the known quantum algorithm for $D=1$ by Ambainis et al., the analysis of complexity is rather complicated. For the precise analysis, we use the saddle-point method, which is a common tool in analytic combinatorics, but has not been widely used in this field. We then show an implementation of this algorithm with time complexity $\text{poly}(n)^{\log n} T_D^n$, and apply it to the Set Multicover problem. In this problem, $m$ subsets of $[n]$ are given, and the task is to find the smallest number of these subsets that cover each element of $[n]$ at least $D$ times. While the time complexity of the best known classical algorithm is $O(m(D+1)^n)$, the time complexity of our quantum algorithm is $\text{poly}(m,n)^{\log n} T_D^n$.

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arXiv2021

Quantum speedup for track reconstruction in particle accelerators

To investigate the fundamental nature of matter and its interactions, particles are accelerated to very high energies and collided inside detectors, producing a multitude of other particles that are scattered in all directions. As charged particles traverse the detector, they leave signals of their passage. The problem of track reconstruction is to recover the original trajectories from these signals. This challenging data analysis task will become even more demanding as the luminosity of future accelerators increases, leading to collision events with a more complex structure. We identify four fundamental routines present in every local tracking method and analyse how they scale in the context of a standard tracking algorithm. We show that for some of these routines we can reach a lower computational complexity with quantum search algorithms. Although the found quantum speedups are mild, this constitutes, to the best of our knowledge, the first rigorous evidence of a quantum advantage for a high-energy physics data processing task.

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arXiv2020

LP WAN Gateway Location Selection Using Modified K-Dominating Set Algorithm

The LP WAN networks use gateways or base stations to communicate with devices distributed on large distances, up to tens of kilometres. The selection of optimal gateway locations in wireless networks should allow providing the complete coverage for a given set of nodes, taking into account the limitations, such as the number of nodes served per access point or required redundancy. In this paper, we describe the problem of selecting the base stations in a network using the concept of $k$-dominating set. In our model, we include information about the required redundancy and spectral efficiency. We consider the additional requirements on the resulting connections and provide the greedy algorithm for solving the problem. The algorithm is evaluated in randomly generated network topologies and using the coordinates of sample real smart metering networks.

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