arXiv subjects

Özlem Salehi

Publications and source records attributed to Özlem Salehi.

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 ansätze 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.

quant-ph↗

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.

quant-ph↗

arXiv2025

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.

quant-ph↗

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.

quant-ph↗

arXiv2024

A Representative Framework for Implementing Quantum Finite Automata on Real Devices

We present a framework for the implementation of quantum finite automata algorithms designed for the language $ MOD_p = \{ a^{i\cdot p } \mid i \geq 0 \}$ on gate-based quantum computers. First, we compile the known theoretical results from the literature to reduce the number of CNOT gates. Second, we demonstrate techniques for modifying the algorithms based on the basis gates of available quantum hardware in order to reduce circuit depth. Lastly, we explore how the number of CNOT gates may be reduced further if the topology of the qubits is known.

quant-ph↗

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.

quant-ph↗

arXiv2023

Fixed interval scheduling problem with minimal idle time with an application to music arrangement problem

The Operational Fixed Interval Scheduling Problem aims to find an assignment of jobs to machines that maximizes the total weight of the completed jobs. We introduce a new variant of the problem where we consider the additional goal of minimizing the idle time, the total duration during which the machines are idle. The problem is expressed using quadratic unconstrained binary optimization (QUBO) formulation, taking into account soft and hard constraints required to ensure that the number of jobs running at a time point is desirably equal to the number of machines. Our choice of QUBO representation is motivated by the increasing popularity of new computational architectures such as neuromorphic processors, coherent Ising machines, and quantum and quantum-inspired digital annealers for which QUBO is a natural input. An optimization problem that can be solved using the presented QUBO formulation is the music reduction problem, the process of reducing a given music piece for a smaller number of instruments. We use two music compositions to test the QUBO formulation and compare the performance of simulated, quantum, and hybrid annealing algorithms.

cs.ET↗

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.

quant-ph↗

arXiv2022

Cost-efficient QFA Algorithm for Quantum Computers

The study of quantum finite automata (QFAs) is one of the possible approaches in exploring quantum computers with finite memory. Despite being one of the most restricted models, Moore-Crutchfield quantum finite automaton (MCQFA) is proven to be exponentially more succinct than classical finite automata models in recognizing certain languages such as $\mathtt{MOD}_p = \{ a^{j} \mid j \equiv 0 \mod p\}$, where $p$ is a prime number. In this paper, we present a modified MCQFA algorithm for the language $\mathtt{MOD}_p$, the operators of which are selected based on the basis gates on the available real quantum computers. As a consequence, we obtain shorter quantum programs using fewer basis gates compared to the implementation of the original algorithm given in the literature.

quant-ph↗

arXiv2022

Quadratic and Higher-Order Unconstrained Binary Optimization of Railway Rescheduling for Quantum Computing

As consequences of disruptions in railway traffic affect passenger experience/satisfaction, appropriate rerouting and/or rescheduling is necessary. These problems are known to be NP-hard, given the numerous restrictions of traffic nature. With the recent advances in quantum technologies, quantum annealing has become an alternative method to solve such optimization problems. To use quantum annealing, the problem needs to be encoded in QUBO (quadratic unconstrained binary optimization) or HOBO (higher-order binary optimization) formulation that can be recast as a QUBO. This paper introduces QUBO and HOBO representations for rescheduling problems of railway traffic management; the latter is a new approach up to our knowledge. This new approach takes into account not only the single-track lines but also the double- and multi-track lines, as well as stations composed of tracks and switches. We consider the conditions of minimal headway between trains, minimal stay on stations, track occupation, and rolling stock circulation. Furthermore, a hybrid quantum-classical procedure is presented that includes rerouting. We demonstrate the proof of concept implementation on the D-Wave Quantum Processing Unit and D-Wave hybrid solver.

cs.ET↗

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.

quant-ph↗

arXiv2022

Music Composition Using Quantum Annealing

With the emergence of quantum computers, a new field of algorithmic music composition has been initiated. The vast majority of previous work focuses on music generation using gate-based quantum computers. An alternative model of computation is adiabatic quantum computing (AQC), and a heuristic algorithm known as quantum annealing running in the framework of AQC is a promising method for solving optimization problems. In this chapter, we lay the groundwork of music composition using quantum annealing. We approach the process of music composition as an optimization problem. We describe the fundamental methodologies needed for generating different aspects of music including melody, rhythm, and harmony. The discussed techniques are illustrated through examples to ease the understanding. The music pieces generated using D-Wave quantum annealers are among the first examples of their kind and presented within the scope of the chapter. The text is an unedited pre-publication version of a chapter which will appear in the book "Quantum Computer Music", Miranda, E. R. (Editor).

quant-ph↗

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.

quant-ph↗

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.

quant-ph↗

arXiv2021

Implementing Quantum Finite Automata Algorithms on Noisy Devices

Quantum finite automata (QFAs) literature offers an alternative mathematical model for studying quantum systems with finite memory. As a superiority of quantum computing, QFAs have been shown exponentially more succinct on certain problems such as recognizing the language $ MOD_p = \{a^j \mid j \equiv 0 \mod p\} $ with bounded error, where $p$ is a prime number. In this paper we present improved circuit based implementations for QFA algorithms recognizing the $ MOD_p $ problem using the Qiskit framework. We focus on the case $p=11$ and provide a 3 qubit implementation for the $MOD_{11}$ problem reducing the total number of required gates using alternative approaches. We run the circuits on real IBM quantum devices but due to the limitation of the real quantum devices in the NISQ era, the results are heavily affected by the noise. This limitation reveals once again the need for algorithms using less amount of resources. Consequently, we consider an alternative 3 qubit implementation which works better in practice and obtain promising results even for the problem $ MOD_{31} $.

quant-ph↗

arXiv2021

A Computer Science-Oriented Approach to Introduce Quantum Computing to a New Audience

Contribution: In this study, an alternative educational approach for introducing quantum computing to a wider audience is highlighted. The proposed methodology considers quantum computing as a generalized probability theory rather than a field emanating from physics and utilizes quantum programming as an educational tool to reinforce the learning process. Background: Quantum computing is a topic mainly rooted in physics, and it has been gaining rapid popularity in recent years. A need for extending the educational reach to groups outside of physics has also been becoming a necessity. Intended outcomes: This study aims to inform academics and organizations interested in introducing quantum computing to a diverse group of participants on an educational approach. It is intended that the proposed methodology would facilitate people from diverse backgrounds to enter the field Application design: The introductory quantum physics content is bypassed and the quantum computing concepts are introduced through linear algebra instead. Quantum programming tasks are prepared in line with the content. Pre/post-test design method and Likert scale satisfaction surveys are utilized to measure knowledge acquisition and to evaluate the perception of the learning process by the participants. Findings: Conducted pre/post-test design survey shows that there is a statistically significant increase in the basic knowledge levels of the participants on quantum computing concepts. Furthermore, no significant difference in the gain scores is observed between the participants from different STEM-related educational backgrounds. The majority of the participants were satisfied and provided positive feedback.

physics.ed-ph↗

arXiv2020

Language Inference with Multi-head Automata through Reinforcement Learning

The purpose of this paper is to use reinforcement learning to model learning agents which can recognize formal languages. Agents are modeled as simple multi-head automaton, a new model of finite automaton that uses multiple heads, and six different languages are formulated as reinforcement learning problems. Two different algorithms are used for optimization. First algorithm is Q-learning which trains gated recurrent units to learn optimal policies. The second one is genetic algorithm which searches for the optimal solution by using evolution inspired operations. The results show that genetic algorithm performs better than Q-learning algorithm in general but Q-learning algorithm finds solutions faster for regular languages.

cs.LG↗

arXiv2019

Extended Models of Finite Automata

Many of the numerous automaton models proposed in the literature can be regarded as a finite automaton equipped with an additional storage mechanism. In this thesis, we focus on two such models, namely the finite automata over groups and the homing vector automata. A finite automaton over a group $ G $ is a nondeterministic finite automaton equipped with a register that holds an element of the group $ G $. The register is initialized to the identity element of the group and a computation is successful if the register is equal to the identity element at the end of the computation after being multiplied with a group element at every step. We investigate the language recognition power of finite automata over integer and rational matrix groups and reveal new relationships between the language classes corresponding to these models. We examine the effect of various parameters on the language recognition power. We establish a link between the decision problems of matrix semigroups and the corresponding automata. We present some new results about valence pushdown automata and context-free valence grammars. We also propose the new homing vector automaton model, which is a finite automaton equipped with a vector that can be multiplied with a matrix at each step. The vector can be checked for equivalence to the initial vector and the acceptance criterion is ending up in an accept state with the value of the vector being equal to the initial vector. We examine the effect of various restrictions on the model by confining the matrices to a particular set and allowing the equivalence test only at the end of the computation. We define the different variants of the model and compare their language recognition power with that of the classical models.

cs.FL↗