arXiv subjects

Sebastian Feld

Publications and source records attributed to Sebastian Feld.

At least 55 records · Page 3Linked to original sources

arXiv2024

YAQQ: Yet Another Quantum Quantizer -- Design Space Exploration of Quantum Gate Sets using Novelty Search

In the standard circuit model of quantum computation, the number and quality of the quantum gates composing the circuit influence the runtime and fidelity of the computation. The fidelity of the decomposition of quantum algorithms, represented as unitary matrices, to bounded depth quantum circuits depends strongly on the set of gates available for the decomposition routine. To investigate this dependence, we explore the design space of discrete quantum gate sets and present a software tool for comparative analysis of quantum processing units and control protocols based on their native gates. The evaluation is conditioned on a set of unitary transformations representing target use cases on the quantum processors. The cost function considers three key factors: (i) the statistical distribution of the decomposed circuits' depth, (ii) the statistical distribution of process fidelities for the approximate decomposition, and (iii) the relative novelty of a gate set compared to other gate sets in terms of the aforementioned properties. The developed software, YAQQ (Yet Another Quantum Quantizer), enables the discovery of an optimized set of quantum gates through this tunable joint cost function. To identify these gate sets, we use the novelty search algorithm, circuit decomposition techniques, and stochastic optimization to implement YAQQ within the Qiskit quantum simulator environment. YAQQ exploits reachability tradeoffs conceptually derived from quantum algorithmic information theory. Our results demonstrate the pragmatic application of identifying gate sets that are advantageous to popularly used quantum gate sets in representing quantum algorithms. Consequently, we demonstrate pragmatic use cases of YAQQ in comparing transversal logical gate sets in quantum error correction codes, designing optimal quantum instruction sets, and compiling to specific quantum processors.

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arXiv2024

Using an Evolutionary Algorithm to Create (MAX)-3SAT QUBOs

A common way of solving satisfiability instances with quantum methods is to transform these instances into instances of QUBO, which in itself is a potentially difficult and expensive task. State-of-the-art transformations from MAX-3SAT to QUBO currently work by mapping clauses of a 3SAT formula associated with the MAX-3SAT instance to an instance of QUBO and combining the resulting QUBOs into a single QUBO instance representing the whole MAX-3SAT instance. As creating these transformations is currently done manually or via exhaustive search methods and, therefore, algorithmically inefficient, we see potential for including search-based optimization. In this paper, we propose two methods of using evolutionary algorithms to automatically create QUBO representations of MAX-3SAT problems. We evaluate our created QUBOs on 500 and 1000-clause 3SAT formulae and find competitive performance to state-of-the-art baselines when using both classical and quantum annealing solvers.

quant-ph↗

arXiv2024

beSnake: A routing algorithm for scalable spin-qubit architectures

As quantum computing devices increase in size with respect to the number of qubits, two-qubit interactions become more challenging, necessitating innovative and scalable qubit routing solutions. In this work, we introduce beSnake, a novel algorithm specifically designed to address the intricate qubit routing challenges in scalable spin-qubit architectures. Unlike traditional methods in superconducting architectures that solely rely on SWAP operations, beSnake also incorporates the shuttle operation to optimize the execution time and fidelity of quantum circuits and achieves fast computation times of the routing task itself. Employing a simple breadth-first search approach, beSnake effectively manages the restrictions created by diverse topologies and qubit positions acting as obstacles, for up to 72\% qubit density. It also has the option to adjust the level of optimization and to dynamically tackle parallelized routing tasks, all the while maintaining noise awareness. Our simulations demonstrate beSnake's advantage over an existing routing solution on random circuits and real quantum algorithms with up to $1,000$ qubits, showing an average improvement of up to $80\%$ in gate overhead and $54\%$ in depth overhead, and up to $8.33$ times faster routing times.

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arXiv2024

SpinQ: Compilation strategies for scalable spin-qubit architectures

Despite NISQ devices being severely constrained, hardware- and algorithm-aware quantum circuit mapping techniques have been developed to enable successful algorithm executions. Not so much attention has been paid to mapping and compilation implementations for spin-qubit quantum processors due to the scarce availability of experimental devices and their small sizes. However, based on their high scalability potential and their rapid progress it is timely to start exploring solutions on such devices. In this work, we discuss the unique mapping challenges of a scalable crossbar architecture with shared control and introduce SpinQ, the first native compilation framework for scalable spin-qubit architectures. At the core of SpinQ is the Integrated Strategy that addresses the unique operational constraints of the crossbar while considering compilation scalability and obtaining a O(n) computational complexity. To evaluate the performance of SpinQ on this novel architecture, we compiled a broad set of well-defined quantum circuits and performed an in-depth analysis based on multiple metrics such as gate overhead, depth overhead, and estimated success probability, which in turn allowed us to create unique mapping and architectural insights. Finally, we propose novel mapping techniques that could increase algorithm success rates on this architecture and potentially inspire further research on quantum circuit mapping for other scalable spin-qubit architectures.

quant-ph↗

arXiv2024

Revisiting the Mapping of Quantum Circuits: Entering the Multi-Core Era

Quantum computing represents a paradigm shift in computation, offering the potential to solve complex problems intractable for classical computers. Although current quantum processors already consist of a few hundred of qubits, their scalability remains a significant challenge. Modular quantum computing architectures have emerged as a promising approach to scale up quantum computing systems. This paper delves into the critical aspects of distributed multi-core quantum computing, focusing on quantum circuit mapping, a fundamental task to successfully execute quantum algorithms across cores while minimizing inter-core communications. We derive the theoretical bounds on the number of non-local communications needed for random quantum circuits and introduce the Hungarian Qubit Assignment (HQA) algorithm, a multi-core mapping algorithm designed to optimize qubit assignments to cores with the aim of reducing inter-core communications. Our exhaustive evaluation of HQA against state-of-the-art circuit mapping algorithms for modular architectures reveals a $4.9\times$ and $1.6\times$ improvement in terms of execution time and non-local communications, respectively, compared to the best performing algorithm. HQA emerges as a very promising scalable approach for mapping quantum circuits into multi-core architectures, positioning it as a valuable tool for harnessing the potential of quantum computing at scale.

quant-ph↗

arXiv2024

Quantum Data Management: From Theory to Opportunities

Quantum computing has emerged as a transformative tool for future data management. Classical problems in database domains, including query optimization, data integration, and transaction management, have recently been addressed using quantum computing techniques. This tutorial aims to establish the theoretical foundation essential for enhancing methodologies and practical implementations in this line of research. Moreover, this tutorial takes a forward-looking approach by delving into recent strides in quantum internet technologies and the nonlocality theory. We aim to shed light on the uncharted territory of future data systems tailored for the quantum internet.

cs.DB↗

arXiv2024

KetGPT - Dataset Augmentation of Quantum Circuits using Transformers

Quantum algorithms, represented as quantum circuits, can be used as benchmarks for assessing the performance of quantum systems. Existing datasets, widely utilized in the field, suffer from limitations in size and versatility, leading researchers to employ randomly generated circuits. Random circuits are, however, not representative benchmarks as they lack the inherent properties of real quantum algorithms for which the quantum systems are manufactured. This shortage of `useful' quantum benchmarks poses a challenge to advancing the development and comparison of quantum compilers and hardware. This research aims to enhance the existing quantum circuit datasets by generating what we refer to as `realistic-looking' circuits by employing the Transformer machine learning architecture. For this purpose, we introduce KetGPT, a tool that generates synthetic circuits in OpenQASM language, whose structure is based on quantum circuits derived from existing quantum algorithms and follows the typical patterns of human-written algorithm-based code (e.g., order of gates and qubits). Our three-fold verification process, involving manual inspection and Qiskit framework execution, transformer-based classification, and structural analysis, demonstrates the efficacy of KetGPT in producing large amounts of additional circuits that closely align with algorithm-based structures. Beyond benchmarking, we envision KetGPT contributing substantially to AI-driven quantum compilers and systems.

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arXiv2024

Interaction graph-based characterization of quantum benchmarks for improving quantum circuit mapping techniques

To execute quantum circuits on a quantum processor, they must be modified to meet the physical constraints of the quantum device. This process, called quantum circuit mapping, results in a gate/circuit depth overhead that depends on both the circuit properties and the hardware constraints, being the limited qubit connectivity a crucial restriction. In this paper, we propose to extend the characterization of quantum circuits by including qubit interaction graph properties using graph theory-based metrics in addition to previously used circuit-describing parameters. This approach allows for in-depth analysis and clustering of quantum circuits and a comparison of performance when run on different quantum processors, aiding in developing better mapping techniques. Our study reveals a correlation between interaction graph-based parameters and mapping performance metrics for various existing configurations of quantum devices. We also provide a comprehensive collection of quantum circuits and algorithms for benchmarking future compilation techniques and quantum devices.

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arXiv2023

Holographic Codes from Hyperinvariant Tensor Networks

Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code's logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections.

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arXiv2023

qgym: A Gym for Training and Benchmarking RL-Based Quantum Compilation

Compiling a quantum circuit for specific quantum hardware is a challenging task. Moreover, current quantum computers have severe hardware limitations. To make the most use of the limited resources, the compilation process should be optimized. To improve currents methods, Reinforcement Learning (RL), a technique in which an agent interacts with an environment to learn complex policies to attain a specific goal, can be used. In this work, we present qgym, a software framework derived from the OpenAI gym, together with environments that are specifically tailored towards quantum compilation. The goal of qgym is to connect the research fields of Artificial Intelligence (AI) with quantum compilation by abstracting parts of the process that are irrelevant to either domain. It can be used to train and benchmark RL agents and algorithms in highly customizable environments.

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arXiv2023

NISQ-ready community detection based on separation-node identification

The analysis of network structure is essential to many scientific areas, ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO based approach that only needs number-of-nodes many qubits and is represented by a QUBO-matrix as sparse as the input graph's adjacency matrix. The substantial improvement on the sparsity of the QUBO-matrix, which is typically very dense in related work, is achieved through the novel concept of separation-nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which -- upon its removal from the graph -- yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept. This work hence displays a promising approach to NISQ ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large scale, real world problem instances.

quant-ph↗

arXiv2023

Approximative lookup-tables and arbitrary function rotations for facilitating NISQ-implementations of the HHL and beyond

Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is prohibitive on near-term quantum computers. Aiming to facilitate such NISQ-implementations, we propose a novel circuit approximation technique that enhances the arithmetic subroutines in the HHL, which resemble a particularly resource-demanding component in small-scale settings. For this, we provide a description of the algorithmic implementation of space-efficient rotations of polynomial functions that do not demand explicit arithmetic calculations inside the quantum circuit. We show how these types of circuits can be reduced in depth by providing a simple and powerful approximation technique. Moreover, we provide an algorithm that converts lookup-tables for arbitrary function rotations into a structure that allows an application of the approximation technique. This allows implementing approximate rotation circuits for many polynomial and non-polynomial functions. Experimental results obtained for realistic early-application dimensions show significant improvements compared to the state-of-the-art, yielding small circuits while achieving good approximations.

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arXiv2023

Mapping quantum circuits to modular architectures with QUBO

Modular quantum computing architectures are a promising alternative to monolithic QPU (Quantum Processing Unit) designs for scaling up quantum devices. They refer to a set of interconnected QPUs or cores consisting of tightly coupled quantum bits that can communicate via quantum-coherent and classical links. In multi-core architectures, it is crucial to minimize the amount of communication between cores when executing an algorithm. Therefore, mapping a quantum circuit onto a modular architecture involves finding an optimal assignment of logical qubits (qubits in the quantum circuit) to different cores with the aim to minimize the number of expensive inter-core operations while adhering to given hardware constraints. In this paper, we propose for the first time a Quadratic Unconstrained Binary Optimization (QUBO) technique to encode the problem and the solution for both qubit allocation and inter-core communication costs in binary decision variables. To this end, the quantum circuit is split into slices, and qubit assignment is formulated as a graph partitioning problem for each circuit slice. The costly inter-core communication is reduced by penalizing inter-core qubit communications. The final solution is obtained by minimizing the overall cost across all circuit slices. To evaluate the effectiveness of our approach, we conduct a detailed analysis using a representative set of benchmarks having a high number of qubits on two different multi-core architectures. Our method showed promising results and performed exceptionally well with very dense and highly-parallelized circuits that require on average 0.78 inter-core communications per two-qubit gate.

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arXiv2023

Pattern QUBOs: Algorithmic construction of 3SAT-to-QUBO transformations

3SAT instances need to be transformed into instances of Quadratic Unconstrained Binary Optimization (QUBO) to be solved on a quantum annealer. Although it has been shown that the choice of the 3SAT-to-QUBO transformation can impact the solution quality of quantum annealing significantly, currently only a few 3SAT-to-QUBO transformations are known. Additionally, all of the known 3SAT-to-QUBO transformations were created manually (and not procedurally) by an expert using reasoning, which is a rather slow and limiting process. In this paper, we will introduce the name Pattern QUBO for a concept that has been used implicitly in the construction of 3SAT-to-QUBO transformations before. We will provide an in-depth explanation for the idea behind Pattern QUBOs and show its importance by proposing an algorithmic method that uses Pattern QUBOs to create new 3SAT-to-QUBO transformations automatically. As an additional application of Pattern QUBOs and our proposed algorithmic method, we introduce approximate 3SAT-to-QUBO transformations. These transformations sacrifice optimality but use significantly fewer variables (and thus physical qubits on quantum hardware) than non-approximate 3SAT-to-QUBO transformations. We will show that approximate 3SAT-to-QUBO transformations can nevertheless be very effective in some cases.

quant-ph↗

arXiv2023

Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes

Flag-style fault-tolerance has become a linchpin in the realization of small fault-tolerant quantum-error correction experiments. The flag protocol's utility hinges on low qubit overhead, which is typically much smaller than in other approaches. However, as in most fault-tolerance protocols, the advantages of flag-style error correction come with a tradeoff: fault tolerance can be guaranteed, but such protocols involve high-depth circuits, due to the need for repeated stabilizer measurements. Here, we demonstrate that a dynamic choice of stabilizer measurements, based on past syndromes, and the utilization of elements from the full stabilizer group, leads to flag protocols with lower-depth syndrome-extraction circuits for the [[5,1,3]] code, as well as for the Steane code when compared to the standard methods in flag fault tolerance. We methodically prove that our new protocols yield fault-tolerant lookup tables, and demonstrate them with a pseudothreshold simulation, showcasing large improvements for all protocols when compared to previously-established methods. This work opens the dialogue on exploiting the properties of the full stabilizer group for reducing circuit overhead in fault-tolerant quantum-error correction.

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arXiv2023

Influence of Different 3SAT-to-QUBO Transformations on the Solution Quality of Quantum Annealing: A Benchmark Study

To solve 3SAT instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different transformations lead to differences in the obtained solution quality. Thus, in this paper we conduct an empirical benchmark study, in which we compare four structurally different QUBO transformations for the 3SAT problem with regards to the solution quality on D-Wave's Advantage_system4.1. We show that the choice of QUBO transformation can significantly impact the number of correct solutions the quantum annealer returns. Furthermore, we show that the size of a QUBO instance (i.e., the dimension of the QUBO matrix) is not a sufficient predictor for solution quality, as larger QUBO instances may produce better results than smaller QUBO instances for the same problem. We also empirically show that the number of different quadratic values of a QUBO instance, combined with their range, can significantly impact the solution quality.

quant-ph↗

arXiv2023

Mapping quantum algorithms to multi-core quantum computing architectures

Current monolithic quantum computer architectures have limited scalability. One promising approach for scaling them up is to use a modular or multi-core architecture, in which different quantum processors (cores) are connected via quantum and classical links. This new architectural design poses new challenges such as the expensive inter-core communication. To reduce these movements when executing a quantum algorithm, an efficient mapping technique is required. In this paper, a detailed critical discussion of the quantum circuit mapping problem for multi-core quantum computing architectures is provided. In addition, we further explore the performance of a mapping method, which is formulated as a partitioning over time graph problem, by performing an architectural scalability analysis.

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arXiv2023

Black Box Optimization Using QUBO and the Cross Entropy Method

Black-box optimization (BBO) can be used to optimize functions whose analytic form is unknown. A common approach to realising BBO is to learn a surrogate model which approximates the target black-box function which can then be solved via white-box optimization methods. In this paper, we present our approach BOX-QUBO, where the surrogate model is a QUBO matrix. However, unlike in previous state-of-the-art approaches, this matrix is not trained entirely by regression, but mostly by classification between 'good' and 'bad' solutions. This better accounts for the low capacity of the QUBO matrix, resulting in significantly better solutions overall. We tested our approach against the state-of-the-art on four domains and in all of them BOX-QUBO showed better results. A second contribution of this paper is the idea to also solve white-box problems, i.e. problems which could be directly formulated as QUBO, by means of black-box optimization in order to reduce the size of the QUBOs to the information-theoretic minimum. Experiments show that this significantly improves the results for MAX-k-SAT.

cs.LG↗