We review the recent quantum advantage experiments by IBM, D-Wave, and Google, focusing on cases where efficient classical simulations of the experiment were demonstrated or attempted using tensor network methods. We assess the strengths and limitations of these tensor network-based approaches and examine how the interplay between classical simulation and quantum hardware has advanced both fields. Our goal is to clarify what these results imply for the next generation of quantum advantage experiments. We identify regimes and system features that remain challenging for current tensor network approaches, and we outline directions where improved classical methods could further raise the standard for claiming quantum advantage. By analyzing this evolving competition, we aim to provide a clear view of where genuine, scalable quantum advantage is most likely to emerge.
We review the recent quantum advantage experiments by IBM, D-Wave, and Google, focusing on cases where efficient classical simulations of the experiment were demonstrated or attempted using tensor network methods. We assess the strengths and limitations of these tensor network-based approaches and examine how the interplay between classical simulation and quantum hardware has advanced both fields. Our goal is to clarify what these results imply for the next generation of quantum advantage experiments. We identify regimes and system features that remain challenging for current tensor network approaches, and we outline directions where improved classical methods could further raise the standard for claiming quantum advantage. By analyzing this evolving competition, we aim to provide a clear view of where genuine, scalable quantum advantage is most likely to emerge.
Quantum computing has generated significant expectations for its potential to enhance machine learning (ML) tasks, with theoretical research proposing computational advantages ranging from polynomial to exponential speedups for specific subroutines.However, a critical disconnect remains: theoretical or asymptotic speedup claims do not automatically imply a practical, end-to-end advantage.Current evidence does not clearly establish whether these claimed advantages translate into measurable superiority over optimised classical approaches.This review critically assesses the relationship between theoretical claims of quantum advantage and the currently available practical and experimental evidence.We critically examine the evidence and assumptions underlying claimed speedups, including the overheads associated with data encoding and access, as well as the use of appropriate and competitive classical baselines for fair comparison.The scope of this assessment covers key limiting factors, such as scalability, trainability, hardware noise in the noisy intermediate-scale quantum (NISQ) era, and overall resource requirements.By distinguishing between theoretical potential and demonstrated practical performance, this work identifies where current evidence is convincing and where it remains insufficient.The review identifies the specific conditions required for the credible validation of quantum advantage and argues that future progress must be positioned around rigorous, realistic, and end-to-end evaluation rather than theoretical complexity claims alone.
In the effort to develop useful quantum computers, simulating quantum machines with conventional classical computing resources is a key capability. Such simulations will always face limits, preventing the emulation of quantum computers at substantial scale; however, by pushing the envelope through optimal choices of algorithms and hardware, the value of simulator tools can be maximized. This work reviews state-of-the-art numerical simulation methods, i.e., classical algorithms that emulate quantum computer evolution under specific operations. We focus on the mainstream state-vector and tensor-network paradigms, while briefly mentioning alternative methods. Moreover, we review the diverse applications of simulation across different facets of quantum computer development, including understanding the fundamental differences between quantum and classical computations, exploring algorithmic design for quantum advantage, predicting quantum processor performance at the design stage, and efficiently characterizing fabricated devices for rapid iterations. This review complements recent surveys of current tools and implementations; here, we aim to provide readers with an essential understanding of the theoretical basis of classical simulation methods, a detailed discussion of their advantages and limitations, and an overview of the demands and challenges arising from practical use cases.
Quantum advantage is when quantum computers can outperform classical computers.One of the first largescale demonstrations of quantum advantage was recently done by Google running random multi-qubit quantum circuits.While Google's quantum computer took 200 seconds, calculations show that the then-fastest classical supercomputer would have taken 10000 years.Since then, different groups have claimed quantum advantage through other quantum systems.This paper will cover why quantum computers can be faster than classical computers by covering the primary differences between classical computing and quantum computing.Then, we will investigate the Deutsch-Jozsa quantum algorithm and Google's claim of quantum advantage.We will review current research regarding "quantum advantage," tying these events to the use cases covered.Additionally, different quantum algorithms that are theoretically faster than any current quantum algorithms will be analyzed, and we will delve into why this is the case.The covered examples will show methods used to improve quantum computers to provide a significant time difference to achieve a quantum advantage.After that, we make predictions concerning two critical quantum hardware limitations.Finally, we will investigate what the future of quantum advantage entails and some future cases of quantum advantage.
The integration of quantum computing and artificial intelligence (AI) constitutes a bidirectional synergy that is reshaping both disciplines. This review investigates the reciprocal relationship in which AI addresses foundational challenges in quantum computing, while quantum computing offers the potential to advance machine learning beyond classical constraints. Recent advancements exemplify this interaction: Google DeepMind’s AlphaQubit neural network decoder has achieved state-of-the-art quantum error correction, improving performance by 6% over tensor networks and 30% over correlated matching methods. Additionally, quantum neural networks have demonstrated exponential improvements in sample complexity for specific learning tasks. This review systematically examines the current landscape of quantum-AI integration across three primary dimensions. First, it addresses AI-enhanced quantum systems, such as transformer-based error correction, reinforcement learning for circuit optimization, and AI-driven hardware calibration. Second, it explores quantum-accelerated machine learning algorithms, including variational quantum neural networks, quantum generative adversarial networks, and quantum reinforcement learning. Third, it evaluates industry deployments in sectors such as life sciences, financial services, climate modeling, and pharmaceutical development. Notable examples include IonQ’s quantum chemistry simulations, which achieved 40% efficiency improvements in carbon capture material design; St. Jude’s identification of KRAS protein inhibitors using quantum machine learning with experimental validation; and JP Morgan Chase’s implementation of quantum portfolio optimization. The analysis indicates that the field has advanced from preliminary demonstrations to production-grade applications, especially in drug discovery and molecular simulation, where quantum computing offers measurable benefits. Nevertheless, several challenges remain, including barren plateaus in variational algorithms, scalability constraints in current noisy intermediate-scale quantum (NISQ) devices, requirements for real-time decoding speed, and the necessity for fault-tolerant quantum computing (FTQC) systems. IBM’s 2029 roadmap, which targets 200 logical qubits capable of executing 100 million gates, together with progress in high-rate quantum low-density parity-check codes, outlines a trajectory toward practical fault tolerance. This review makes two principal research contributions: Comprehensive Evaluation Framework for Quantum Advantage Assessment: We establish the first systematic, integrated methodology for determining quantum computing feasibility that combines problem characterization, resource estimation, quantum advantage assessment, and quantum algorithm paradigm selection. This framework consolidates criteria scattered across academic literature and industry practice into a unified decision-making tool applicable across chemistry, optimization, machine learning, and simulation domains. The framework addresses a critical industry need: enabling non-expert practitioners (chemists, financial analysts, materials scientists) to objectively assess quantum computing suitability without requiring deep quantum expertise. Novel Quantum Resource Optimization Algorithms: We present three concrete algorithmic contributions advancing quantum-AI integration: • Data Encoding Efficiency Algorithm that automatically selects optimal qubit encoding strategies (amplitude vs. angle encoding) minimizing total quantum resource consumption • Error Budget Optimization Algorithm that iteratively determines optimal quantum error correction code distance balancing logical error rate targets against physical qubit overhead • Real-time Hardware Specification Aggregation from multiple quantum cloud platforms (IBM Quantum, Amazon Braket, Google, IonQ) enabling dynamic feasibility assessment as hardware capabilities evolve Combined, these contributions establish quantum computing advantage assessment as a rigorous, data-driven discipline rather than ad-hoc expert judgment. The framework enables strategic quantum computing investment decisions, accelerates problem identification for early quantum utility, and provides a reference methodology for standardizing quantum advantage evaluation across academia and industry. This review synthesizes insights from recent academic literature, industry implementations, and expert perspectives to deliver a comprehensive assessment of quantum-AI synergies grounded in this evaluation framework. The mathematical foundations, ranging from quantum Fourier transforms to Gaussian processes, are examined. Best practices for researchers and practitioners are also outlined. The findings suggest that, although universal quantum advantage has not yet been realized, domain-specific quantum-AI applications in chemistry, optimization, and sensing are achieving practical utility in 2024-2025. This development marks a significant transition from theoretical potential to commercial realization, informed by rigorous evaluation methodologies.
Quantum computational advantage was claimed for the first time in 2019 and several experiments since then have reinforced and strengthened the claim. At the same time, a new generation of quantum computing devices with 100 logical qubits is being built. This raises two questions: Has quantum advantage actually been achieved? And what should our next milestones be for the upcoming 100-logical-qubit era? In this perspective, I argue that, in fact, quantum advantage has been achieved. The status today is analogous to Bell-inequality violations in the 1980s where some loopholes remain open, specifically, scalability and verifiability. I then outline three milestones for the 100-logical-qubit era aiming to close those loopholes: demonstrate fault-tolerant quantum advantage, perform efficiently verifiable advantage using random circuits with symmetries, and eventually demonstrate classically verifiable advantage with applications to certified randomness. These milestones are also natural stepping stones towards running algorithms with cryptographic applications.
In recent years, the rapidly advancing field of quantum computing has become a focal point of attention. However, issues such as scarcity of quantum hardware and noise pose challenges, leading to the reliance on quantum simulators running on classical computers for tasks like researching quantum algorithms and validating quantum chips. This paper discusses the main simulation methods used by different quantum simulators and explores various optimizations for mainstream full-amplitude state vector simulators and tensor network-based quantum simulators. Finally, we summarize the current status and future directions of quantum simulators. This paper also discusses algorithm-level and system-level optimizations that enhance simulator performance. Looking ahead, the development of quantum simulators faces challenges such as maximizing the use of quantum state properties and creating algorithms to overcome exponential growth issues in simulations. The future will likely focus on integrating high-performance computing resources, advancing optimization strategies, and tailoring simulations to specific applications, aiming for higher efficiency and precision in quantum simulations.