Quantum computing holds unparalleled potentials to enhance machine learning. However, a demonstration of quantum learning advantage has not been achieved so far. We make a step forward by rigorously establishing a noise-robust, unconditional quantum learning advantage in expressivity, inference speed, and training efficiency, compared to commonly-used classical models. Our proof is information-theoretic and pinpoints the origin of this advantage: entanglement can be used to reduce the communication required by non-local tasks. In particular, we design a task that can be solved with certainty by quantum models with a constant number of parameters using entanglement, whereas commonly-used classical models must scale linearly to achieve a larger-than-exponentially-small accuracy. We show that the quantum model is trainable with constant resources and robust against constant noise. Through numerical and trapped-ion experiments on IonQ Aria, we demonstrate the desired advantage. Our results provide valuable guidance for demonstrating quantum learning advantages with current noisy intermediate-scale devices.
Quantum computing holds unparalleled potentials to enhance machine learning. However, a demonstration of quantum learning advantage has not been achieved so far. We make a step forward by rigorously establishing a noise-robust, unconditional quantum learning advantage in expressivity, inference speed, and training efficiency, compared to commonly-used classical models. Our proof is information-theoretic and pinpoints the origin of this advantage: entanglement can be used to reduce the communication required by non-local tasks. In particular, we design a task that can be solved with certainty by quantum models with a constant number of parameters using entanglement, whereas commonly-used classical models must scale linearly to achieve a larger-than-exponentially-small accuracy. We show that the quantum model is trainable with constant resources and robust against constant noise. Through numerical and trapped-ion experiments on IonQ Aria, we demonstrate the desired advantage. Our results provide valuable guidance for demonstrating quantum learning advantages with current noisy intermediate-scale devices.
Learning unknown noise processes in quantum systems reveals their physical origin and informs error suppression, mitigation, and correction. Characterizing a general quantum process requires exponentially many parameters inferred from noncommuting measurements. Because these measurements cannot be performed simultaneously, the sample complexity grows exponentially. For Pauli channels, quantum memory and entangling operations can transform this task into measurements of commuting observables, reducing complexity exponentially. However, noise in these resources increases the overhead, leaving open whether any advantage remains in realistic devices. Here, we introduce error-mitigated entanglement-enhanced learning, analyze it theoretically, and demonstrate it experimentally. We quantify the noise-induced overhead, perform hypothesis testing with up to 64 qubits, and learn intrinsic noise in parallel-gate layers using up to 16 qubits of a superconducting processor. We show that noisy quantum memory provides a learning advantage, with a current experimental overhead of 1.33 ± 0.05 per qubit, below the no-entanglement lower bound of 2. The authors show that entanglement with noisy quantum memory can significantly speed up learning of quantum processes. With error mitigation, their method characterizes quantum noise at scale and outperforms entanglement-free approaches.
A longstanding goal in quantum information science is to demonstrate quantum computations that cannot be feasibly reproduced on a classical computer. Such demonstrations mark major milestones: they showcase fine control over quantum systems and are prerequisites for useful quantum computation. To date, quantum advantage has been demonstrated, for example, through violations of Bell inequalities and sampling-based quantum supremacy experiments. However, both forms of advantage come with important caveats: Bell tests are not computationally difficult tasks, and the classical hardness of sampling experiments relies on unproven complexity-theoretic assumptions. Here we demonstrate an unconditional quantum advantage in information resources required for a computational task, realized on Quantinuum's H1-1 trapped-ion quantum computer operating at a median two-qubit partial-entangler fidelity of 99.941(7)%. We construct a task for which the most space-efficient classical algorithm provably requires between 62 and 382 bits of memory, and solve it using only 12 qubits. Our result provides the most direct evidence yet that currently existing quantum processors can generate and manipulate entangled states of sufficient complexity to access the exponentiality of Hilbert space. This form of quantum advantage -- which we call quantum information supremacy -- represents a new benchmark in quantum computing, one that does not rely on unproven conjectures.
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.
The advent of noisy intermediate-scale quantum computers has put the search for possible applications to the forefront of quantum information science. One area where hopes for an advantage through near-term quantum computers are high is quantum machine learning, where variational quantum learning models based on parametrized quantum circuits are discussed. In this work, we introduce the concept of a classical surrogate, a classical model which can be efficiently obtained from a trained quantum learning model and reproduces its input-output relations. As inference can be performed classically, the existence of a classical surrogate greatly enhances the applicability of a quantum learning strategy. However, the classical surrogate also challenges possible advantages of quantum schemes. As it is possible to directly optimize the Ansatz of the classical surrogate, they create a natural benchmark the quantum model has to outperform. We show that large classes of well-analyzed reuploading models have a classical surrogate. We conducted numerical experiments and found that these quantum models show no advantage in performance or trainability in the problems we analyze. This leaves only generalization capability as a possible point of quantum advantage and emphasizes the dire need for a better understanding of inductive biases of quantum learning models.
Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data outperforms fixed-measurement schemes followed by classical processing. It remained uncertain whether this performance gap persists at a finite scale, and in the presence of noise that is unavoidable with current quantum devices. In this work, we present simulations and analysis of the performance of existing hardware on a learning problem known to exhibit asymptotic advantage, now subjected to noisy quantum data. Comparing coherent quantum processing directly against fixed-measurement schemes, our results demonstrate a clear performance separation at a scale of just 30 to 40 noisy qubits. Already at this scale, the fundamental bottleneck is no longer classical computation but data acquisition; matching the noisy coherent protocol with measure-first strategies would still require months or even years of measurements. By systematically evaluating hardware constraints such as state preparation, gate errors, readout errors, connectivity, and coherence times, we provide evidence that a demonstration of such a strong learning advantage is accessible on near-term devices.
The advent of noisy intermediate-scale quantum computers has put the search for possible applications to the forefront of quantum information science. One area where hopes for an advantage through near-term quantum computers are high is quantum machine learning, where variational quantum learning models based on parametrized quantum circuits are discussed. In this work, we introduce the concept of a classical surrogate, a classical model which can be efficiently obtained from a trained quantum learning model and reproduces its input-output relations. As inference can be performed classically, the existence of a classical surrogate greatly enhances the applicability of a quantum learning strategy. However, the classical surrogate also challenges possible advantages of quantum schemes. As it is possible to directly optimize the Ansatz of the classical surrogate, they create a natural benchmark the quantum model has to outperform. We show that large classes of well-analyzed reuploading models have a classical surrogate. We conducted numerical experiments and found that these quantum models show no advantage in performance or trainability in the problems we analyze. This leaves only generalization capability as a possible point of quantum advantage and emphasizes the dire need for a better understanding of inductive biases of quantum learning models.