Quantum advantage in learning from experiments (2112.00778v1)

Abstract: Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes are processed using a classical computer. We prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than those required in conventional experiments. The exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. In some tasks, the quantum processing needed to achieve the exponential advantage can be modest; for example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. Our results highlight how quantum technology can enable powerful new strategies to learn about nature.

• The paper shows that quantum-enhanced methods predict observables with exponentially fewer experiments than classical procedures.
• It applies quantum principal component analysis to estimate state properties with dramatically reduced data requirements.
• Experimental tests on Google's Sycamore processor validate that quantum techniques robustly outperform classical approaches even in noisy settings.

Quantum Advantage in Learning from Experiments

The paper explores the potential of quantum technologies to enhance the efficiency and effectiveness of learning from experimental data. By leveraging quantum memory and quantum computing, it posits that certain quantum-enhanced experiments can achieve exponentially greater efficiency than their classical counterparts. This exploration is motivated by the limitations of classical methods when analyzing quantum phenomena and aims to unlock new methodologies that could redefine our understanding and capabilities in processing quantum data.

Theoretical Demonstration

The paper provides rigorous proof that quantum machines have the capacity to learn about specific properties of quantum systems using exponentially fewer experimental trials than would be required in a classical framework. In particular, the authors demonstrate this quantum advantage in tasks such as predicting observables, performing principal component analysis (PCA) on quantum states, and learning evolution processes.

1. Predicting Observables: The paper proves that for certain states and sets of target observables, the number of experiments required classically is exponential in the system size, whereas a quantum-enhanced procedure requires only a constant number of experiments. This advantage arises from the ability of quantum systems to simultaneously process and utilize the state copies through entanglement and superposition, aspects inherently inaccessible to classical systems.
2. Quantum Principal Component Analysis (PCA): The authors extend the exponential advantage to PCA, where they prove that estimating properties related to the principal components of quantum states requires exponentially fewer copies in the quantum scenario. Specifically, tasks that are computationally trivial in a quantum setup face exponential complexity barriers when tackled classically.
3. Learning Quantum Processes: A crucial result of the paper is the assertion that quantum systems provide an exponential advantage when learning models of quantum processes. By simulating classical algorithms and comparing them with quantum-enhanced methods, the results indicate that for certain model learning tasks, classical approaches require exponentially more data to achieve comparable predictive power.

Experimental Validation

With empirical evidence gathered using Google's Sycamore quantum processor, the paper undertakes proof-of-principle experiments that underscore the theoretical results. These experiments examine the quantum advantage in learning the operations of quantum dynamics and nuclear observables, with quantum-enhanced methods displaying superior performance despite the presence of noise in current quantum processors.

1. Observables and Dynamics: The processed quantum data, acquired from quantum experiments, was analyzed using machine learning models that confirmed the quantum advantage in recognizing structure and correlations that would typically remain obscured in classical sets.
2. Impact of Quantum Noise: Notably, even with noisy intermediate-scale quantum devices, quantum technologies prove resilient, maintaining substantial advantages over classical methodologies in tasks tested, thereby validating the practical realization and resilience of the theoretically proposed quantum advantage.

Implications and Future Directions

The implications of these findings suggest a transformative potential for quantum technologies in scientific research and data analysis. The capacity to extract meaningful insights from fewer data and reduced experimental iterations can lead to substantial cost and time savings in various scientific fields. Moreover, further development and scaling of quantum sensors and transducers will likely enhance these quantum advantages, allowing for direct and more robust applications across scientific disciplines.

As noted, the advances in learning from quantum experiments may extend beyond scientific instrumentation to broader applications like quantum machine learning, optimization problems, and cryptographic systems. The robustness of quantum-enhanced strategies with noisy processors supports the feasibility of deploying practical quantum systems in complex and noisy real-world environments, suggesting an exciting frontier in the development and application of quantum technologies.

Future research can focus on extending these quantum advantages to more complex systems and noisy quantum processors, improving error mitigation techniques, and building quantum sensors capable of interfacing naturally with quantum computers to maximize learning efficacy. As quantum technology matures, these theoretical insights will be pivotal in transitioning from conventional methodology to quantum-enhanced reality, fostering innovations in fields ranging from fundamental physics to applied cybersecurity.