Quantum advantage in learning from experiments

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.

Revisiting dequantization and quantum advantage in learning tasks

“…For example, when comparing to quantum algorithms with quantum state inputs, we could consider classical algorithms with access to classical data obtained by measuring the quantum states. Classical algorithms with access to measurement data are still very powerful, being capable of predicting outcomes of quantum experiments [2,4,9,10], classifying quantum phases of matter [11], predicting ground state properties [11], etc. However, classical algorithms with measurement data access will never be more powerful than quantum algorithms with quantum state inputs because quantum algorithms can always perform the measurements within the algorithm.…”

“…It is likely that various learning tasks considered to have no exponential quantum advantage are thought of as such due to the power of SQ access. For example, we established an exponential quantum advantage for quantum principal component analysis (quantum PCA) in [9] when we compare quantum algorithms with quantum state inputs to classical algorithms with access to measurement data. This result contrasts with the lack of exponential advantage in quantum PCA [15] when we compare to classical algorithms with SQ access.…”

“…For instance, we could let ̃︁ SQ access just have the sample operation. Or alternatively, we could allow ̃︁ SQ to access outcomes of a polynomial-time POVM measurement applied to |𝑥⟩ (see, for instance, [2,4,9,10]).…”

Quantum Computing 2022

“…The progress spurred in experimental and theoretical efforts makes this an exciting area to remain abreast of in 2022. Some newer quantum primacy proposals are targeting more practical efforts [78], making the race between quantum and conventional technologies an interesting area to follow. Next, we turn toward practical applications and quantum algorithms.…”

Learning Noise via Dynamical Decoupling of Entangled Qubits

“…Producing interesting, large-scale, quantum dynamics in engineered systems is being made increasingly possible by the advancement of superconducting qubits. Transmon qubits that use frequency tunable couplers to realize inter-qubit interactions have been successful at this task in the areas of quantum simulation [1-3], quantum chemistry [4], and theoretical computer science [5][6][7][8]. Imperative to this is the ability to generate entanglement using high-fidelity two-qubit gates [9,10].…”