TY - JOUR T1 - Provably efficient machine learning for quantum many-body problems JF - Science Y1 - 2022 A1 - Hsin-Yuan Huang A1 - Richard Kueng A1 - Giacomo Torlai A1 - Victor V. Albert A1 - John Preskill AB -

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

VL - 377 UR - https://arxiv.org/abs/2106.12627 U5 - 10.1126/science.abk3333 ER - TY - JOUR T1 - Recovering quantum gates from few average gate fidelities JF - Phys. Rev. Lett. Y1 - 2018 A1 - Ingo Roth A1 - Richard Kueng A1 - Shelby Kimmel A1 - Yi-Kai Liu A1 - David Gross A1 - Jens Eisert A1 - Martin Kliesch AB -

Characterising quantum processes is a key task in and constitutes a challenge for the development of quantum technologies, especially at the noisy intermediate scale of today's devices. One method for characterising processes is randomised benchmarking, which is robust against state preparation and measurement (SPAM) errors, and can be used to benchmark Clifford gates. A complementing approach asks for full tomographic knowledge. Compressed sensing techniques achieve full tomography of quantum channels essentially at optimal resource efficiency. So far, guarantees for compressed sensing protocols rely on unstructured random measurements and can not be applied to the data acquired from randomised benchmarking experiments. It has been an open question whether or not the favourable features of both worlds can be combined. In this work, we give a positive answer to this question. For the important case of characterising multi-qubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured respect to random Clifford unitaries. Moreover, for general unital quantum channels we provide an explicit expansion into a unitary 2-design, allowing for a practical and guaranteed reconstruction also in that case. As a side result, we obtain a new statistical interpretation of the unitarity -- a figure of merit that characterises the coherence of a process. In our proofs we exploit recent representation theoretic insights on the Clifford group, develop a version of Collins' calculus with Weingarten functions for integration over the Clifford group, and combine this with proof techniques from compressed sensing.

VL - 121 U4 - 170502 UR - https://arxiv.org/abs/1803.00572 U5 - https://doi.org/10.1103/PhysRevLett.121.170502 ER -