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Experimental learning of quantum states.

Andrea Rocchetto, Scott Aaronson, Simone Severini B +5 more

The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling limits our ability to characterize and simulate the evolution of arbitrary states to systems, with no more than a few qubits. However, from a computational learning theory perspective, it can be shown that quantum states can be approximately learned using a number of measurements growing linearly with the number of qubits. Here, we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of the computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales.The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling limits our ability to characterize and simulate the evolution of arbitrary states to systems, with no more than a few qubits. However, from a computational learning theory perspective, it can be shown that quantum states can be approximately learned using a number of measurements growing linearly with the number of qubits. Here, we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of the computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales.

Mar 1, 201966 citations

Learning photonic quantum states

Hugo Thomas, Ulysse Chabaud, Pierre-Emmanuel Emeriau

PRX QuantumOct 16, 20260 citations

Learning the tensor network model of a quantum state using a few single-qubit measurements

Sergei S. Kuzmin, Varvara Mikhailova, I. V. Dyakonov +1 more

The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth of the required number of measurements. The conceptual solution for this dimensionality curse relies on a simple idea---a complete description of a quantum state is excessive and can be discarded in favor of experimentally accessible information about the system. The probably approximately correct learning theory has been recently successfully applied to a problem of building accurate predictors for the measurement outcomes using a data set which scales only linearly with the number of qubits. Here, we present a constructive and numerically efficient protocol which learns a tensor network model of an unknown quantum system. We discuss the limitations and the scalability of the proposed method.The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth of the required number of measurements. The conceptual solution for this dimensionality curse relies on a simple idea---a complete description of a quantum state is excessive and can be discarded in favor of experimentally accessible information about the system. The probably approximately correct learning theory has been recently successfully applied to a problem of building accurate predictors for the measurement outcomes using a data set which scales only linearly with the number of qubits. Here, we present a constructive and numerically efficient protocol which learns a tensor network model of an unknown quantum system. We discuss the limitations and the scalability of the proposed method.

arXiv:2309.00397Physical Review AMay 9, 20247 citations

Photonic quantum states for quantum applications

Virginia O. Lorenz

Bulletin of the American Physical SocietyMar 4, 20200 citations

Entanglement as a complexity measure for quantum state preparation.

Israel F. Araujo, Carsten Blank, Adenilton José da Silva

State preparation algorithms are routines used in many quantum computing applications, from solving a linear system of equations to quantum machine learning. In this paper, we present an exact state preparation algorithm that considers entanglement to reduce the complexity of the generated quantum circuit. The proposed method allows approximation by entanglement reduction. The approximation of an entangled state by two separable states allows a quadratic decrease in the number of CNOT gates in exchange for an approximation error. Through experimental analysis with 7-qubits devices, the approximation error observed through measurements is smaller than the error due to the noise generated by the circuit to prepare the original state.State preparation algorithms are routines used in many quantum computing applications, from solving a linear system of equations to quantum machine learning. In this paper, we present an exact state preparation algorithm that considers entanglement to reduce the complexity of the generated quantum circuit. The proposed method allows approximation by entanglement reduction. The approximation of an entangled state by two separable states allows a quadratic decrease in the number of CNOT gates in exchange for an approximation error. Through experimental analysis with 7-qubits devices, the approximation error observed through measurements is smaller than the error due to the noise generated by the circuit to prepare the original state.

Nov 7, 20213 citations

Quantum state engineering with photonic qubits

Klaus M. Gheri, Päivi Törmä, P. Zoller

Acta Physica Slovaca Reviews and TutorialsAug 1, 19990 citations

Experimental learning of quantum states

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Experimental learning of quantum states

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