Abstract
Currently available quantum hardware allows for small-scale implementations of quantum machine learning algorithms. Such experiments aid the search for applications of quantum computers by benchmarking the near-term feasibility of candidate algorithms. Here we demonstrate the quantum learning of a two-qubit unitary by a sequence of three parameterized quantum circuits containing a total of 21 variational parameters. Moreover, we variationally diagonalize the unitary to learn its spectral decomposition, i.e., its eigenvalues and eigenvectors. We illustrate how this can be used as a subroutine to compress the depth of dynamical quantum simulations. One can view our implementation as a demonstration of entanglement-enhanced machine learning, as only a single (entangled) training data pair is required to learn a $4\ifmmode\times\else\texttimes\fi{}4$ unitary matrix.
Highlights
Quantum simulation and machine learning are among the most promising applications of large-scale quantum computers
The discovery of algorithms with provable exponential speedup has been more challenging in the machine learning domain, in part because it is harder to port established machine learning techniques to the quantum setting [1]
Variational quantum algorithms [21–23] will likely facilitate near-term implementations for these applications. Such algorithms employ a problem-specific cost function that is evaluated on a quantum computer, while a classical optimizer trains a parameterized quantum circuit to minimize this cost
Summary
Quantum simulation and machine learning are among the most promising applications of large-scale quantum computers. Variational quantum algorithms to learn and diagonalize density matrices have been developed [33–35], which is a fundamental subroutine that will have many uses including principal component analysis and estimation of quantum information quantities [36,37]. A hybrid protocol for learning a unitary is provided by the quantum-assisted quantum compiling algorithm [38] This is a low-depth subroutine appropriate for both near-term and fault-tolerant quantum computing. More challenging than state learning, learning a unitary can be used for a wide variety of quantum information applications, including circuit depth compression, 2643-1564/2021/3(3)/033200(8). One can use quantum-assisted quantum compiling to variationally diagonalize a unitary This is useful for a variety of quantum information science applications, since access to the spectral decomposition of a unitary U enables arbitrary powers of U to be implemented using a fixed depth circuit. Transverse field about the qubits used in the experiment are provided in Appendix A
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