Abstract
Quantum process tomography is an experimental technique to fully characterize an unknown quantum process. Standard quantum process tomography suffers from exponentially scaling of the number of measurements with the increasing system size. In this work, we put forward a quantum machine learning algorithm which approximately encodes the unknown unitary quantum process into a relatively shallow depth parametric quantum circuit. We demonstrate our method by reconstructing the unitary quantum processes resulting from the quantum Hamiltonian evolution and random quantum circuits up to $8$ qubits. Results show that those quantum processes could be reconstructed with high fidelity, while the number of input states required are at least $2$ orders of magnitude less than required by the standard quantum process tomography.
Highlights
Quantum process tomography is an indispensable technique in quantum information processing to fully characterize an unknown quantum process [1]
We demonstrate our quantum machine learning algorithm using numerical simulations based on a classical parametric quantum circuit (PQC) simulator
We concentrate on two cases: (1) the unknown unitary process is produced by a quantum Hamiltonian evolution and (2) by random quantum circuits, respectively
Summary
Quantum process tomography is an indispensable technique in quantum information processing to fully characterize an unknown quantum process [1]. [27] demonstrated that one could efficiently encode the information of certain quantum states into a PQC using a gradient-based quantum machine learning algorithm, after which the unknown quantum state can be reconstructed classically with high fidelity using the optimal parameters of the PQC. We demonstrate our approach on the reconstruction of two unitary processes produced by quantum Hamiltonian evolution and random quantum circuits, respectively. In both examples our numerical results show that we could reconstruct a quantum process up to eight qubits with a similarity value [defined in Eq (6)] higher than 99%, and the number of required input quantum states is smaller than that required by SQPT by at least two orders of magnitude. During the training process, we use an additional set of random input states as the validation set, similar to that used in classical machine learning algorithms, which tests the generalization ability of the training outcomes for a particular PQC and set of input states
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