Self-testing of Quantum Circuits

Robert Wille, Lukas Burgholzer

Shuquan Ma, Changhua Zhu, Min Nie +1 more

Verification in quantum computations is crucial since quantum systems are extremely vulnerable to the environment. However, verifying directly the output of a quantum computation is difficult since we know that efficiently simulating a large-scale quantum computation on a classical computer is usually thought to be impossible. To overcome this difficulty, we propose a self-testing system for quantum computations, which can be used to verify if a quantum computation is performed correctly by itself. Our basic idea is using some extra ancilla qubits to test the output of the computation. We design two kinds of permutation circuits into the original quantum circuit: one is applied on the ancilla qubits whose output indicates the testing information, the other is applied on all qubits (including ancilla qubits) which is aiming to uniformly permute the positions of all qubits. We show that both permutation circuits are easy to achieve. By this way, we prove that any quantum computation has an efficient self-testing system. In the end, we also discuss the relation between our self-testing system and interactive proof systems, and show that the two systems are equivalent if the verifier is allowed to have some quantum capacity.

Simon Storz, Anatoly Kulikov, Josua Schär +6 more

Self-testing protocols enable the certification of quantum systems in a device-independent manner, i.e., without knowledge of the inner workings of the quantum devices under test. Here, we demonstrate this high standard for characterization routines with superconducting circuits, a prime platform for building large-scale quantum computing systems. We first develop the missing theory allowing for the self-testing of Pauli measurements. We then self-test Bell pair generation and measurements at the same time, performing a complete self-test in a system composed of two entangled superconducting circuits operated at a separation of 30 m. In an experiment based on 17 million trials, we measure an average CHSH (Clauser-Horne-Shimony-Holt) S value of 2.236. Without relying on additional assumptions on the experimental setup, we certify an average Bell state fidelity of at least 58.9% and an average measurement fidelity of at least 89.5% in a device-independent manner, both with 99% confidence. This enables applications in the field of distributed quantum computing and communication with superconducting circuits, such as delegated quantum computing.

Yu-Hao Wang, Xing-Fu Wang, Ming-Ming Du +4 more

Hyperentanglement, which refers to entanglement encoded in two or more independent degrees of freedom (DOFs), is a valuable resource for the future high-capacity quantum network. Certifying hyperentanglement sources work as intended is critical for the hyperentanglement-based quantum information tasks. Self testing is the strongest certification method for quantum state and measurement under minimal assumptions, even without any knowledge of the devices' inner workings. However, the existing self testing protocols all focus on one-DOF entanglement, which cannot self test the multi-DOF entanglement. In the paper, we propose a hyperentanglement self testing framework. We take the self testing for the polarization-spatial-mode hyperentangled Bell states as an example. The self testing is based on the violation of two-dimension CHSH test in each DOF independently. The two-step swap isometry circuits are proposed for self testing the entanglement in spatial-mode and polarization DOFs, respectively. All the sixteen polarization-spatial-mode hyperentangled Bell states can be self tested. Our hyperentanglement self testing framework has three advantages. First, it is a general hyperentanglement self testing framework, and can be extended to self test multi-DOF hyperentanglement and multipartite hyperentanglement. Second, it can provide the robust hyperentanglement self testing and establish the relation between the lower bound of fidelity and the imperfect violation of Bell-like inequality in each DOF. Third, it is feasible with current experimental technology. Our hyperentanglement self testing framework provides a promising way to certify complex hyperentanglement sources, and has potential application in future high-capacity quantum network.

Robert Wille, Lukas Burgholzer

Margareta Vamos