Solving independent set problems with photonic quantum circuits.

An independent set (IS) is a set of vertices in a graph such that no edge connects any two vertices. In adiabatic quantum computation [E. Farhi, et al., Science 292, 472-475 (2001); A. Das, B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061-1081 (2008)], a given graph G(V, E) can be naturally mapped onto a many-body Hamiltonian [Formula: see text], with edges [Formula: see text] being the two-body interactions between adjacent vertices [Formula: see text]. Thus, solving the IS problem is equivalent to finding all the computational basis ground states of [Formula: see text]. Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of [Formula: see text] [B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]. Here, we solve a representative IS problem [Formula: see text] by simulating the NAAM digitally using a linear optical quantum network, consisting of three C-Phase gates, four deterministic two-qubit gate arrays (DGA), and ten single rotation gates. The maximum IS has been successfully identified with sufficient Trotterization steps and a carefully chosen evolution path. Remarkably, we find IS with a total probability of 0.875(16), among which the nontrivial ones have a considerable weight of about 31.4%. Our experiment demonstrates the potential advantage of NAAM for solving IS-equivalent problems.

Full-Period Quantum Phase Estimation.

Quantum sensing can provide the superior sensitivity for sensing a physical quantity beyond the shot-noise limit. In practice, however, this technique has been limited to the issues of phase ambiguity and low sensitivity for small-scale probe states. Here, we propose and demonstrate a full-period quantum phase estimation approach by adopting the Kitaev's phase estimation algorithm to eliminate the phase ambiguity and using the GHZ states to obtain phase value, simultaneously. For an N-party entangled state, our approach can achieve an upper bound of sensitivity of δθ=sqrt[3/(N^{2}+2N)], which beats the limit of adaptive Bayesian estimation. By performing an eight-photon experiment, we demonstrate the estimation of unknown phases in a full period, and observe the phase superresolution and sensitivity beyond the shot-noise limit. Our Letter provides a new way for quantum sensing and represents a solid step towards its general applications.

Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver.

The recognition of entanglement states is a notoriously difficult problem when no prior information is available. Here, we propose an efficient quantum adversarial bipartite entanglement detection scheme to address this issue. Our proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits, where a two-outcome measurement can be used to query a classical binary result about whether the input state is bipartite entangled or not. In principle, for an N-qubit quantum state, the runtime complexity of our proposal is O(poly(N)T) with T being the number of iterations. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states. Our work paves the way for using near-term quantum machines to tackle entanglement detection on multipartite entangled quantum systems.

Counting Classical Nodes in Quantum Networks.

Quantum networks illustrate the use of connected nodes of quantum systems as the backbone of distributed quantum information processing. When the network nodes are entangled in graph states, such a quantum platform is indispensable to almost all the existing distributed quantum tasks. Unfortunately, real networks unavoidably suffer from noise and technical restrictions, making nodes transit from quantum to classical at worst. Here, we introduce a figure of merit in terms of the number of classical nodes for quantum networks in arbitrary graph states. Such a network property is revealed by exploiting a novel Einstein-Podolsky-Rosen steerability. Experimentally, we demonstrate photonic quantum networks of n_{q} quantum nodes and n_{c} classical nodes with n_{q} up to 6 and n_{c} up to 18 using spontaneous parametric down-conversion entanglement sources. We show that the proposed method is faithful in quantifying the classical defects in prepared multiphoton quantum networks. Our results provide novel identification of generic quantum networks and nonclassical correlations in graph states.

Measurement-Device-Independent Entanglement Witness of Tripartite Entangled States and Its Applications.

Entanglement witness is of great importance in characterizing quantum systems. The imperfections in conventional entanglement witness schemes could lead to the misidentification of a separated state as an entangled state. Measurement-device-independent entanglement witness (MDIEW) has been proposed and demonstrated to resolve the imperfect measurement devices. So far, however, the MDIEW has been restricted to a two-party qubit entangled state. Here, for the first time, we demonstrate MDIEW for multipartite entangled states. We experimentally detect the genuine entanglement and the entanglement structure of a tripartite entangled state based on an eight-photon interferometry. Furthermore, with the verified multipartite entangled state, we demonstrate quantum randomness generation and open-destination quantum key distribution in an measurement-device-independent manner. Our research presents an important step toward building a robust and secure quantum network.