Review on Quantum Walk Computing: Theory, Implementation, and Application

Classical random walk formalism shows a significant role across a wide range of applications. As its quantum counterpart, the quantum walk is proposed as an important theoretical model for quantum computing. By exploiting the quantum effects such as superposition, interference and entanglement, quantum walks and their variety have been extensively studied for achieving beyond classical computing power, and they have been broadly used in designing quantum algorithms in fields ranging from algebraic and optimization problems, graph and network analysis, to quantum Hamiltonian and biochemical process simulations, and even further quantum walk models have proven their capabilities for universal quantum computation. Compared to the conventional quantum circuit models, quantum walks show a feasible path for implementing application-specific quantum computing in particularly the noisy intermediate-scale quantum era. Recently remarkable progress has been achieved in implementing a wide variety of quantum walks and quantum walk applications, demonstrating the great potential of quantum walks. In this review, we provide a thorough summary of quantum walks and quantum walk computing, including aspects of quantum walk theories and characteristics, advances in their physical implementations and the flourishingly developed quantum walk computing applications. We also discuss the challenges facing quantum walk computing, toward realizing a practical quantum computer in the near future.Comment: 61 pages, 8 figure

Fidelity estimation of quantum states on a silicon photonic chip

As a measure of the 'closeness' of two quantum states, fidelity plays a fundamental role in quantum information theory. Fidelity estimation protocols try to strike a balance between information gleaned from an experiment, and the efficiency of its implementation, in terms of the number of states consumed by the protocol. Here we adapt a previously reported optimal state verification protocol (Phys. Rev. Lett. 120, 170502, 2018) for fidelity estimation of two-qubit states. We demonstrate the protocol experimentally using a fully-programmable silicon photonic two-qubit chip. Our protocol outputs significantly smaller error bars of its point estimate in comparison with another widely-used estimation protocol, showing a clear step forward in the ability to estimate the fidelity of quantum states produced by a practical device

Fidelity estimation of quantum states on a silicon photonic chip

As a measure of the 'closeness' of two quantum states, fidelity plays a fundamental role in quantum information theory. Fidelity estimation protocols try to strike a balance between information gleaned from an experiment, and the efficiency of its implementation, in terms of the number of states consumed by the protocol. Here we adapt a previously reported optimal state verification protocol (Phys. Rev. Lett. 120, 170502, 2018) for fidelity estimation of two-qubit states. We demonstrate the protocol experimentally using a fully-programmable silicon photonic two-qubit chip. Our protocol outputs significantly smaller error bars of its point estimate in comparison with another widely-used estimation protocol, showing a clear step forward in the ability to estimate the fidelity of quantum states produced by a practical device

Efficient quantum walk on a quantum processor

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor

Plasma metabolomic signatures of breast cancer

BackgroundBreast cancer is a common malignant tumor. A large number of medical evidence shows that breast cancer screening can improve the early diagnosis rate and reduce the mortality rate of breast cancer. In the present study, a wide range of targeted metabolomics profiling was conducted to investigate the plasma signatures of breast cancer.MethodsA total of 86 patients with benign breast abnormalities (L group) and 143 patients with breast cancer (E group) were recruited. We collected their plasma samples and clinical information. Metabolomic analysis, based on the coverage of a wide range of targeted metabolomics was conducted with ultraperformance liquid chromatography- triple quadrupole-linear ion trap mass spectrometer (UPLC-QTRAP-MS).ResultsWe identified 716 metabolites through widely-targeted metabolomics. Serotonergic synapse was the main different metabolic pathway. The fold change of 14 metabolites was considered significantly different (fold change <0.67 or fold change >2; p < 0.05). By combining all the 14 metabolites, we achieved differentiation of L group vs. E group (AUC = 0.792, 95%Cl: 0.662–0.809).ConclusionThis study provided new insights into plasma biomarkers for differential diagnosis of benign abnormalities and breast cancer