Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor

Abstract

Applications of quantum walks can depend on the number, exchange symmetry and indistinguishability of the particles involved, and the underlying graph structures where they move. Here, we show that silicon photonics, by exploiting an entanglement-driven scheme, can realize quantum walks with full control over all these properties in one device. The device we realize implements entangled two-photon quantum walks on any five-vertex graph, with continuously tunable particle exchange symmetry and indistinguishability. We show how this simulates single-particle walks on larger graphs, with size and geometry controlled by tuning the properties of the composite quantum walkers. We apply the device to quantum walk algorithms for searching vertices in graphs and testing for graph isomorphisms. In doing so, we implement up to 100 sampled time steps of quantum walk evolution on each of 292 different graphs. This opens the way to large-scale, programmable quantum walk processors for classically intractable applications.

Implementation of Pruned Backpropagation Neural Network Based on Photonic Integrated Circuits

“…Future work is likely to extend to optical quantum neural networks, as many features of quantum optics can be directly mapping to neural networks [42], and technological advances driven by the trends of the photon quantum computing and optoelectronic industry provide possible venues for the large-scale and high bandwidth localization of quantum optical neural networks. Programmable silicon photonic devices can simulate the quantum walking dynamics of relevant particles, and all important parameters can be fully controlled, including the hamiltonian structure, evolution time, particle resolution and exchange symmetry [43]. Removing redundant photon devices in the universal unitary process by weight-elimination can facilitate the construction of large-scale and low-cost optical quantum neural networks.…”

Electric-Circuit Realization of Fast Quantum Search

“…That means, to realize the CTQW algorithm, the resources we need in our classical circuit scheme have the same complexity to that of those quantum schemes as described in Refs. [ 13 , 40 ].…”

“…In such a case, the maximum success probability of finding the target vertex is 1, and the minimum evolution time is π ffiffiffiffi N p /2 [4,5]. Up to now, quantum search algorithm has been implemented under many standard quantum circuit models, such as optical experiments [8][9][10][11][12][13], NMR systems [14,15], trapped ion [16][17][18], NV centers [19][20][21], and superconducting systems [22]. However, these quantum schemes face two bottlenecks: scalability and decoherence.…”

“…Up to now, quantum search algorithm has been implemented under many standard quantum circuit models, such as optical experiments [ 8 – 13 ], NMR systems [ 14 , 15 ], trapped ion [ 16 – 18 ], NV centers [ 19 – 21 ], and superconducting systems [ 22 ]. However, these quantum schemes face two bottlenecks: scalability and decoherence.…”

Advances in Chip‐Scale Quantum Photonic Technologies

“…They have shown great potential for realizing system integration and performance required by QIP. [19][20][21][22][23][24][25][26] Generally, integrated quantum photonic information processor demands three functions: efficient generation of on-demand quantum states, their manipulation in various degrees of freedom, and single photon detection. Different material platforms have their own strengths to realize the three functions individually or partially.…”