Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip

Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, non-fault tolerant, quantum devices. Here we report experimental results demonstrating that this intuition need not be true. We implement a recently proposed adaptive Bayesian approach to quantum phase estimation and use it to simulate molecular energies on a Silicon quantum photonic device. The approach is verified to be well suited for pre-threshold quantum processors by investigating its superior robustness to noise and decoherence compared to the iterative phase estimation algorithm. This shows a promising route to unlock the power of quantum phase estimation much sooner than previously believed

Classifying Subset Feedback Vertex Set for H-free graphs

In the FEEDBACK VERTEX SET problem, we aim to find a small set S of vertices in a graph intersecting every cycle. The SUBSET FEEDBACK VERTEX SET problem requires S to intersect only those cycles that include a vertex of some specified set T. We also consider the WEIGHTED SUBSET FEEDBACK VERTEX SET problem, where each vertex u has weight w(u)>0 and we ask that S has small weight. By combining known NP-hardness results with new polynomial-time results we prove full complexity dichotomies for SUBSET FEEDBACK VERTEX SET and WEIGHTED SUBSET FEEDBACK VERTEX SET for H-free graphs, that is, graphs that do not contain a graph H as an induced subgraph

Generation and sampling of quantum states of light in a silicon chip

Implementing large instances of quantum algorithms requires the processing of many quantum information carriers in a hardware platform that supports the integration of different components. While established semiconductor fabrication processes can integrate many photonic components, the generation and algorithmic processing of many photons has been a bottleneck in integrated photonics. Here we report the on-chip generation and processing of quantum states of light with up to eight photons in quantum sampling algorithms. Switching between different optical pumping regimes, we implement the Scattershot, Gaussian and standard boson sampling protocols in the same silicon chip, which integrates linear and nonlinear photonic circuitry. We use these results to benchmark a quantum algorithm for calculating molecular vibronic spectra. Our techniques can be readily scaled for the on-chip implementation of specialised quantum algorithms with tens of photons, pointing the way to efficiency advantages over conventional computers

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it provide a new quantum approach which combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled-unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32-bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with minor typos corrected.

Multidimensional quantum entanglement with large-scale integrated optics

The ability to control multidimensional quantum systems is key for the investigation of fundamental science and for the development of advanced quantum technologies. Here we demonstrate a multidimensional integrated quantum photonic platform able to robustly generate, control and analyze high-dimensional entanglement. We realize a programmable bipartite entangled system with dimension up to $15 \times 15$ on a large-scale silicon-photonics quantum circuit. The device integrates more than 550 photonic components on a single chip, including 16 identical photon-pair sources. We verify the high precision, generality and controllability of our multidimensional technology, and further exploit these abilities to demonstrate key quantum applications experimentally unexplored before, such as quantum randomness expansion and self-testing on multidimensional states. Our work provides a prominent experimental platform for the development of multidimensional quantum technologies.Comment: Science, (2018