Kwek, Leong Chuan

We study a Rabi type Hamiltonian system in which a qubit and a d-level quantum system (qudit) are coupled through a common resonator. In the weak and strong coupling limits the spectrum is analysed through suitable perturbative schemes. The analysis show that the presence of the multilevels of the qudit effectively enhance the qubit-qudit interaction. The ground state of the strongly coupled system is found to be of Greenberger-Horne-Zeilinger (GHZ) type. Therefore, despite the qubit-qudit strong coupling, the nature of the specific tripartite entanglement of the GHZ state suppresses the bipartite entanglement. We analyze the system dynamics under quenching and adiabatic switching of the qubit-resonator and qudit-resonator couplings. In the quench case, we found that the non-adiabatic generation of photons in the resonator is enhanced by the number of levels in the qudit. The adiabatic control represents a possible route for preparation of GHZ states. Our analysis provides relevant information for future studies on coherent state transfer in qubit-qudit systems.

Integrated photonic chips leverage the recent developments in integrated circuit technology, along with the control and manipulation of light signals, to realize the integration of multiple optical components onto a single chip. By exploiting the power of light, integrated photonic chips offer numerous advantages over traditional optical and electronic systems, including miniaturization, high-speed data processing and improved energy efficiency. In this review, we survey the current status of quantum computation, optical neural networks and the realization of some algorithms on integrated optical chips.

Periodic driving has a longstanding reputation for generating exotic phases of matter with no static counterparts. This work explores the interplay between periodic driving, interaction effects, and Z₂ symmetry that leads to the emergence of Floquet symmetry protected second-order topological phases in a simple but insightful two-dimensional spin-1/2 lattice. Through a combination of analytical and numerical treatments, we verify the formation of corner-localized 0 and π modes, i.e., Z₂ symmetry broken operators that commute and anticommute, respectively, with the one-period time evolution operator, as well as establish the topological nature of these modes by demonstrating their presence over a wide range of parameter values and explicitly deriving their associated topological invariants under special conditions. Finally, we propose a means to detect the signature of such modes in experiments, and we discuss the effect of imperfections.

Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of molecular systems. Here, we extend near-term quantum simulations of chemistry to time-dependent processes by simulating energy transfer in organic semiconducting molecules. We developed a multiscale modeling workflow that combines conventional molecular dynamics and quantum chemistry simulations with hybrid variational quantum algorithm to compute the exciton dynamics in both the single excitation subspace (i.e., Frenkel Hamiltonian) and the full-Hilbert space (i.e., multiexciton) regimes. Our numerical examples demonstrate the feasibility of our approach, and simulations on IBM Q devices capture the qualitative behaviors of exciton dynamics, but with considerable errors. We present an error mitigation technique that combines experimental results from the variational and Trotter algorithms, and obtain significantly improved quantum dynamics. Our approach opens up new opportunities for modeling quantum dynamics in chemical, biological, and material systems with quantum computers.

Universal quantum entangling gates are a crucial building block in the large-scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the implementation of a controlled-NOT (CNOT) gate is constructed by introducing a non-computational quantum state in the auxiliary space. Furthermore, the method is extended to the construction of a general n-control-qubit Toffoli gate with (2𝑛−1) qubit–qudit gates and (2𝑛−2) single-qudit gates. Based on the presented quantum circuits, the polarization CNOT and Toffoli gates with linear optics are designed by operating on the spatial-mode degree of freedom of photons. The proposed optical schemes can be achieved with a higher success probability and no extra auxiliary photons are needed.

Quantum plasmonic systems suffer from significant decoherence due to the intrinsically large dissipative and radiative dampings. Based on our quantum simulations νiα a quantum tensor network algorithm, we numerically demonstrate the mitigation of this restrictive drawback by hybridizing a plasmonic nanocavity with an emitter ensemble with inhomogeneously broadened transition frequencies. By burning two narrow spectral holes in the spectral density of the emitter ensemble, the coherent time of Rabi oscillation for the hybrid system is increased tenfold. With the suppressed decoherence, we move one step further in bringing plasmonic systems into practical quantum applications.

The calculation of off-diagonal matrix elements has various applications in fields such as nuclear physics and quantum chemistry. In this paper, we present a noisy intermediate scale quantum algorithm for estimating the diagonal and off-diagonal matrix elements of a generic observable in the energy eigenbasis of a given Hamiltonian without explicitly preparing its eigenstates. By means of numerical simulations we show that this approach finds many of the matrix elements for the one and two qubits cases. Specifically, while in the first case, one can initialize the ansatz parameters over a broad interval, in the latter the optimization landscape can significantly slow down the speed of convergence and one should therefore be careful to restrict the initialization to a smaller range of parameters.

Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at effectively using the currently available quantum hardware. For quantum simulation, various types of NISQ algorithms have been proposed with individual advantages as well as challenges. In this work, we propose a new algorithm, truncated Taylor quantum simulator (TQS), that shares the advantages of existing algorithms and alleviates some of the shortcomings. Our algorithm does not have any classical-quantum feedback loop and bypasses the barren plateau problem by construction. The classical part in our hybrid quantum-classical algorithm corresponds to a quadratically constrained quadratic program (QCQP) with a single quadratic equality constraint, which admits a semidefinite relaxation. The QCQP based classical optimization was recently introduced as the classical step in quantum assisted eigensolver (QAE), a NISQ algorithm for the Hamiltonian ground state problem. Thus, our work provides a conceptual unification between the NISQ algorithms for the Hamiltonian ground state problem and the Hamiltonian simulation. We recover differential equation-based NISQ algorithms for Hamiltonian simulation such as quantum assisted simulator (QAS) and variational quantum simulator (VQS) as particular cases of our algorithm. We test our algorithm on some toy examples on current cloud quantum computers. We also provide a systematic approach to improve the accuracy of our algorithm.

In recent experiments, the compression from qutrit to qubit is realized by the autoencoder. Inspired by the idea of dimensionality reduction, we apply the rotation transformation to compress the states. Starting from Lie algebra, we construct a 3*3 unitary matrix acting on 3*1 state and realize the rotation transformation of the states and then achieve compression of 3*1 state. Each rotation of a state is a compression, and each compression-only needs to adjust two parameters. According to the compression of 3*1 and 4*1 states by unitary matrices, we further discuss the compression law of N*1 states by unitary matrices. In the process of compression, we can adjust the form of the unitary matrix according to the system condition to change the compression position. In this paper, we focus on the compression law along the diagonal from top to bottom. We redesigned the autoencoder and added the waveplate combination to reduce the parameters without affecting the results and achieve the purpose of state compression.

Self-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set B_Q of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, B_Q is difficult to characterize, so it is also difficult to prove whether or not a given matrix of quantum correlations allows for self-testing. Here, we show how some tools from graph theory can help to address this problem. We observe that B_Q is strictly contained in an easy-to-characterize set associated with a graph, Θ(G). Therefore, whenever the optimum over B_Q and the optimum over Θ(G)) coincide, self-testing can be demonstrated by simply proving self-testability with Θ(G). Interestingly, these maxima coincide for the quantum correlations that maximally violate many families of Bell-like inequalities. Therefore, we can apply this approach to prove the self-testability of many quantum correlations, including some that are not previously known to allow for self-testing. In addition, this approach connects self-testing to some open problems in discrete mathematics. We use this connection to prove a conjecture [M. Araujo et a/., Phys. Rev. A, 88, 022118 (2013)] about the closed-form expression of the Lovasz theta number for a family of graphs called the Mobius ladders. Although there are a few remaining issues (e.g., in some cases, the proof requires the assumption that measurements are of rank 1). this approach provides an alternative method to self-testing and draws interesting connections between quantum mechanics and discrete mathematics.