# All

Optimization problems in disciplines such as machine learning are commonly

solved with iterative methods. Gradient descent algorithms find local minima by

moving along the direction of steepest descent while Newton's method takes into

account curvature information and thereby often improves convergence. Here, we

develop quantum versions of these iterative optimization algorithms and apply

them to polynomial optimization with a unit norm constraint. In each step,

The resonance fluorescence of a four-level atom in J = 1/2 to J = 1/2

transition driven by two coherent fields is studied. We find that the

incoherent fluorescence spectrum shows a direct indication of vacuum-induced

coherence in the atomic system. We show that such coherence manifests itself

via an enhancement or suppression of the spectral peaks in the $\pi$-polarized

fluorescence. The effect of the relative phase of the driving fields on the

spectral features is also investigated. We show that phase-dependent

We introduce a protocol capable of generating a general measurement operator

for a mechanical resonator. The technique requires a qubit-resonator

interaction and uses a coherent pulse to drive qubit transitions. This is

followed by projective measurement of the qubit's energy, constraining the

resonator in a state that depends on the pulse shape. The freedom to choose a

pulse shape for the coherent drive enables an arbitrary position-basis

measurement operator. Using this measurement operator, we outline a two pulse

Quantum computers, which take advantage of the superposition and entanglement

of physical states, could outperform their classical counterparts in solving

problems with technological impact, such as factoring large numbers and

searching databases. A quantum processor executes algorithms by applying a

programmable sequence of gates to an initialized state of qubits, which

coherently evolves into a final state containing the result of the computation.

Although quantum processors with a few qubits have been demonstrated on

We propose the concept of machine learning configuration interaction (MLCI)

whereby an artificial neural network is trained on-the-fly to predict important

new configurations in an iterative selected configuration interaction

procedure. We demonstrate that the neural network can discriminate between

important and unimportant configurations, that it has not been trained on, much

better than by chance. MLCI is then used to find compact wavefunctions for

carbon monoxide at both stretched and equilibrium geometries. We also consider

Valid transformations between quantum states are necessarily described by

completely positive maps, instead of just positive maps. Positive but not

completely positive maps such as the transposition map cannot be implemented

due to the existence of entanglement in composite quantum systems, but there

are classes of states for which the positivity is guaranteed, e.g., states not

correlated to other systems. In this paper, we introduce the concept of N-copy

The color excitations of interacting fermions carrying an $SU(3)$ color and

$U(N_f)$ flavor index in one spatial dimension are studied in the framework of

a perturbed $SU(3)_{N_f}$ Wess-Zumino-Novikov-Witten model. Using Bethe ansatz

methods the low energy quasi-particles are found to be massive solitons forming

$SU(3)$ quark and antiquark multiplets. In addition to the color index the

solitons carry an internal degree of freedom with non-integer quantum

dimension. These zero modes are identified as non-Abelian anyons satisfying

We show that a pulsed stimulus can be used to generate many-body quantum

coherences in light-matter systems of general size. Specifically, we calculate

the exact real-time evolution of a driven, generic out-of-equilibrium system

comprising an arbitrary number N qubits coupled to a global boson field. A

novel form of dynamically-driven quantum coherence emerges for general N and

without having to access the empirically challenging strong-coupling regime.

Its properties depend on the speed of the changes in the stimulus.

In free-space quantum key distribution (QKD) between moving parties, e.g.,

free-space QKD via satellite, the reference frame rotation and fluctuation

degrades the performance of QKD. Reference-frame-independent QKD (RFI-QKD)

provides a simple but efficient way to overcome this problem. While there has

been a number of theoretical and experimental studies on RFI-QKD, the

experimental verification of the robustness of RFI-QKD over other QKD protocols

under the reference frame rotation and fluctuation is still missing. Here, we

We study perfect state transfer in Kendon's model of discrete quantum walks.

In particular, we give a characterization of perfect state transfer purely in

terms of the graph spectra, and construct an infinite family of $4$-regular

circulant graphs that admit perfect state transfer. Prior to our work, the only

known infinite families of examples were variants of cycles and diamond chains.