Accurate computation of non-covalent, intermolecular interaction energies is important to understand various chemical phenomena, and quantum computers are anticipated to accelerate it. Although the state-of-the-art quantum computers are still noisy and intermediate-scale ones, development of theoretical frameworks those are expected to work on a fault-tolerant quantum computer is an urgent issue. In this work, we explore resource-efficient implementation of the quantum phase estimation-based complete active space configuration interaction (QPE-CASCI) calculations, with the aid of the second-order Møller--Plesset perturbation theory (MP2)-based active space selection with Boys localized orbitals. We performed numerical simulations of QPE for the supramolecular approach-based intermolecular interaction energy calculations of the hydrogen-bonded water dimer, using 6 system and 6 ancilla qubits. With the aid of algorithmic error mitigation, the QPE-CASCI simulations achieved interaction energy predictions with an error of 0.02 kcal mol$^{-1}$ relative to the CASCI result, demonstrating the accuracy and efficiency of the proposed methodology. Preliminary results on quantum circuit compression for QPE are also presented to reduce the number of two-qubit gates and depth.

We present two Device Independent Quantum Random Number Generator (DI-QRNG) protocols using two self-testing methodologies in Preparation \& Measure (P\&M) scenario. These two methodologies are the variants of two well-known non-local games, namely, CHSH and pseudo-telepathy games, in P\&M framework. We exploit them as distinguishers in black-box settings to differentiate the classical and the quantum paradigms and hence to certify the Device Independence. The first self-test was proposed by Tavakoli et al. (Phys. Rev. A, 2018). We show that this is actually a P\&M variant of the CHSH game. Then based on this self-test, we design our first DI-QRNG protocol. We also propose a new self-testing methodology, which is the first of its kind that is reducible from pseudo-telepathy game in P\&M framework. Based on this new self-test, we design our second DI-QRNG protocol.

Although many quantum channels satisfy Completely Positive Trace Preserving (CPTP) condition, there are valid quantum channels that can be non-completely positive (NCP). In a search of the conditions of noisy evolution to be a useful resource for quantum computing, we study the relation of complete positivity (CP) with unitality, where we find that a map must be non-unital in order to be NCP, but not vice-versa. As memory effects can provide advantages in the dynamics of noisy quantum systems, we investigate the relative CP condition and the CP-divisibility condition of the system and environment subsystems of a joint system-environment quantum state evolving noiselessly. We show that the system and environment channels must be both CP (NCP) or CP-divisible (CP-indivisible) for the evolution in the joint system-environment space to be unitary. We illustrate our results with examples of Bell state created from $|00\rangle$, GHZ state created from $|000\rangle$, W state created from $|100\rangle$, and the partial transpose (PT) operation acting on the Bell state.