##### MODELING MOLECULAR TECHNOLOGIES FOR QUANTUM COMPUTING

Molecules encode quantum information onto electron or nuclear spins and they can be candidates for building a scalable and universal-quantum-gate-set hardware for Quantum Computing. In order to compare them with other technologies proposed for building a quantum computer, the development of a classical simulator taking into account their main properties could be useful for understanding which are their limitations in the execution of quantum circuits for concrete use-cases, as optimization problem solving or Machine Learning applications.

The objective of this thesis is to analyze, starting from physical level, molecules employable for the implementation of quantum computers. As a first step, physical level simulations will be employed to validate and eventually optimize the system behavior. Finally, high-level models, enhanced by information obtained from physical simulation, will be developed to allow the simulation of complex quantum circuits with molecular quantum computers. If interested, please write at mariagrazia.graziano@polito.it or giovanna.turvani@polito.it.

##### MODELING SILICON TECHNOLOGIES FOR QUANTUM COMPUTING

Electron spins in quantum dots have been proposed as a potential technology for fabricating quantum computers. The main advantages of silicon Quantum Computing are the higher operating temperatures than those of superconducting devices and the possibility to facilitate the interface between quantum and classical processing units. In order to compare them with other technologies proposed for building a quantum computer, the development of a classical simulator taking into account their main properties could be useful for understanding which are their limitations in the execution of quantum circuits for concrete use-cases as optimization problem solving or Machine Learning applications.

The objective of this thesis is developing high-level models, enhanced by information obtained from physical simulations or experiments in the state of the art, for silicon quantum technologies to be integrated in a classical simulation infrastructure, thus allowing their simulation of complex quantum circuits. If interested, please write at mariagrazia.graziano@polito.it or giovanna.turvani@polito.it.

##### MODELING SUPERCONDUCTING AND TRAPPED-ION QUBITS

Superconducting and trapped-ion qubits are the currently most advanced technologies for quantum computing in terms of compromising on qubits connectivity, gate errors and coherence timescales. Companies as IBM Q and Honeywell permit to program their hardware through a cloud interface. However, it is not in general ensured to tune the polarization or manipulation parameters of hardware. The development of models with tunable parameters and taking into account the main physical features of these technologies could help their engineering.

The objective of this thesis is developing high-level models, enhanced by information obtained from physical simulations or experiments in the state of the art, for superconducting and trapped-ion quantum technologies to be integrated in a classical simulation infrastructure. Validation of the accuracy

of the models is going to be done with the comparison of the results provided by simulation and execution on real hardware. If interested, please write at mariagrazia.graziano@polito.it or giovanna.turvani@polito.it.

##### DESIGN OF APPLICATION-SPECIFIC QUANTUM CIRCUITS

Quantum circuits and algorithms permit to solve some problems with a total number of operations than those required by a classical computer. For example, Grover’s algorithm permit to find a solution in a disordered database with a quadratic speedup with the respect to a classical approach. Many problems could be solved with a quantum computer, but the corresponding quantum circuits, behaving as computationally accelerating subroutines, have not already been designed for these purposes.

The aim of this thesis is to design application-specific circuits, e.g. for optimization problems solving and Quantum Machine Learning applications. Circuits are going to be optimized and tested on different technologies (superconducting, molecular, trapped ions, etc.) through executions on real hardware (e.g. IBM Q superconducting quantum computers) or simulations on a technology-dependent classical simulator (currently involving molecules). If interested, please write at maurizio.zamboni@polito.it or mariagrazia.graziano@polito.it or giovanna.turvani@polito.it.

##### DESIGN OF QUANTUM CIRCUITS FOR A QUANTUM COMPUTER ARITHMETIC CIRCUIT LIBRARY

The intrinsic description of a qubits system based on complex linear algebra could significantly facilitate the design of quantum circuits for arithmetic. In fact, quantum circuits affecting a qubits state vector can be seen as the Quantum Basic Linear Algebra Subprograms (QBLAS) of a quantum computer architecture to be employed as computational accelerators for hard problems as those in the Machine Learning area. Moreover, the design of quantum arithmetic circuits could be useful for designing sophisticated oracles for solving optimization or Machine Learning problems with Grover-like strategies.

The aim of this thesis is to design quantum circuits for a multi-technology arithmetic library. Circuits are going to be optimized and tested on different technologies (superconducting, molecular, trapped ions, etc.) through executions on real hardware (e.g. IBM Q superconducting quantum computers) or simulations on a technology-dependent classical simulator (currently involving molecules). If interested, please write at maurizio.zamboni@polito.it or mariagrazia.graziano@polito.it or giovanna.turvani@polito.it.

##### DEVELOPMENT OF QUANTUM CIRCUIT COMPILERS

Circuit optimization is fundamental for ensuring the execution of operations with negligible errors. Compilation strategies could be significantly different for superconducting, trapped-ion, molecular and silicon technologies – because of native gates set and qubits connectivity – and an optimal approach has not been already found.

The aim of this thesis is to define quantum circuit compilers for multiple technologies to be tested on real hardware (e.g. IBM Q superconducting quantum computers) or simulations on a technology-dependent classical simulator (currently involving molecules). If interested, please write atmaurizio.zamboni@polito.it or mariagrazia.graziano@polito.it or giovanna.turvani@polito.it.

##### DEVELOPMENT OF ADVANCED CLASSICAL SIMULATORS FOR QUANTUM COMPUTERS

A N-ideal-qubit system is described by a state vector of dimension 2N. On the other hand, a more complete representation for N noisy qubits is provided by a density matrix 2N× 2N. Their evolution is described by products involving matrices and vectors. It is quite clear that the number of classical resources required for simulating qubits increases exponentially with the number of qubits. In the case of ideal qubits, some strategies for reducing the required hardware have been already proposed.

The aim of this thesis is to develop a C++ high-performance classical simulator of non-ideal qubits, to be integrated in a technology-dependent simulation infrastructure. The first step of the thesis requires the definition of computationally easier description models of quantum states, then code development – for implementing the alternative qubits description and for interfacing the high-performance simulator to the other levels of the infrastructure – is going to be done. If interested, write at maurizio.zamboni@polito.it or mariagrazia.graziano@polito.it or giovanna.turvani@polito.it.