Entanglement and superposition are fundamental properties of quantum-mechanical states, with no classical counterparts. It is well-established that elementary particles, such as electrons and photons, follow the rules of quantum mechanics in the microscopic world. Over the past few decades, significant advancements in quantum computing have been achieved, with microwave and optical photons playing crucial roles in several leading quantum computing platforms, including superconducting qubits and linear optical quantum computing (LOQC). This dissertation explores the possibility of using phonons—the single quanta of sound or vibrations—as quantum information carriers instead of photons. Unlike photons, phonons are relatively macroscopic, representing the collective motion of quadrillions of atoms. It has been shown that superconducting qubits can emit and capture single phonons when the entire system is well-isolated and cooled to near absolute zero temperatures. We demonstrate a phononic beam splitter element, using two superconducting qubits to fully characterize it with single phonons. We use the beam splitter to demonstrate two-phonon interference, a requirement for phonon two-qubit gates. We further present the advancement in deterministic phonon phase gates and phonon number-resolving detection schemes. We also proposed a transmon-controlled phonon routing architecture as one future direction for this hybrid quantum platform. The thesis work provides a complete toolbox for linear mechanical quantum computing (LMQC) based on individual quanta of sound and establishes a hybrid quantum computing platform integrated with superconducting qubits.