Shortcuts to adiabaticity and applications to Quantum Computation

Abstract

Adiabatic evolution is a powerful technique in quantum information and computation. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. In this dissertation we introduce two different models to perform universal superadiabatic quantum computing, which are based on the use of shortcuts to adiabaticity by counter-diabatic Hamiltonians. The first model is based on the use of superadiabatic quantum teleportation, introduced in this dissertation, as a primitive to quantum computing. Thus, we provide the counter-diabatic driving for arbitrary $n$-qubit gates. In addition, our approach maps the counter-diabatic Hamiltonian for an arbitrary $n$-qubit {\it gate} teleportation into the implementation of a rotated counter-diabatic Hamiltonian for an $n$-qubit {\it state} teleportation. In the second model we use the concept of controlled superadiabatic evolutions to show how we can implement arbitrary $n$-controlled quantum gates. Remarkably, this task can be performed by simple time-independent counter-diabatic Hamiltonians. These two models can be used to design different sets of universal quantum gates. We show that the use of the quantum speed limit suggests that the superadiabatic time evolution is compatible with arbitrarily small time intervals, where this arbitrariness is constrained to the energetic cost necessary to perform the superadiabatic evolution.

arXiv comment101 pages, in Portuguese. 11 figures. Master thesis submitted to Physical Institute of the Federal University Fluminense, RJ, Brazil. Date: february 24, 2016

References in corpus (20)

• Quantum Mechanics helps in searching for a needle in a haystack
• Elementary gates for quantum computation
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Quantum Teleportation is a Universal Computational Primitive
• Quantum annealing with more than one hundred qubits
• Quantum teleportation using active feed-forward between two Canary Islands
• Experimental realization of a quantum algorithm
• Quantum speed limit for non-Markovian dynamics
• Quantum speed limits in open system dynamics
• Energy-time uncertainty relation for driven quantum systems
• Consistency of the Adiabatic Theorem
• Towards Fault Tolerant Adiabatic Quantum Computation
• A Simple Proof that Toffoli and Hadamard are Quantum Universal
• Superadiabatic dynamics in open quantum systems
• Experimental Performance of a Quantum Simulator: Optimizing Adiabatic Evolution and Identifying Many-Body Ground States
• Role of Single Qubit Decoherence Time in Adiabatic Quantum Computation
• Experimental realization of a fetching algorithm in a 7 qubit NMR quantum computer
• Quantum Gates with Controlled Adiabatic Evolutions
• On The Power Of Coherently Controlled Quantum Adiabatic Evolutions
• Scalable universal holonomic quantum computation realized with an adiabatic quantum data bus and potential implementation using superconducting flux qubits