We present a simplified yet rigorous explanation of the ideas from Bomb́ın’s paper Gauge Color Codes [1]. Our discussion is self-contained, and assumes only basic concepts from quantum error correction. We provide an explicit construction of a family of color codes in arbitrary dimensions and describe some of their crucial properties. Within this framework, we explicitly show how to transversall...

Presented in this paper are lower bounds on energy-efficiency of the mirror noise-tolerant dynamic circuit technique. These lower bounds are derived by solving an energy optimization problem subject to an information-theoretic constraint. Design overheads associated with the noise-tolerant circuit techniques are discussed and incorporated into the optimization problem. Simulation results for a ...

With the Gottesman-Kitaev-Preskill (GKP) encoding, Clifford gates and error correction can be carried out using simple Gaussian operations. Still, non-Clifford gates, required for universality, require non-Gaussian elements. In their original proposal, GKP suggested a particularly method of single application cubic phase gate to perform logical $T$ gate. Here we show that this approach performs...

In the high voltage (HV) electrical power systems, different materials are used as the role of insul ation to protect the incipient failure inside the HV power equipments. One of the common phenomenas in insulations is Partial Discharge (PD). Because of the high voltage stress, the weak section i nside the insulator causes the partial discharge (PD), which is known as a local electrical breakdo...

Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods which apply to codes of high rate, encoding k qubits per block with k > 1. It is shown that the logical qubits within a given block can be prepared by a single recovery operation in any state whose stabilizer generator separates into X and Z parts. Optimized methods to move logical qubits a...

Title of dissertation: QUANTUM GATE AND QUANTUM STATE PREPARATION THROUGH NEIGHBORING OPTIMAL CONTROL Yuchen Peng, Doctor of Philosophy, 2016 Dissertation directed by: Dr. Frank Gaitan Laboratory for Physical Sciences Professor Victor Yakovenko Department of Physics Successful implementation of fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used t...

Nonadiabatic Abelian geometric quantum computation has been extensively studied, due to its fast manipulation and inherent noise resistance. However, obtain the pure phase, state is required evolve along some special paths eliminate dynamical phase. This leads increasing evolution time weakened gate robustness. The unconventional an effective way solve above problems. Here, we propose a general...

Among the list of major threats to quantum computation, decoherence poses one largest because it generates losses environment within a computational system which cannot be recovered via error correction methods. These methods require assumption that environmental interaction forces qubit state into some linear combination eigenstates. In reality, causes enter mixed where original is no longer r...