1. INTRODUCTION In the quantum computational framework there are polynomial time solving algorithms, for problems having exponential classical solutions. The quest is – on one hand – to search if there are other possible effective quantum algorithms and – on the other hand – to be able to produce efficient implementations for the already known algorithms. The most feasible implementation of qua...

I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor gates are available, and present explicit constructions. In two or three dimensions, I also show how nearestneighbor gates can give a threshold result. In a...

When coherent states of the electromagnetic field are used to drive the evolution of a quantum computer, a decoherence results due to the back reaction from the qubits onto the fields. We show how to calculate this effect. No assumptions about the environment are necessary, so this represents a useful model to test the fidelity of quantum error correcting codes. We examine two cases of interest...

The design and optimization of realistic architectures for fault-tolerant quantum computation requires error models that are both reliable and amenable to large-scale classical simulation. Perhaps the simplest and most practical general-purpose method for constructing such an error model is to twirl a given completely positive channel over the Pauli basis, a procedure we refer to as the Pauli t...

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...

One of the most significant challenges facing the development of linear optics quantum computing (LOQC) is mode-mismatch, whereby photon distinguishability is introduced within circuits, undermining quantum interference effects. We examine the effects of mode-mismatch on the parity (or fusion) gate, the fundamental building block in several recent LOQC schemes. We derive simple error models for...

We propose a new class of unconventional geometric gates involving nonzero dynamic phases, and elucidate that geometric quantum computation can be implemented by using these gates. Comparing with the conventional geometric gate operation, in which the dynamic phase shift must be removed or avoided, the gates proposed here may be operated more simply. We illustrate in detail that unconventional ...

Recently, Bravyi and König have shown that there is a trade-off between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant-depth geometrically-local circuit and are thus fault-tolerant by construction. In particular, they shown that, for local stabilizer codes in D spatial dime...

In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a CNOT gate is 8.3 × 10. We also compute the fidelities of Z, X, Swap, and Controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable...