Quantum information and statistical mechanics: an introduction to frontier

This is a short review on an interdisciplinary field of quantum information science and statistical mechanics. We first give a pedagogical introduction to the stabilizer formalism, which is an efficient way to describe an important class of quantum states, the so-called stabilizer states, and quantum operations on them. Furthermore, graph states, which are a class of stabilizer states associated with graphs, and their applications for measurement-based quantum computation are also mentioned. Based on the stabilizer formalism, we review two interdisciplinary topics. One is the relation between quantum error correction codes and spin glass models, which allows us to analyze the performances of quantum error correction codes by using the knowledge about phases in statistical models. The other is the relation between the stabilizer formalism and partition functions of classical spin models, which provides new quantum and classical algorithms to evaluate partition functions of classical spin models.Comment: 15pages, 4 figures, to appear in Proceedings of 4th YSM-SPIP (Sendai, 14-16 December 2012

Optimized Surface Code Communication in Superconducting Quantum Computers

Quantum computing (QC) is at the cusp of a revolution. Machines with 100 quantum bits (qubits) are anticipated to be operational by 2020 [googlemachine,gambetta2015building], and several-hundred-qubit machines are around the corner. Machines of this scale have the capacity to demonstrate quantum supremacy, the tipping point where QC is faster than the fastest classical alternative for a particular problem. Because error correction techniques will be central to QC and will be the most expensive component of quantum computation, choosing the lowest-overhead error correction scheme is critical to overall QC success. This paper evaluates two established quantum error correction codes---planar and double-defect surface codes---using a set of compilation, scheduling and network simulation tools. In considering scalable methods for optimizing both codes, we do so in the context of a full microarchitectural and compiler analysis. Contrary to previous predictions, we find that the simpler planar codes are sometimes more favorable for implementation on superconducting quantum computers, especially under conditions of high communication congestion.Comment: 14 pages, 9 figures, The 50th Annual IEEE/ACM International Symposium on Microarchitectur

Architecture and noise analysis of continuous variable quantum gates using two-dimensional cluster states

Due to its unique scalability potential, continuous variable quantum optics is a promising platform for large scale quantum computing and quantum simulation. In particular, very large cluster states with a two-dimensional topology that are suitable for universal quantum computing and quantum simulation can be readily generated in a deterministic manner, and routes towards fault-tolerance via bosonic quantum error-correction are known. In this article we propose a complete measurement-based quantum computing architecture for the implementation of a universal set of gates on the recently generated two-dimensional cluster states [1,2]. We analyze the performance of the various quantum gates that are executed in these cluster states as well as in other two-dimensional cluster states (the bilayer-square lattice and quad-rail lattice cluster states [3,4]) by estimating and minimizing the associated stochastic noise addition as well as the resulting gate error probability. We compare the four different states and find that, although they all allow for universal computation, the quad-rail lattice cluster state performs better than the other three states which all exhibit similar performance