Reducing the Cost of Single Error Correction With Parity Sharing

2013 ◽  
Vol 13 (3) ◽  
pp. 420-422 ◽  
Author(s):  
Pedro Reviriego ◽  
Salvatore Pontarelli ◽  
Juan Antonio Maestro ◽  
Marco Ottavi
2009 ◽  
Vol 9 (5&6) ◽  
pp. 487-499
Author(s):  
S.S. Bullock ◽  
D.P. O'Leary

In this paper, we study the complexity of Hamiltonians whose groundstate is a stabilizer code. We introduce various notions of $k$-locality of a stabilizer code, inherited from the associated stabilizer group. A choice of generators leads to a Hamiltonian with the code in its groundspace. We establish bounds on the locality of any other Hamiltonian whose groundspace contains such a code, whether or not its Pauli tensor summands commute. Our results provide insight into the cost of creating an energy gap for passive error correction and for adiabatic quantum computing. The results simplify in the cases of XZ-split codes such as Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations.


2018 ◽  
Vol 10 (3) ◽  
pp. 1
Author(s):  
Louisa Kammerer ◽  
Miguel Ramirez

This paper examines the challenges firms (and policymakers) encounter when confronted by a recession at the zero lower bound, when traditional monetary policy is ineffective in the face of deteriorated balance sheets and high costs of credit. Within the larger body of literature, this paper focuses on the cost of credit during a recession, which constrains smaller firms from borrowing and investing, thus magnifying the contraction. Extending and revising a model originally developed by Walker (2010) and estimated by Pandey and Ramirez (2012), this study uses a Vector Error Correction Model with structural breaks to analyze the effects of relevant economic and financial factors on the cost of credit intermediation for small and large firms. Specifically, it tests whether large firms have advantageous access to credit, especially during recessions. The findings suggest that during the Great Recession of 2007-09 the cost of credit rose for small firms while it decreased for large firms, ceteris paribus. From the results, the paper assesses alternative ways in which the central bank can respond to a recession facing the zero lower bound.


Author(s):  
Luis-J. Saiz-Adalid ◽  
Pedro Gil ◽  
Joaquin Gracia-Moran ◽  
Daniel Gil-Tomas ◽  
J.-Carlos Baraza-Calvo

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