Perturbative 2-body Parent Hamiltonians for Projected Entangled Pair States

We construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). Making use of perturbation gadget techniques, we define a perturbative Hamiltonian acting on the virtual PEPS space with a finite order low energy effective Hamiltonian that is a gapped, frustration-free parent Hamiltonian for an encoded version of a desired PEPS. For topologically ordered PEPS, the ground space of the low energy effective Hamiltonian is shown to be in the same phase as the desired state to all orders of perturbation theory. An encoded parent Hamiltonian for the double semion string net ground state is explicitly constructed as a concrete example.Comment: 26 pages, 4 figures, v2 published versio

Toric codes and quantum doubles from two-body Hamiltonians

We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models

Cellular automaton decoders of topological quantum memories in the fault tolerant setting

Active error decoding and correction of topological quantum codes—in particular the toric code—remains one of the most viable routes to large scale quantum information processing. In contrast, passive error correction relies on the natural physical dynamics of a system to protect encoded quantum information. However, the search is ongoing for a completely satisfactory passive scheme applicable to locally interacting two-dimensional systems. Here, we investigate dynamical decoders that provide passive error correction by embedding the decoding process into local dynamics. We propose a specific discrete time cellular-automaton decoder in the fault tolerant setting and provide numerical evidence showing that the logical qubit has a survival time extended by several orders of magnitude over that of a bare unencoded qubit. We stress that (asynchronous) dynamical decoding gives rise to a Markovian dissipative process. We hence equate cellular-automaton decoding to a fully dissipative topological quantum memory, which removes errors continuously. In this sense, uncontrolled and unwanted local noise can be corrected for by a controlled local dissipative process. We analyze the required resources, commenting on additional polylogarithmic factors beyond those incurred by an ideal constant resource dynamical decoder

Homogeneous MGMT Immunoreactivity Correlates with an Unmethylated MGMT Promoter Status in Brain Metastases of Various Solid Tumors

The O6-methylguanine-methyltransferase (MGMT) promoter methylation status is a predictive parameter for the response of malignant gliomas to alkylating agents such as temozolomide. First clinical reports on treating brain metastases with temozolomide describe varying effects. This may be due to the fact that MGMT promoter methylation of brain metastases has not yet been explored in depth. Therefore, we assessed MGMT promoter methylation of various brain metastases including those derived from lung (n = 91), breast (n = 72) kidney (n = 49) and from malignant melanomas (n = 113) by methylation-specific polymerase chain reaction (MS-PCR) and MGMT immunoreactivity. Fifty-nine of 199 brain metastases (29.6%) revealed a methylated MGMT promoter. The methylation rate was the highest in brain metastases derived from lung carcinomas (46.5%) followed by those from breast carcinoma (28.8%), malignant melanoma (24.7%) and from renal carcinoma (20%). A significant correlation of homogeneous MGMT-immunoreactivity (>95% MGMT positive tumor cells) and an unmethylated MGMT promoter was found. Promoter methylation was detected in 26 of 61 (43%) tumors lacking MGMT immunoreactivity, in 17 of 63 (27%) metastases with heterogeneous MGMT expression, but only in 5 of 54 brain metastases (9%) showing a homogeneous MGMT immunoreactivity. Our results demonstrate that a significant number of brain metastases reveal a methylated MGMT-promoter. Based on an obvious correlation between homogeneous MGMT immunoreactivity and unmethylated MGMT promoter, we hypothesize that immunohistochemistry for MGMT may be a helpful diagnostic tool to identify those tumors that probably will not benefit from the use of alkylating agents. The discrepancy between promoter methylation and a lack of MGMT immunoreactivity argues for assessing MGMT promoter methylation both by immunohistochemical as well as by molecular approaches for diagnostic purposes

Targeted antiangiogenic agents in combination with cytotoxic chemotherapy in preclinical and clinical studies in sarcoma

Sarcomas are a heterogeneous group of mesenchymal malignancies. In recent years, studies have demonstrated that inhibition of angiogenic pathways or disruption of established vasculature can attenuate the growth of sarcomas. However, when used as monotherapy in the clinical setting, these targeted antiangiogenic agents have only provided modest survival benefits in some sarcoma subtypes, and have not been efficacious in others. Preclinical and early clinical data suggest that the addition of conventional chemotherapy to antiangiogenic agents may lead to more effective therapies for patients with these tumors. In the current review, the authors summarize the available evidence and possible mechanisms supporting this approach