The complexity of antiferromagnetic interactions and 2D lattices

Estimation of the minimum eigenvalue of a quantum Hamiltonian can be formalised as the Local Hamiltonian problem. We study the natural special case of the Local Hamiltonian problem where the same 2-local interaction, with differing weights, is applied across each pair of qubits. First we consider antiferromagnetic/ferromagnetic interactions, where the weights of the terms in the Hamiltonian are restricted to all be of the same sign. We show that for symmetric 2-local interactions with no 1-local part, the problem is either QMA-complete or in StoqMA. In particular the antiferromagnetic Heisenberg and antiferromagnetic XY interactions are shown to be QMA-complete. We also prove StoqMA-completeness of the antiferromagnetic transverse field Ising model. Second, we study the Local Hamiltonian problem under the restriction that the interaction terms can only be chosen to lie on a particular graph. We prove that nearly all of the QMA-complete 2-local interactions remain QMA-complete when restricted to a 2D square lattice. Finally we consider both restrictions at the same time and discover that, with the exception of the antiferromagnetic Heisenberg interaction, all of the interactions which are QMA-complete with positive coefficients remain QMA-complete when restricted to a 2D triangular lattice.Comment: 35 pages, 11 figures; v2 added reference

Oracle Complexity Classes and Local Measurements on Physical Hamiltonians

The canonical problem for the class Quantum Merlin-Arthur (QMA) is that of estimating ground state energies of local Hamiltonians. Perhaps surprisingly, [Ambainis, CCC 2014] showed that the related, but arguably more natural, problem of simulating local measurements on ground states of local Hamiltonians (APX-SIM) is likely harder than QMA. Indeed, [Ambainis, CCC 2014] showed that APX-SIM is P^QMA[log]-complete, for P^QMA[log] the class of languages decidable by a P machine making a logarithmic number of adaptive queries to a QMA oracle. In this work, we show that APX-SIM is P^QMA[log]-complete even when restricted to more physical Hamiltonians, obtaining as intermediate steps a variety of related complexity-theoretic results. We first give a sequence of results which together yield P^QMA[log]-hardness for APX-SIM on well-motivated Hamiltonians: (1) We show that for NP, StoqMA, and QMA oracles, a logarithmic number of adaptive queries is equivalent to polynomially many parallel queries. These equalities simplify the proofs of our subsequent results. (2) Next, we show that the hardness of APX-SIM is preserved under Hamiltonian simulations (a la [Cubitt, Montanaro, Piddock, 2017]). As a byproduct, we obtain a full complexity classification of APX-SIM, showing it is complete for P, P^||NP, P^||StoqMA, or P^||QMA depending on the Hamiltonians employed. (3) Leveraging the above, we show that APX-SIM is P^QMA[log]-complete for any family of Hamiltonians which can efficiently simulate spatially sparse Hamiltonians, including physically motivated models such as the 2D Heisenberg model. Our second focus considers 1D systems: We show that APX-SIM remains P^QMA[log]-complete even for local Hamiltonians on a 1D line of 8-dimensional qudits. This uses a number of ideas from above, along with replacing the "query Hamiltonian" of [Ambainis, CCC 2014] with a new "sifter" construction.Comment: 38 pages, 3 figure

Universal Quantum Hamiltonians

Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We first characterise precisely what it means for one quantum many-body system to replicate the entire physics of another. We then show that certain very simple spin-lattice models are universal in this very strong sense. Examples include the Heisenberg and XY models on a 2D square lattice (with non-uniform coupling strengths). We go on to fully classify all two-qubit interactions, determining which are universal and which can only simulate more restricted classes of models. Our results put the practical field of analogue Hamiltonian simulation on a rigorous footing and take a significant step towards justifying why error correction may not be required for this application of quantum information technology.Comment: 78 pages, 9 figures, 44 theorems etc. v2: Trivial fixes. v3: updated and simplified proof of Thm. 9; 82 pages, 47 theorems etc. v3: Small fix in proof of time-evolution lemma (this fix not in published version

Efflux in Acinetobacter baumannii can be determined by measuring accumulation of H33342 (bis-benzamide)

10.1093/jac/dkt052Journal of Antimicrobial Chemotherapy6871594-160

The Role of PI3K Isoforms in Regulating Bone Marrow Microenvironment Signaling Focusing on Acute Myeloid Leukemia and Multiple Myeloma

Despite the development of novel treatments in the past 15 years, many blood cancers still remain ultimately fatal and difficult to treat, particularly acute myeloid leukaemia (AML) and multiple myeloma (MM). While significant progress has been made characterising small-scale genetic mutations and larger-scale chromosomal translocations that contribute to the development of various blood cancers, less is understood about the complex microenvironment of the bone marrow (BM), which is known to be a key player in the pathogenesis of chronic lymphocytic leukaemia (CLL), AML and MM. This niche acts as a sanctuary for the cancerous cells, protecting them from chemotherapeutics and encouraging clonal cell survival. It does this by upregulating a plethora of signalling cascades within the malignant cell, with the phosphatidylinositol-3-kinase (PI3K) pathway taking a critical role. This review will focus on how the PI3K pathway influences disease progression and the individualised role of the PI3K subunits. We will also summarise the current clinical trials for PI3K inhibitors and how these trials impact the treatment of blood cancers

Diplomatic procedures at Rome in the second century B.C

The diplomatic season was a development of the period after 189 which was unparallelled led but explicable in the context to Rome's new hegemony. It reflects the constitutional role ascribed to the consuls by Polybius, which could only be fulfilled early in the consular year; but there was sufficient flexibility to allow numerous exceptions. It belongs to an annual cycle, artificial in diplomacy but which suited Rome's administrative requirements. Embassies approached a senior magistrate who allocated a senatorial audience and public hospitality. The magistrates thus had power over the order and timing of audiences which could be manipulated for purposes of etiquette or expediency. Abuse of this power and the scope for corruption were limited by the Lex Gabinia, probably of Ciceronian date. Only limited hospitality was provided. The official audience is ignored in some evidence which concentrates on pre-audience unofficial activity which became standard procedure. The motlf of bribery is often associated with this. Because of their influence over senatorial decisions the consulares figured prominently in such activity, but privately connected patroni and hospites played an important part and were thus cultivated by states and dynasts. Senators could interrupt and question ambassadors but this did not facilitate negotiation. The character of the audience as a simple exchange of statements was determined by certain "democratic" features of ancient diplomacy: openness, which suited Rome's purposes and made possible "collective audiences" (these helped the organisation of diplomatic activity and underlined the senate's arbitral role); and restricted ambassadorial competence which was hardly modified in the new conditions. Interpretation of ambassadorial speeches was required for dignity rather than intelligibility. The impression created at an audience might influence the senate; but Polybius often overstates the importance of ambassadors' speeches, since other factors influencing the senate's decisions (unofficial activity and the dependence on senatorial experts) could render the audience proceedings irrelevant

Functional genomics to identify the factors contributing to successful persistence and global spread of an antibiotic resistance plasmid

Background: The spread of bacterial plasmids is an increasing global problem contributing to the widespread dissemination of antibiotic resistance genes including β-lactamases. Our understanding of the details of the biological mechanisms by which these natural plasmids are able to persist in bacterial populations and are able to establish themselves in new hosts via conjugative transfer is very poor. We recently identified and sequenced a globally successful plasmid, pCT, conferring β-lactam resistance. Results: Here, we investigated six plasmid encoded factors (tra and pil loci; rci shufflon recombinase, a putative sigma factor, a putative parB partitioning gene and a pndACB toxin-antitoxin system) hypothesised to contribute to the 'evolutionary success' of plasmid pCT. Using a functional genomics approach, the role of these loci was investigated by systematically inactivating each region and examining the impact on plasmid persistence, conjugation and bacterial host biology. While the tra locus was found to be essential for all pCT conjugative transfer, the second conjugation (pil) locus was found to increase conjugation frequencies in liquid media to particular bacterial host recipients (determined in part by the rci shufflon recombinase). Inactivation of the pCT pndACB system and parB did not reduce the stability of this plasmid. Conclusions: Our findings suggest the success of pCT may be due to a combination of factors including plasmid stability within a range of bacterial hosts, a lack of a fitness burden and efficient transfer rates to new bacterial hosts rather than the presence of a particular gene or phenotype transferred to the host. The methodology used in our study could be applied to other 'successful' globally distributed plasmids to discover the role of currently unknown plasmid backbone genes or to investigate other factors which allow these elements to persist and spread

A Method for generating marker-less gene deletions in multidrug-resistant Acinetobacter baumannii

10.1186/1471-2180-13-158BMC Microbiology131581-1