Guidable Local Hamiltonian Problems with Implications to Heuristic Ans\"atze State Preparation and the Quantum PCP Conjecture

We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem, which we call 'Guidable Local Hamiltonian' problems. Unlike their guided counterparts, these problems do not have a guiding state provided as a part of the input, but merely come with the promise that one exists. We consider in particular two classes of guiding states: those that can be prepared efficiently by a quantum circuit; and those belonging to a class of quantum states we call classically evaluatable, for which it is possible to efficiently compute expectation values of local observables classically. We show that guidable local Hamiltonian problems for both classes of guiding states are $\mathsf{QCMA}$-complete in the inverse-polynomial precision setting, but lie within $\mathsf{NP}$ (or $\mathsf{NqP}$) in the constant precision regime when the guiding state is classically evaluatable. Our completeness results show that, from a complexity-theoretic perspective, classical Ans\"atze selected by classical heuristics are just as powerful as quantum Ans\"atze prepared by quantum heuristics, as long as one has access to quantum phase estimation. In relation to the quantum PCP conjecture, we (i) define a complexity class capturing quantum-classical probabilistically checkable proof systems and show that it is contained in $\mathsf{BQP}^{\mathsf{NP}[1]}$ for constant proof queries; (ii) give a no-go result on 'dequantizing' the known quantum reduction which maps a $\mathsf{QPCP}$-verification circuit to a local Hamiltonian with constant promise gap; (iii) give several no-go results for the existence of quantum gap amplification procedures that preserve certain ground state properties; and (iv) propose two conjectures that can be viewed as stronger versions of the NLTS theorem. Finally, we show that many of our results can be directly modified to obtain similar results for the class $\mathsf{MA}$.Comment: 61 pages, 6 figure

Complexity of the Guided Local Hamiltonian Problem: Improved Parameters and Extension to Excited States

Recently it was shown that the so-called guided local Hamiltonian problem -- estimating the smallest eigenvalue of a $k$-local Hamiltonian when provided with a description of a quantum state ('guiding state') that is guaranteed to have substantial overlap with the true groundstate -- is BQP-complete for $k \geq 6$ when the required precision is inverse polynomial in the system size $n$, and remains hard even when the overlap of the guiding state with the groundstate is close to a constant $\left(\frac12 - \Omega\left(\frac{1}{\mathop{poly}(n)}\right)\right)$. We improve upon this result in three ways: by showing that it remains BQP-complete when i) the Hamiltonian is 2-local, ii) the overlap between the guiding state and target eigenstate is as large as $1 - \Omega\left(\frac{1}{\mathop{poly}(n)}\right)$, and iii) when one is interested in estimating energies of excited states, rather than just the groundstate. Interestingly, iii) is only made possible by first showing that ii) holds.Comment: 22 pages, 3 figure

Do ether functionalized ionic liquids improve the CO2 solubility?

CO2 absorption using a solvent is accepted as the most compatible technology. In the recent years ionic liquids (ILs) have shown to be good candidates for CO2 capture. They exhibit major advantages compared to amine-based systems. Their negligible vapor pressure, high thermal and chemical stability and tunability outweigh the disadvantages of lower absorptive capacity and kinetics. In this work a comprehensive study of the ILs [C2mim]-, [C4mim]-, [C6mim]-, [C7mim]- and [C8mim] tricyanomethanide (TCM) has been carried out. Furthermore, in order to evaluate the presence of ether groups in the alkyl chain of the imidazolium, this work includes 1-(2-methoxythyl)-3-methylimidazolium- and 1[2-(2- methoxyethoxy)ethyl]-3-methylimidazolium tricyanomethanide. These non-flourinated and low-viscous ILs are studied for the first time as a solvent for CO2 capture. Two different methods (volumetric vs gravimetric) were applied to study the thermodynamics (i.e., absorptive capacity and Henry’s law coefficient) and kinetics (i.e., diffusion coefficient) at several temperatures and pressures up to 150 bars. The experimentally determined phase behavior of the IL and CO2 systems are correlated using the Peng-Robinson equation of state. Furthermore, the thermal operating window (e.g., glass transition and decomposition temperature) and physical properties (e.g., density, viscosity, conductivity and surface tension) were determined. It will be shown at the conference that TCM-based ILs are promising sorbents for pre-combustion CO2 capture due to their high (physical) absorptive capacity, their low regeneration energy consumption (low heat of absorption) and improved kinetics (due to their low viscosity) compared to the conventional ILs

Genetic disposition and response of blood lipids to diet : studies on gene-diet interaction in humans

Even though a cholesterol-lowering diet is effective for most people, it is not for all. Identification of genetic determinants of the serum lipid response to diet may be of help in the identification of subjects who will not benefit from a cholesterol-lowering diet. It may also clarify the role of certain proteins in cholesterol metabolism. The objective of our research was to determine whether genetic polymorphisms affect the response of serum lipids to diet in humans.We first assessed sex differences in the response of serum lipids to changes in the diet. Men had larger responses of total and low-density lipoprotein cholesterol to saturated fat and cafestol than women. There were no sex differences in the responses to trans fat and dietary cholesterol. We also used these data to study the effect of 11 genetic polymorphisms on responses of serum lipids to the various dietary treatments. Apoprotein E, A4 347 and 360, and cholesteryl-ester transfer protein TaqIb polymorphisms affected the lipid response to diet slightly.We further studied the effect of the apoprotein A4 360-1/2 polymorphism on response of serum lipids to dietary cholesterol in a controlled trial specially designed for this purpose. The apoprotein A4 360-1/2 polymorphism did not affect the response of serum lipids to a change in the intake of cholesterol in a group of healthy Dutch subjects who consumed a background diet high in saturated fat.Although it is not directly related to genetic polymorphisms and lipid response, we finally reviewed the effect of dietary cholesterol on the ratio of total to high-density lipoprotein cholesterol, which is a more specific predictor of coronary heart disease than either lipid value alone. Dietary cholesterol raised the ratio of total to high-density lipoprotein cholesterol.In conclusion, the effect of genetic polymorphisms on serum lipid response to diet is small. It is therefore not possible to identify individuals who will not benefit from a cholesterol-lowering diet on the basis of a specific genetic polymorphism.</p

Antidemocratische bewegingen in de Nederlandse democratie: een blik op Hizb ut-Tahrir

In de maatschappelijke discussie over antidemocratische bewegingen lijkt stelselmatig voorbij te worden gegaan aan de vraag die als eerste beantwoord zou moeten worden, namelijk: Wat is democratie (en hoe deze te beschermen)? Antwoorden op deze vra(a)g(en) kunnen gevonden worden in het debat over weerbare democratie. Dit artikel heeft daarom hoofdzakelijk tot doel om het debat over weerbare democratie en het debat over antidemocratische bewegingen dichter bij elkaar te brengen.Een van de bewegingen die centraal staat in het debat over antidemocratische bewegingen is Hizb ut-Tahrir. In het artikel ‘Eigen koers richting kalifaat, een beeld van Hizb ut-Tahrir in Nederland’, dat eerder in dit tijdschrift is gepubliceerd, hebben we een beeld geschetst van Hizb ut-Tahrir in Nederland. Deze in de jaren vijftig van de vorige eeuw opgerichte beweging is wereldwijd actief, manifesteert zich als politieke partij en streeft naar de heroprichting van een ‘islamitisch kalifaat’. Hoewel de beweging fel gekant is tegen de heersende politieke elite en overheden wereldwijd, en democratie in zijn algemeenheid, wijst ze het gebruik van geweld om politieke verandering te verwezenlijken af. Inmiddels is Hizb ut-Tahrir ook al enkele decennia actief in Nederland, waar de beweging, in tegenstelling tot in veel andere landen wereldwijd, waaronder Duitsland, niet verboden is. Echter, ook in Nederland pleitten politici de afgelopen jaren geregeld voor een stevige aanpak van of zelfs een verbod op de beweging.In dit artikel zullen we allereerst illustreren hoe het debat over Hizb ut-Tahrir zich de afgelopen decennia ontwikkelde, en laten we zien dat er parallellen te trekken zijn met de wijze waarop het debat over het salafisme wordt gevoerd. We zullen daarbij ook kort de relevante maatschappelijke context schetsen en enkele nuanceringen plaatsen met betrekking tot de (vermeende) gewelddadige aard van deze bewegingen. Vervolgens zullen we laten zien dat de moderne weerbare democratietheorie mogelijk een waardevolle rol kan spelen in de verdere ontwikkeling van dit debat.Security and Global Affair

Improved Hardness Results for the Guided Local Hamiltonian Problem

Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC 2022) recently introduced the guided local Hamiltonian problem (GLH), which is a variant of the local Hamiltonian problem where an approximation of a ground state (which is called a guiding state) is given as an additional input. Gharibian and Le Gall showed quantum advantage (more precisely, BQP-completeness) for GLH with 6-local Hamiltonians when the guiding state has fidelity (inverse-polynomially) close to 1/2 with a ground state. In this paper, we optimally improve both the locality and the fidelity parameter: we show that the BQP-completeness persists even with 2-local Hamiltonians, and even when the guiding state has fidelity (inverse-polynomially) close to 1 with a ground state. Moreover, we show that the BQP-completeness also holds for 2-local physically motivated Hamiltonians on a 2D square lattice or a 2D triangular lattice. Beyond the hardness of estimating the ground state energy, we also show BQP-hardness persists when considering estimating energies of excited states of these Hamiltonians instead. Those make further steps towards establishing practical quantum advantage in quantum chemistry

Op Vrije Voeten: Herintreding van Maatschappelijk Gevoelige Ex-Gedetineerden

De rol van publieke belangstelling na de vrijlating van ex-gedetineerden is tot op heden veelal verwaarloosd in eerder wetenschappelijk onderzoek. Dit vormde het startpunt van deze verkennende studie. Aan de hand van een select aantal interviews hebben we een aantal aspecten van de problematiek van deze groep ex-gedetineerden in kaart proberen te brengen.Security and Global Affair