Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians

A key feature of ground states of gapped local 1D Hamiltonians is their relatively low entanglement --- they are well approximated by matrix product states (MPS) with bond dimension scaling polynomially in the length $N$ of the chain, while general states require a bond dimension scaling exponentially. We show that the bond dimension of these MPS approximations can be improved to a constant, independent of the chain length, if we relax our notion of approximation to be more local: for all length-$k$ segments of the chain, the reduced density matrices of our approximations are $\epsilon$-close to those of the exact state. If the state is a ground state of a gapped local Hamiltonian, the bond dimension of the approximation scales like $(k/\epsilon)^{1+o(1)}$, and at the expense of worse but still $\text{poly}(k,1/\epsilon)$ scaling of the bond dimension, we give an alternate construction with the additional features that it can be generated by a constant-depth quantum circuit with nearest-neighbor gates, and that it applies generally for any state with exponentially decaying correlations. For a completely general state, we give an approximation with bond dimension $\exp(O(k/\epsilon))$, which is exponentially worse, but still independent of $N$. Then, we consider the prospect of designing an algorithm to find a local approximation for ground states of gapped local 1D Hamiltonians. When the Hamiltonian is translationally invariant, we show that the ability to find $O(1)$-accurate local approximations to the ground state in $T(N)$ time implies the ability to estimate the ground state energy to $O(1)$ precision in $O(T(N)\log(N))$ time.Comment: 24 pages, 3 figures. v2: Theorem 1 extended to include construction for general states; Lemma 7 & Theorem 2 slightly improved; figures added; lemmas rearranged for clarity; typos fixed. v3: Reformatted & additional references inserte

Giving God Glory

In Nepal, ethnicity is often constituted through ritual practice. If ritual participation is a key way of exercising membership in an ethnic group, how might Christians--who no longer participate in many community rituals--demonstrate their belonging in ethnic communities? In this article, I argue that modifying traditional songs and dances for a church context is one way that Christian Tharus continue to identify with their ethnic communities within a multicultural Christian community. I examine two Christian Tharu performances: performing the huri nāc (a Kathariya Tharu song and dance genre performed during Holi) at interchurch events and arranging an original, Nepali-language hymn as a maghauta nāc (a song and dance genre performed during Tharu celebrations of Māghī). The first performance contends that Tharu religion can comprise of more than one religious tradition, challenging essentialist narratives of what Tharu religion should be. The second performance declares that Christian Nepali practice is wide enough to encompass Tharu cultural signifiers. I draw on my ethnographic research in Tharu communities in Kailali and Dang districts, which ranged from attending church events, seasonal music competitions, and community festivals to interviewing lay men and women, pastors, and other church leaders. Discussing the musical choices of these Christian Tharus allows me enter the conversation about belonging within Himalayan studies. I demonstrate how a focus on belonging does not negate the importance of identity, but is a complement to studies of difference

Giving God Glory: How Christian Tharus Negotiate Belonging through Ritual Music in Nepal

In Nepal, ethnicity is often constituted through ritual practice. If ritual participation is a key way of exercising membership in an ethnic group, how might Christians--who no longer participate in many community rituals--demonstrate their belonging in ethnic communities? In this article, I argue that modifying traditional songs and dances for a church context is one way that Christian Tharus continue to identify with their ethnic communities within a multicultural Christian community. I examine two Christian Tharu performances: performing the huri nāc (a Kathariya Tharu song and dance genre performed during Holi) at interchurch events and arranging an original, Nepali-language hymn as a maghauta nāc (a song and dance genre performed during Tharu celebrations of Māghī). The first performance contends that Tharu religion can comprise of more than one religious tradition, challenging essentialist narratives of what Tharu religion should be. The second performance declares that Christian Nepali practice is wide enough to encompass Tharu cultural signifiers. I draw on my ethnographic research in Tharu communities in Kailali and Dang districts, which ranged from attending church events, seasonal music competitions, and community festivals to interviewing lay men and women, pastors, and other church leaders. Discussing the musical choices of these Christian Tharus allows me enter the conversation about belonging within Himalayan studies. I demonstrate how a focus on belonging does not negate the importance of identity, but is a complement to studies of difference

Alien Registration- Dalzell, Lillie M. (Rockland, Knox County)

https://digitalmaine.com/alien_docs/14801/thumbnail.jp

Workshop on Institutional Aspects of Proliferation Resistance

Prepared for the U.S. Dept. of Energy under Contract no. EN-77-S-02-4571.A000. Organized by the MIT Dept. of Nuclear Engineering, PSIA, and the U.S. Dept. of Energy

Genotypic Effects on Condensed Tannins in the Leucaena Genus

One hundred and eighteen accessions of the Leucaena genus were assayed for extractable and bound condensed tannins (CT). Leucaena taxa varied from low or no CT (0-1%) to extremely high levels (\u3e15%). There was considerable intraspecific variation in CT within key taxa. The proportion of bound tannin decreased with increasing total CT content

Fixed-point adiabatic quantum search

Fixed-point quantum search algorithms succeed at finding one of M target items among N total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster than a classical computer, it lacks the fixed-point property—the fraction of target items must be known precisely to know when to terminate the algorithm. Recently, Yoder, Low, and Chuang [Phys. Rev. Lett. 113, 210501 (2014)] gave an optimal gate-model search algorithm with the fixed-point property. Previously, it had been discovered by Roland and Cerf [Phys. Rev. A 65, 042308 (2002)] that an adiabatic quantum algorithm, operating by continuously varying a Hamiltonian, can reproduce the quadratic speedup of gate-model Grover search. We ask, can an adiabatic algorithm also reproduce the fixed-point property? We show that the answer depends on what interpolation schedule is used, so as in the gate model, there are both fixed-point and non-fixed-point versions of adiabatic search, only some of which attain the quadratic quantum speedup. Guided by geometric intuition on the Bloch sphere, we rigorously justify our claims with an explicit upper bound on the error in the adiabatic approximation. We also show that the fixed-point adiabatic search algorithm can be simulated in the gate model with neither loss of the quadratic Grover speedup nor of the fixed-point property. Finally, we discuss natural uses of fixed-point algorithms such as preparation of a relatively prime state and oblivious amplitude amplification.American Society for Engineering Education. National Defense Science and Engineering Graduate FellowshipMIT-Harvard Center for Ultracold Atoms MIT International Science and Technology InitiativeNational Science Foundation (U.S.) (RQCC Project 1111337)Massachusetts Institute of Technology. Undergraduate Research Opportunities Program (Paul E. Gray Endowed Fund