Hamiltonian simulation with optimal sample complexity

© 2017 Author(s). We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631-633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states.S.K. and C.Y.L. are funded by the Department of Defense. G.H.L. is funded by the NSF CCR and the ARO quantum computing projects. M.O. acknowledges Leverhulme Trust Early Career Fellowship (ECF-2015-256) and European Union project QALGO (Grant Agreement No. 600700) for financial support. T.J.Y. thanks the DoD, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a. The authors are grateful to the University of Maryland Libraries’ Open Access Publishing Fund and the Massachusetts Institute of Technology Open Access Publishing Fund for partial funding for open access

Improved techniques for preparing eigenstates of fermionic Hamiltonians

Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation. First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing the initial states required for simulation of fermions in first quantization. This is an exponential improvement over the previous state-of-the-art. Next, we show how to reduce the overhead due to repeated state preparation in phase estimation when the goal is to prepare the ground state to high precision and one has knowledge of an upper bound on the ground state energy that is less than the excited state energy (often the case in quantum chemistry). Finally, we explain how one can perform the time evolution necessary for the phase estimation based preparation of Hamiltonian eigenstates with exactly zero error by using the recently introduced qubitization procedure

Classical skyrmions in SU(N)/SO(N) cosets

We construct the skyrmion solutions appearing in the coset spaces SU(N)/SO(N) for N > 2 and compute their classical mass. For N = 3, the third homotopy group pi_3(SU(3)/SO(3)) = Z_4 implies the existence of two distinct solutions: the skyrmion of winding number two has spherical symmetry and is found to be the lightest non-trivial field configuration; the skyrmion and antiskyrmion of winding number plus and minus one are slightly heavier and of toroidal shape. For N >= 4, there is only one skyrmion since the third homotopy group is Z_2. It is found to have spherical symmetry and is significantly lighter than the N = 3 solutions.Comment: 14 pages, 3 figures; v2: discussion improve

Basolateral Sorting of Syntaxin 4 Is Dependent on Its N-terminal Domain and the AP1B Clathrin Adaptor, and Required for the Epithelial Cell Polarity

Generation of epithelial cell polarity requires mechanisms to sort plasma membrane proteins to the apical and basolateral domains. Sorting involves incorporation into specific vesicular carriers and subsequent fusion to the correct target membranes mediated by specific SNARE proteins. In polarized epithelial cells, the SNARE protein syntaxin 4 localizes exclusively to the basolateral plasma membrane and plays an important role in basolateral trafficking pathways. However, the mechanism of basolateral targeting of syntaxin 4 itself has remained poorly understood. Here we show that newly synthesized syntaxin 4 is directly targeted to the basolateral plasma membrane in polarized Madin-Darby canine kidney (MDCK) cells. Basolateral targeting depends on a signal that is centered around residues 24–29 in the N-terminal domain of syntaxin 4. Furthermore, basolateral targeting of syntaxin 4 is dependent on the epithelial cell-specific clathrin adaptor AP1B. Disruption of the basolateral targeting signal of syntaxin 4 leads to non-polarized delivery to both the apical and basolateral surface, as well as partial intercellular retention in the trans-Golgi network. Importantly, disruption of the basolateral targeting signal of syntaxin 4 leads to the inability of MDCK cells to establish a polarized morphology which suggests that restriction of syntaxin 4 to the basolateral domain is required for epithelial cell polarity

Star forming dwarf galaxies

Star forming dwarf galaxies (SFDGs) have a high gas content and low metallicities, reminiscent of the basic entities in hierarchical galaxy formation scenarios. In the young universe they probably also played a major role in the cosmic reionization. Their abundant presence in the local volume and their youthful character make them ideal objects for detailed studies of the initial stellar mass function (IMF), fundamental star formation processes and its feedback to the interstellar medium. Occasionally we witness SFDGs involved in extreme starbursts, giving rise to strongly elevated production of super star clusters and global superwinds, mechanisms yet to be explored in more detail. SFDGs is the initial state of all dwarf galaxies and the relation to the environment provides us with a key to how different types of dwarf galaxies are emerging. In this review we will put the emphasis on the exotic starburst phase, as it seems less important for present day galaxy evolution but perhaps fundamental in the initial phase of galaxy formation.Comment: To appear in JENAM Symposium "Dwarf Galaxies: Keys to Galaxy Formation and Evolution", P. Papaderos, G. Hensler, S. Recchi (eds.). Lisbon, September 2010, Springer Verlag, in pres

Operative versus non-operative management of pediatric medial epicondyle fractures: a systematic review

There is ongoing debate about the management of medial epicondyle fractures in the pediatric population. This systematic review evaluated non-operative versus operative treatment of medial epicondyle fractures in pediatric and adolescent patients over the last six decades. A systematic review of the available literature was performed. Frequency-weighted mean union times were used to compare union rates for closed versus open treatments. Moreover, functional outcomes and range-of-motion variables were correlated with varying treatment modalities. Any complications, including ulnar nerve symptoms, pain, instability, infection, and residual deformity, were cataloged. Fourteen studies, encompassing 498 patients, met the inclusion/exclusion criteria. There were 261 males and 132 female patients; the frequency-weighted average age was 11.93 years. The follow-up range was 6–216 months. Under the cumulative random effects model, the odds of union with operative fixation was 9.33 times the odds of union with non-operative treatment (P < 0.0001). There was no significant difference between operative and non-operative treatments in terms of pain at final follow-up (P = 0.73) or ulnar nerve symptoms (P = 0.412). Operative treatment affords a significantly higher union rate over the non-operative management of medial epicondyle fractures. There was no difference in pain at final follow-up between operative and non-operative treatments. As surgical indications evolve, and the functional demands of pediatric patients increase, surgical fixation should be strongly considered to achieve stable fixation and bony union

Multivariable regression analysis of febrile neutropenia occurrence in early breast cancer patients receiving chemotherapy assessing patient-related, chemotherapy-related and genetic risk factors.

BACKGROUND: Febrile neutropenia (FN) is common in breast cancer patients undergoing chemotherapy. Risk factors for FN have been reported, but risk models that include genetic variability have yet to be described. This study aimed to evaluate the predictive value of patient-related, chemotherapy-related, and genetic risk factors. METHODS: Data from consecutive breast cancer patients receiving chemotherapy with 4-6 cycles of fluorouracil, epirubicin, and cyclophosphamide (FEC) or three cycles of FEC and docetaxel were retrospectively recorded. Multivariable logistic regression was carried out to assess risk of FN during FEC chemotherapy cycles. RESULTS: Overall, 166 (16.7%) out of 994 patients developed FN. Significant risk factors for FN in any cycle and the first cycle were lower platelet count (OR = 0.78 [0.65; 0.93]) and haemoglobin (OR = 0.81 [0.67; 0.98]) and homozygous carriers of the rs4148350 variant T-allele (OR = 6.7 [1.04; 43.17]) in MRP1. Other significant factors for FN in any cycle were higher alanine aminotransferase (OR = 1.02 [1.01; 1.03]), carriers of the rs246221 variant C-allele (OR = 2.0 [1.03; 3.86]) in MRP1 and the rs351855 variant C-allele (OR = 2.48 [1.13; 5.44]) in FGFR4. Lower height (OR = 0.62 [0.41; 0.92]) increased risk of FN in the first cycle. CONCLUSIONS: Both established clinical risk factors and genetic factors predicted FN in breast cancer patients. Prediction was improved by adding genetic information but overall remained limited. Internal validity was satisfactory. Further independent validation is required to confirm these findings

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO