A Note on Quantum Phase Estimation

In this work, we study the phase estimation problem. We show an alternative, simpler and self-contained proof of query lower bounds. Technically, compared to the previous proofs [NW99, Bes05], our proof is considerably elementary. Specifically, our proof consists of basic linear algebra without using the knowledge of Boolean function analysis and adversary methods. Qualitatively, our bound is tight in the low success probability regime and offers a more fine-grained trade-off. In particular, we prove that for any $\epsilon > 0, p \geq 0$, every algorithm requires at least $\Omega(p/{\epsilon})$ queries to obtain an ${\epsilon}$-approximation for the phase with probability at least p. However, the existing bounds hold only when $p > 1/2$. Quantitatively, our bound is tight since it matches the well-known phase estimation algorithm of Cleve, Ekert, Macchiavello, and Mosca [CEMM98] which requires $O(1/{\epsilon})$ queries to obtain an ${\epsilon}$-approximation with a constant probability. Following the derivation of the lower bound in our framework, we give a new and intuitive interpretation of the phase estimation algorithm of [CEMM98], which might be of independent interest

Numerical Study Of The Effect Of Air Terminal Layouts On The Performance Of Stratum Ventilation System

It has been found that air terminal layouts could affect ventilation performance in a room. As a new ventilation system, stratum ventilation was proposed to accommodate the elevated room temperature. Its performance with various air terminal layouts was investigated by numerical method in this research. Totally four different exhausts locations were studied to determine the optimal exhaust locations. Exhausts were located at (a) low level of the same wall of the supplies; (b) middle level of the wall opposite to the supplies; (c) low level of the wall opposite to the supplies and (d) ceiling level, respectively. Ventilation performances were evaluated by airflow pattern, temperature distribution, percentage of dissatisfied people due to draft (PD), air diffusion performance index (ADPI) and local mean age of air. The computational results were validated by experimental results. Simulated results indicated that performance with exhausts located at ceiling level was the worst. Therefore it is not suggested for stratum ventilation. For the other three layouts, similar airflow pattern and temperature distribution was observed with exhausts located at middle and low level of the wall opposite to supplies. Indoor environment could achieve thermal comfort and good air quality with exhausts located at low level of the same wall of the supplies. This arrangement also helps to save the space for system installation. It is therefore a better choice for stratum ventilation design if performance requirements are met

Pseudorandom Strings from Pseudorandom Quantum States

A fundamental result in classical cryptography is that pseudorandom generators are equivalent to one-way functions and in fact implied by nearly every classical cryptographic primitive requiring computational assumptions. In this work, we consider a variant of pseudorandom generators called quantum pseudorandom generators (QPRGs), which are quantum algorithms that (pseudo)deterministically map short random seeds to long pseudorandom strings. We provide evidence that QPRGs can be as useful as PRGs by providing cryptographic applications of QPRGs such as commitments and encryption schemes. Our main result is showing that QPRGs can be constructed assuming the existence of logarithmic-length quantum pseudorandom states. This raises the possibility of basing QPRGs on assumptions weaker than one-way functions. We also consider quantum pseudorandom functions (QPRFs) and show that QPRFs can be based on the existence of logarithmic-length pseudorandom function-like states. Our primary technical contribution is a method for pseudodeterministically extracting uniformly random strings from Haar-random states.Comment: 45 pages, 1 figur

Pseudorandom Isometries

We introduce a new notion called ${\cal Q}$-secure pseudorandom isometries (PRI). A pseudorandom isometry is an efficient quantum circuit that maps an $n$-qubit state to an $(n+m)$-qubit state in an isometric manner. In terms of security, we require that the output of a $q$-fold PRI on $\rho$, for $\rho \in {\cal Q}$, for any polynomial $q$, should be computationally indistinguishable from the output of a $q$-fold Haar isometry on $\rho$. By fine-tuning ${\cal Q}$, we recover many existing notions of pseudorandomness. We present a construction of PRIs and assuming post-quantum one-way functions, we prove the security of ${\cal Q}$-secure pseudorandom isometries (PRI) for different interesting settings of ${\cal Q}$. We also demonstrate many cryptographic applications of PRIs, including, length extension theorems for quantum pseudorandomness notions, message authentication schemes for quantum states, multi-copy secure public and private encryption schemes, and succinct quantum commitments

On the Impossibility of General Parallel Fast-Forwarding of Hamiltonian Simulation

Hamiltonian simulation is one of the most important problems in the field of quantum computing. There have been extended efforts on designing algorithms for faster simulation, and the evolution time T for the simulation greatly affect algorithm runtime as expected. While there are some specific types of Hamiltonians that can be fast-forwarded, i.e., simulated within time o(T), for some large classes of Hamiltonians (e.g., all local/sparse Hamiltonians), existing simulation algorithms require running time at least linear in the evolution time T. On the other hand, while there exist lower bounds of ?(T) circuit size for some large classes of Hamiltonian, these lower bounds do not rule out the possibilities of Hamiltonian simulation with large but "low-depth" circuits by running things in parallel. As a result, physical systems with system size scaling with T can potentially do a fast-forwarding simulation. Therefore, it is intriguing whether we can achieve fast Hamiltonian simulation with the power of parallelism. In this work, we give a negative result for the above open problem in various settings. In the oracle model, we prove that there are time-independent sparse Hamiltonians that cannot be simulated via an oracle circuit of depth o(T). In the plain model, relying on the random oracle heuristic, we show that there exist time-independent local Hamiltonians and time-dependent geometrically local Hamiltonians on n qubits that cannot be simulated via an oracle circuit of depth o(T/n^c), where the Hamiltonians act on n qubits, and c is a constant. Lastly, we generalize the above results and show that any simulators that are geometrically local Hamiltonians cannot do the simulation much faster than parallel quantum algorithms

A mammalian Wnt5a-Ror2-Vangl2 axis controls the cytoskeleton and confers cellular properties required for alveologenesis.

Alveolar formation increases the surface area for gas-exchange and is key to the physiological function of the lung. Alveolar epithelial cells, myofibroblasts and endothelial cells undergo coordinated morphogenesis to generate epithelial folds (secondary septa) to form alveoli. A mechanistic understanding of alveologenesis remains incomplete. We found that the planar cell polarity (PCP) pathway is required in alveolar epithelial cells and myofibroblasts for alveologenesis in mammals. Our studies uncovered a Wnt5a-Ror2-Vangl2 cascade that endows cellular properties and novel mechanisms of alveologenesis. This includes PDGF secretion from alveolar type I and type II cells, cell shape changes of type I cells and migration of myofibroblasts. All these cellular properties are conferred by changes in the cytoskeleton and represent a new facet of PCP function. These results extend our current model of PCP signaling from polarizing a field of epithelial cells to conferring new properties at subcellular levels to regulate collective cell behavior

Paxillin facilitates timely neurite initiation on soft-substrate environments by interacting with the endocytic machinery.

Neurite initiation is the first step in neuronal development and occurs spontaneously in soft tissue environments. Although the mechanisms regulating the morphology of migratory cells on rigid substrates in cell culture are widely known, how soft environments modulate neurite initiation remains elusive. Using hydrogel cultures, pharmacologic inhibition, and genetic approaches, we reveal that paxillin-linked endocytosis and adhesion are components of a bistable switch controlling neurite initiation in a substrate modulus-dependent manner. On soft substrates, most paxillin binds to endocytic factors and facilitates vesicle invagination, elevating neuritogenic Rac1 activity and expression of genes encoding the endocytic machinery. By contrast, on rigid substrates, cells develop extensive adhesions, increase RhoA activity and sequester paxillin from the endocytic machinery, thereby delaying neurite initiation. Our results highlight paxillin as a core molecule in substrate modulus-controlled morphogenesis and define a mechanism whereby neuronal cells respond to environments exhibiting varying mechanical properties

VI-Band Follow-Up Observations of Ultra-Long-Period Cepheid Candidates in M31

The ultra-long period Cepheids (ULPCs) are classical Cepheids with pulsation periods exceeding $\approx 80$ days. The intrinsic brightness of ULPCs are ~1 to ~3 mag brighter than their shorter period counterparts. This makes them attractive in future distance scale work to derive distances beyond the limit set by the shorter period Cepheids. We have initiated a program to search for ULPCs in M31, using the single-band data taken from the Palomar Transient Factory, and identified eight possible candidates. In this work, we presented the VI-band follow-up observations of these eight candidates. Based on our VI-band light curves of these candidates and their locations in the color-magnitude diagram and the Period-Wesenheit diagram, we verify two candidates as being truly ULPCs. The six other candidates are most likely other kinds of long-period variables. With the two confirmed M31 ULPCs, we tested the applicability of ULPCs in distance scale work by deriving the distance modulus of M31. It was found to be $\mu_{M31,ULPC}=24.30\pm0.76$ mag. The large error in the derived distance modulus, together with the large intrinsic dispersion of the Period-Wesenheit (PW) relation and the small number of ULPCs in a given host galaxy, means that the question of the suitability of ULPCs as standard candles is still open. Further work is needed to enlarge the sample of calibrating ULPCs and reduce the intrinsic dispersion of the PW relation before re-considering ULPCs as suitable distance indicators.Comment: 13 pages, with 14 Figures and 4 Tables (one online table). AJ accepte

Pseudorandom Strings from Pseudorandom Quantum States

A fundamental result in classical cryptography is that pseudorandom generators are equivalent to one-way functions and in fact implied by nearly every classical cryptographic primitive requiring computational assumptions. In this work, we consider a variant of pseudorandom generators called quantum pseudorandom generators (QPRGs), which are quantum algorithms that (pseudo)deterministically map short random seeds to long pseudorandom strings. We provide evidence that QPRGs can be as useful as PRGs by providing cryptographic applications of QPRGs such as commitments and encryption schemes. Our main result is showing that QPRGs can be constructed assuming the existence of logarithmic-length quantum pseudorandom states. This raises the possibility of basing QPRGs on assumptions weaker than one-way functions. We also consider quantum pseudorandom functions (QPRFs) and show that QPRFs can be based on the existence of logarithmic-length pseudorandom function-like states. Our primary technical contribution is a method for pseudodeterministically extracting uniformly random strings from Haar-random states