stateQIP = statePSPACE

Complexity theory traditionally studies the hardness of solving classical computational problems. In the quantum setting, it is also natural to consider a different notion of complexity, namely the complexity of physically preparing a certain quantum state. We study the relation between two such state complexity classes: statePSPACE, which contains states that can be generated by space-uniform polynomial-space quantum circuits, and stateQIP, which contains states that a polynomial-time quantum verifier can generate by interacting with an all-powerful untrusted quantum prover. The latter class was recently introduced by Rosenthal and Yuen (ITCS 2022), who proved that statePSPACE $\subseteq$ stateQIP. Our main result is the reverse inclusion, stateQIP $\subseteq$ statePSPACE, thereby establishing equality of the two classes and providing a natural state-complexity analogue to the celebrated QIP = PSPACE theorem of Jain, et al. (J. ACM 2011). To prove this, we develop a polynomial-space quantum algorithm for solving a large class of exponentially large "PSPACE-computable" semidefinite programs (SDPs), which also prepares an optimiser encoded in a quantum state. Our SDP solver relies on recent block-encoding techniques from quantum algorithms, demonstrating that these techniques are also useful for complexity theory. Using similar techniques, we also show that optimal prover strategies for general quantum interactive protocols can be implemented in quantum polynomial space. We prove this by studying an algorithmic version of Uhlmann's theorem and establishing an upper bound on the complexity of implementing Uhlmann transformations.Comment: 61 page

FPGA implementation of adaptive interference canceler for periodic signal.

This thesis describes the design, implementation and testing of an adaptive digital interference canceler for periodic signals. This canceler uses the least mean-square (LMS) adaptive filtering technique to eliminate interference from an input signal. An advantage of the adaptive interference cancelling approach is that it requires no prior knowledge of both the signal and the interference characteristics. A digital design approach is used in this thesis because of its reliability and accuracy. The canceler implemented using a Xilinx FPGA chip. A prototype design demonstrated that the canceler was able to reduce the input interference power by about 40%.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1995 .Y83. Source: Masters Abstracts International, Volume: 34-06, page: 2448. Adviser: H. K. Kwan. Thesis (M.A.Sc.)--University of Windsor (Canada), 1995

Plexcitons: Dirac points and topological modes

Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. We consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional bandstructure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. These Dirac cones may open up in energy by simultaneously interfacing the metal with a magneto-optical layer and subjecting the whole system to a perpendicular magnetic field. The resulting energy gap becomes populated with topologically protected one-way modes which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter as well as of novel ways to direct energy flow at the nanoscale

Method for multiplex cellular detection of mRNAs using quantum dot fluorescent in situ hybridization

The photostability and narrow emission spectra of non-organic quantum dot fluorophores (QDs) make them desirable candidates for fluorescent in situ hybridization (FISH) to study the expression of specific mRNA transcripts. We developed a novel method for direct QD labeling of modified oligonucleotide probes through streptavidin and biotin interactions, as well as protocols for their use in multiple-label FISH. We validated this technique in mouse brainstem sections. The subcellular localization of the vesicular monoamine transporter (Vmat2) mRNA corresponds when using probes labeled with two different QDs in the same hybridization. We developed protocols for combined direct QD FISH and QD immunohistochemical labeling within the same neurons as well as for simultaneous study of the subcellular distribution of multiple mRNA targets. We demonstrated increased sensitivity of FISH using QDs in comparison with organic fluorophores. These techniques gave excellent histological results both for multiplex FISH and combined FISH and immunohistochemistry. This approach can facilitate the ultrasensitive simultaneous study of multiple mRNA and protein markers in tissue culture and histological section

Broadband amplitude squeezing in a periodically poled KTiOPO_4 waveguide

We generated -2.2 dB of broadband amplitude squeezing at 1064 nm in a periodically poled KTiOPO_4 (PPKTP) waveguide, by coupling of the fundamental and second harmonic continuous-wave fields. This is the largest amount of squeezing obtained to date in a KTP waveguide, limited by propagation losses. This result paves the way for further improvements by use of lower-loss buried ion-exchanged waveguides.Comment: 3 pages, 2 figures, submitted for publicatio

Unitary Complexity and the Uhlmann Transformation Problem

State transformation problems such as compressing quantum information or breaking quantum commitments are fundamental quantum tasks. However, their computational difficulty cannot easily be characterized using traditional complexity theory, which focuses on tasks with classical inputs and outputs. To study the complexity of such state transformation tasks, we introduce a framework for unitary synthesis problems, including notions of reductions and unitary complexity classes. We use this framework to study the complexity of transforming one entangled state into another via local operations. We formalize this as the Uhlmann Transformation Problem, an algorithmic version of Uhlmann's theorem. Then, we prove structural results relating the complexity of the Uhlmann Transformation Problem, polynomial space quantum computation, and zero knowledge protocols. The Uhlmann Transformation Problem allows us to characterize the complexity of a variety of tasks in quantum information processing, including decoding noisy quantum channels, breaking falsifiable quantum cryptographic assumptions, implementing optimal prover strategies in quantum interactive proofs, and decoding the Hawking radiation of black holes. Our framework for unitary complexity thus provides new avenues for studying the computational complexity of many natural quantum information processing tasks.Comment: 126 pages, comments welcom

Simple constructions of linear-depth t-designs and pseudorandom unitaries

Uniformly random unitaries, i.e., unitaries drawn from the Haar measure, have many useful properties, but cannot be implemented efficiently. This has motivated a long line of research into random unitaries that ``look\u27\u27 sufficiently Haar random while also being efficient to implement. Two different notions of derandomisation have emerged: $t$-designs are random unitaries that information-theoretically reproduce the first $t$ moments of the Haar measure, and pseudorandom unitaries (PRUs) are random unitaries that are computationally indistinguishable from Haar random. In this work, we take a unified approach to constructing $t$-designs and PRUs. For this, we introduce and analyse the ``$PFC$ ensemble\u27\u27, the product of a random computational basis permutation $P$, a random binary phase operator $F$, and a random Clifford unitary $C$. We show that this ensemble reproduces exponentially high moments of the Haar measure. We can then derandomise the $PFC$ ensemble to show the following: 1. Linear-depth $t$-designs. We give the first construction of a (diamond-error) approximate $t$-design with circuit depth linear in $t$. This follows from the $PFC$ ensemble by replacing the random phase and permutation operators with their $2t$-wise independent counterparts. 2. Non-adaptive PRUs. We give the first construction of PRUs with non-adaptive security, i.e., we construct unitaries that are indistinguishable from Haar random to polynomial-time distinguishers that query the unitary in parallel on an arbitary state. This follows from the $PFC$ ensemble by replacing the random phase and permutation operators with their pseudorandom counterparts. 3. Adaptive pseudorandom isometries. We show that if one considers isometries (rather than unitaries) from $n$ to $n + \omega(\log n)$ qubits, a small modification of our PRU construction achieves adaptive security, i.e., even a distinguisher that can query the isometry adaptively in sequence cannot distinguish it from Haar random isometries. This gives the first construction of adaptive pseudorandom isometries. Under an additional conjecture, this proof also extends to adaptive PRUs

Vitamin C Prevents Hypogonadal Bone Loss

Epidemiologic studies correlate low vitamin C intake with bone loss. The genetic deletion of enzymes involved in de novo vitamin C synthesis in mice, likewise, causes severe osteoporosis. However, very few studies have evaluated a protective role of this dietary supplement on the skeleton. Here, we show that the ingestion of vitamin C prevents the low-turnover bone loss following ovariectomy in mice. We show that this prevention in areal bone mineral density and micro-CT parameters results from the stimulation of bone formation, demonstrable in vivo by histomorphometry, bone marker measurements, and quantitative PCR. Notably, the reductions in the bone formation rate, plasma osteocalcin levels, and ex vivo osteoblast gene expression 8 weeks post-ovariectomy are all returned to levels of sham-operated controls. The study establishes vitamin C as a skeletal anabolic agent. © 2012 Zhu et al

a trimolecular composition

Photochemical upconversion based on triplet–triplet annihilation (TTA-UC) is employed to enhance the short-circuit currents generated by two varieties of thin-film solar cells, a hydrogenated amorphous silicon (a-Si:H) solar cell and a dye-sensitized solar cell (DSC). TTA-UC is exploited to harvest transmitted sub-bandgap photons, combine their energies and re-radiate upconverted photons back towards the solar cells. In the present study we employ a dual-emitter TTA-UC system which allows for significantly improved UC quantum yields as compared to the previously used single-emitter TTA systems. In doing so we achieve record photo-current enhancement values for both the a-Si:H device and the DSC, surpassing 10−3 mA cm−2 sun−2 for the first time for a TTA-UC system and marking a record for upconversion-enhanced solar cells in general. We discuss pertinent challenges of the TTA-UC technology which need to be addressed in order to achieve its viable device application

Increased upconversion performance for thin film solar cells: A trimolecular composition

Photochemical upconversion based on triplet-triplet annihilation (TTA-UC) is employed to enhance the short-circuit currents generated by two varieties of thin-film solar cells, a hydrogenated amorphous silicon (a-Si:H) solar cell and a dye-sensitized solar cell (DSC). TTA-UC is exploited to harvest transmitted sub-bandgap photons, combine their energies and re-radiate upconverted photons back towards the solar cells. In the present study we employ a dual-emitter TTA-UC system which allows for significantly improved UC quantum yields as compared to the previously used single-emitter TTA systems. In doing so we achieve record photo-current enhancement values for both the a-Si:H device and the DSC, surpassing 10-3 mA cm-2 sun-2 for the first time for a TTA-UC system and marking a record for upconversion-enhanced solar cells in general. We discuss pertinent challenges of the TTA-UC technology which need to be addressed in order to achieve its viable device application