scholarly journals Quantum Factoring Algorithm: Resource Estimation and Survey of Experiments

2020 ◽  
pp. 39-55
Author(s):  
Noboru Kunihiro
Keyword(s):  
Large Scale ◽  
Quantum Circuit ◽  
The Other ◽  
Quantum Circuits ◽  
Small Scale ◽  
Quantum Computers ◽  
Resource Estimation ◽  
Shor's Algorithm ◽  
Order Of An Element ◽  
Factoring Algorithm

Abstract It is known that Shor’s algorithm can break many cryptosystems such as RSA encryption, provided that large-scale quantum computers are realized. Thus far, several experiments for the factorization of the small composites such as 15 and 21 have been conducted using small-scale quantum computers. In this study, we investigate the details of quantum circuits used in several factoring experiments. We then indicate that some of the circuits have been constructed under the condition that the order of an element modulo a target composite is known in advance. Because the order must be unknown in the experiments, they are inappropriate for designing the quantum circuit of Shor’s factoring algorithm. We also indicate that the circuits used in the other experiments are constructed by relying considerably on the target composite number to be factorized.

scholarly journals On the depth overhead incurred when running quantum algorithms on near-term quantum computers with limited qubit connectivity

2020 ◽  
Vol 20 (9&10) ◽  
pp. 787-806 ◽  
Author(s):  
Steven Herbert
Keyword(s):  
Quantum Algorithms ◽  
Quantum Circuit ◽  
The Other ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Interaction Graph ◽  
Finite Degree ◽  
Near Term

This paper addresses the problem of finding the depth overhead that will be incurred when running quantum circuits on near-term quantum computers. Specifically, it is envisaged that near-term quantum computers will have low qubit connectivity: each qubit will only be able to interact with a subset of the other qubits, a reality typically represented by a qubit interaction graph in which a vertex represents a qubit and an edge represents a possible direct 2-qubit interaction (gate). Thus the depth overhead is unavoidably incurred by introducing swap gates into the quantum circuit to enable general qubit interactions. This paper proves that there exist quantum circuits where a depth overhead in Omega(\log n) must necessarily be incurred when running quantum circuits with n qubits on quantum computers whose qubit interaction graph has finite degree, but that such a logarithmic depth overhead is achievable. The latter is shown by the construction of a 4-regular qubit interaction graph and associated compilation algorithm that can execute any quantum circuit with only a logarithmic depth overhead.

scholarly journals Cost function dependent barren plateaus in shallow parametrized quantum circuits

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
M. Cerezo ◽  
Akira Sone ◽  
Tyler Volkoff ◽  
Lukasz Cincio ◽  
Patrick J. Coles
Keyword(s):  
Cost Function ◽  
Large Scale ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Heuristic Methods ◽  
Practical Applications ◽  
Local Observables ◽  
Large Scale Simulations

AbstractVariational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is $${\mathcal{O}}(\mathrm{log}\,n)$$ O ( log n ) . Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

The Perks and Perils of Interdisciplinary Research

2018 ◽  
Vol 26 (S2) ◽  
pp. S55-S67 ◽  
Author(s):  
Erin Leahey
Keyword(s):  
Interdisciplinary Research ◽  
Large Scale ◽  
Policy Implications ◽  
The Other ◽  
Small Scale ◽  
Extra Time ◽  
Empirical Assessment ◽  
Cognitive Challenges

This paper synthesizes findings from two studies the author conducted that examine how engagement in interdisciplinary research (IDR) influences scholars’ careers. Results from these two studies, one large-scale and quantitative and the other small-scale and qualitative, provide a much needed empirical assessment of IDR’s effects on individual careers. In essence, they provide a nice antidote (and some caution) to the rhetoric and enthusiasm surrounding IDR. My co-authors of these studies and I find that engaging in interdisciplinary research increases a scholar’s visibility in terms of citations, but also presents challenges, including reduced productivity, cognitive challenges, lack of support, extra time and commitment, and framing of one’s work. This paper concludes by discussing the policy implications of this research.

scholarly journals Balanced reconnection intervals: four case studies

2008 ◽  
Vol 26 (12) ◽  
pp. 3897-3912 ◽  
Author(s):  
A. D. DeJong ◽  
A. J. Ridley ◽  
C. R. Clauer
Keyword(s):  
Case Studies ◽  
Large Scale ◽  
The Other ◽  
Small Scale ◽  
Polar Cap ◽  
Reconnection Rate ◽  
Magnetospheric Convection ◽  
The Third ◽  
New Name ◽  
Definition Of

Abstract. During steady magnetospheric convection (SMC) events the magnetosphere is active, yet there are no data signatures of a large scale reconfiguration, such as a substorm. While this definition has been used for years it fails to elucidate the true physics that is occurring within the magnetosphere, which is that the dayside merging rate and the nightside reconnection rate balance. Thus, it is suggested that these events be renamed Balanced Reconnection Intervals (BRIs). This paper investigates four diverse BRI events that support the idea that new name for these events is needed. The 3–4 February 1998 event falls well into the classic definition of an SMC set forth by Sergeev et al. (1996), while the other challenge some previous notions about SMCs. The 15 February 1998 event fails to end with a substorm expansion and concludes as the magnetospheric activity slowly quiets. The third event, 22–23 December 2000, begins with a slow build up of magnetospheric activity, thus there is no initiating substorm expansion. The last event, 17 February 1998, is more active (larger AE, AL and cross polar cap potential) than previously studied SMCs. It also has more small scale activity than the other events studied here.

A Method for Bonding PDMS Without Using Plasma

2010 ◽  
Author(s):  
Cristina Martin ◽  
Aarash Y. N. Sofla
Keyword(s):  
Hydrochloric Acid ◽  
Adhesion Strength ◽  
Glass Sample ◽  
Large Scale ◽  
The Other ◽  
Laboratory Research ◽  
Small Scale ◽  
Manufacturing Processes ◽  
Inexpensive Method ◽  
Chlorine Gas

The vapor-assisted treatment constitutes a simple and inexpensive method to increase the adhesion strength of polydimethylsiloxane and glass without using plasma. In this method, the targeted PDMS-glass sample is exposed to a vapor in an enclosed container for a certain time. Different chemicals were tested as possible vapor sources. No increase in the adhesion strength of PDMS-glass samples was observed when silanes without chloro functional groups were used. On the other hand, all alkyl trichlorosilanes tested in this study led to permanent bondings. In addition, an increase in the strength of the PDMS-glass adhesion was obtained with di- and monochlorosilanes as well as with hydrochloric acid solution. These results experimentally demonstrate that the hydrogen chlorine gas assists with the PDMS-glass bonding, making the vapor-assisted treatment a method with multiple applications in both small scale laboratory research and large scale manufacturing processes.

Mesoscale Spectra of Mars’s Atmosphere Derived from MGS TES Infrared Radiances

2007 ◽  
Vol 64 (5) ◽  
pp. 1717-1726 ◽  
Author(s):  
Takeshi Imamura ◽  
Yasuhiro Kawasaki ◽  
Tetsuya Fukuhara
Keyword(s):  
Seasonal Variation ◽  
Large Scale ◽  
Thermal Emission ◽  
The Other ◽  
Small Scale ◽  
High Latitudes ◽  
Mars Global Surveyor ◽  
Infrared Radiance ◽  
Infrared Radiances ◽  
Radiance Data

Abstract Wavenumber spectra of the atmospheric potential energy of Mars at mesoscales (wavelengths of 64–957 km) were obtained as a function of latitude, season, and Martian year using infrared radiance data obtained by the Thermal Emission Spectrometer (TES) onboard the Mars Global Surveyor (MGS) spacecraft. Spectral slopes tend to be flatter at smaller scales, and the slopes are usually flatter than −1 near small-scale ends. Near large-scale ends, the spectra sometimes show prominent steepening with slopes from −2 to −3. The power peaks in the high latitudes in winter and equinoxes, suggesting that eddies are generated preferentially in baroclinic zones. The seasonal variation at each latitude band, on the other hand, tends to be obscured by large interannual variability. An enhancement in the power was observed around the storm tracks in the Southern Hemisphere. Spectra of the terrestrial stratosphere were also obtained with a similar method from data taken by the Aura satellite and compared to the results for Mars.

QUANTUM CIRCUITS FOR PROBABILISTIC ENTANGLEMENT TELEPORTATION VIA A PARTIALLY ENTANGLED PAIR

2007 ◽  
Vol 05 (05) ◽  
pp. 717-728 ◽  
Author(s):  
XIU-BO CHEN ◽  
QIAO-YAN WEN ◽  
FU-CHEN ZHU
Keyword(s):  
Quantum Circuit ◽  
The Other ◽  
Quantum Circuits ◽  
Entangled State ◽  
Practical Realization ◽  
Entanglement Teleportation ◽  
Probabilistic Teleportation ◽  
Partially Entangled State ◽  
Positive Operator Valued Measure ◽  
Many Particles

It deserves mentioning that the quantum circuit, i.e. quantum logic network, is essential to the practical realization of teleportation in experiment. Using only one partially entangled pair, we first propose two novel strategies for probabilistically teleporting any partially entangled state of a bipartite system. The feature of the present protocol is to weaken the requirement for the quantum channel, and also to cut down the number of entangled particles initially shared by the sender and receiver. On the other hand, we explicitly construct the generalized measurement described by the positive operator-valued measure (POVM). Two kinds of efficient quantum circuits for implementing the teleportation are offered. In addition, we generalize the two-particle probabilistic teleportation to the system of many particles.

scholarly journals Micro Disasters: The Case of Serial Killer Jeffrey Dahmer

2017 ◽  
Vol 7 (3) ◽  
pp. 444-452 ◽  
Author(s):  
Jeffrey M. Jentzen
Keyword(s):  
Heat Wave ◽  
Human Activity ◽  
Disaster Response ◽  
Large Scale ◽  
Crime Scene ◽  
The Other ◽  
Serial Killer ◽  
Small Scale ◽  
Community Or ◽  
Major Disaster

Disasters are commonly experienced as major devastating events that exceed the resources of an agency to respond, with effects emanating throughout a community or region. There are, however, those events that are more measured, more subtle, and with few actual deaths, which still distract investigators from their daily duties and routines and project long lasting and crippling effects to a community or nation. Disasters can occur from natural forces or be the result of human activity. Most forensic pathologists who practice over a significant time will encounter one or the other types of disaster, sometimes more than a few. In my own career, I have witnessed large-scale disasters, such as hundreds of deaths occurring as the result of a major heat wave, to small-scale disasters such as factory explosions or small airplane crashes at sea—each with their own challenges. In addition to the extent of the initial disaster, many require the detailed, exhaustive evidentiary recovery and examination of a crime scene. The Jeffrey Dahmer case, although only involving 11 actual victims, required a major disaster response, and continues to influence and affect a community over 25 years later.

Dependencies of Polychlorinated Biphenyl Concentrations Measured at the Great Lakes on Climate Variables

2020 ◽  
Author(s):  
Sandy Ubl ◽  
Martin Scheringer
Keyword(s):  
Wind Speed ◽  
Great Lakes ◽  
Wind Direction ◽  
Seasonal Cycle ◽  
Large Scale ◽  
Polychlorinated Biphenyl ◽  
The Other ◽  
Small Scale ◽  
Local Conditions ◽  
Pcb Congeners

<p>Polychlorinated biphenyls (PCBs) are persistent and hazardous chemicals that are still detected in the atmosphere and other environmental compartments although their production was banned several decades ago. At the Great Lakes region PCBs have been monitored via the IADN network since 1993. In this study, we report results from seven different PCB congeners measured at six different sites around the Great Lakes. The PCBs exhibit a strong seasonal cycle with highest concentrations in summer and lowest concentrations in winter. The concentrations measured in Chicago and Cleveland are higher compared to the concentrations reported from more remote stations. We evaluated the correlations for the seven PCB congeners at each station. PCB-53,-101,-118 and -138 are highly correlated at each of the six stations. PCB-180 is the least correlated with all the other PCBs. This is explicitly true for Eagle Harbor, where PCB-180 and -153 are not correlated with the other 6 PCBs. This may be explained by the less pronounced seasonal cycle of these heavier PCBs at Eagle Harbor. We observed significant correlations between PCB-28 concentrations at the remote stations, but PCB concentrations at the stations of Chicago and Cleveland are only poorly correlated with PCB concentrations at the other stations. The weak correlation of the PCB concentrations measured at the different stations and the relatively high concentrations of the PCB congeners at each station indicate that local conditions and small scale processes (sources, temperature, wind direction, wind speed) dictate the spatial distribution of the  PCBs. We will feed available data on temperature, wind speed, wind direction, emissions, precipitation, ice cover of the Great Lakes and large scale atmospheric teleconnection patterns into a General Additive Model (GAM) to further investigate the relationships between the measured PCB concentrations and selected environmental conditions and atmospheric parameters.<span> </span></p>

TOWARD ULTRA-LOW POWER III-V QUANTUM LARGE SCALE INTEGRATED CIRCUITS FOR UBIQUITOUS NETWORK ERA

2006 ◽  
Vol 16 (02) ◽  
pp. 421-436 ◽  
Author(s):  
HIDEKI HASEGAWA ◽  
SEIYA KASAI ◽  
TAKETOMO SATO
Keyword(s):  
Integrated Circuits ◽  
Low Power ◽  
Large Scale ◽  
Quantum Circuit ◽  
Small Scale ◽  
Logic Function ◽  
Ultra Low Power ◽  
Binary Decision ◽  
Nanowire Networks ◽  
Ubiquitous Network

In an attempt to realize tiny "knowledge vehicles" called intelligent quantum (IQ) chips for use in the coming ubiquitous network society, this paper presents the present status and future prospects of ultra-small-size and ultra-low-power III-V quantum logic large scale integrated circuits based on a novel hexagonal binary-decision diagram (BDD) quantum circuit architecture. Here, quantum transport in path switching node devices formed on III-V semiconductor-based hexagonal nanowire networks is controlled by nanometer scale Schottky wrap gates (WPGs) to realize arbitrary combinational logic function. Feasibility of the approach is shown through fabrication of basic node devices and various small-scale circuits, and approaches for higher density integration and larger scale circuits are discussed.

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