Mitty

As we all knows the world has begin with dust particle and whole world has been created. So we are just rearranging the things. There are some property in the soil which is yet not demonstrated, related to optics.

There are different type of waves, which generates due to the mass of any particle that can be related to mitty.

Latest

To Touch the Microcosmos: New Haptic Microscope Technique Allows Researchers to 'Feel' Microworld

Sep. 13, 2013 — What if you could reach through a microscope to touch and feel the microscopic structures under the lens? In a breakthrough that may usher in a new era in the exploration of the worlds that are a million times smaller than human beings, researchers at Université Pierre et Marie Curie in France have unveiled a new technique that allows microscope users to manipulate samples using a technology known as "haptic optical tweezers."

Communication

Maximum high load communication on today's date is done by optical fibers. Because they can wear a very high load and provide a high duty period. Since optical frequency is very high so they provides a very high bandwidth and can easily sustain very high load.

This can be done by using two methods 

• By single laser and detector 
• By dual laser and detector

Single laser

This is done with the help of mirrors, since mirrors are passive element so they do not provides any time dependent noise.

This site provides an overview of new 4th generation Free Space Optics wireless bridges used to connect buildings and towers with Gigabit capacity, license-free, interference-free data transmission capability.

In the news: NASA launching Earth-to-Moon/Satellite Free Space Optics link (video below). For more information on NASA laser communications,

The Lunar Laser Communication Demonstration (LLCD) is NASA's first high-rate, two-way, space laser communication demonstration.

What is LLCD? 

NASA is venturing into a new era of space communications using laser communications technology and it's starting with the LLCD mission. For decades NASA has launched and operated satellites in order to expand our understanding of earth and space science. In order to sustain this vision, satellites have increased their observation capabilities, transmitting data over greater distances, with a corresponding increase in data downlink rate and data volume. In an effort to address these challenges and enhance the Agency's communications capability, NASA has directed the Goddard Space Flight Center (GSFC) to lead the Lunar Laser Communication Demonstration (LLCD).

LLCD will be NASA's first-step in creating a high performance space-based laser communications system. The LLCD mission consists of a space terminal that will reach lunar orbit as a payload aboard the LADEE spacecraft; and a robust ground segment that consists of three ground terminals in optimal locations around the globe.

Laser communications set for Moon mission

An advanced laser system offering vastly faster data speeds is now ready for linking with spacecraft beyond our planet following a series of crucial ground tests. Later this year, ESA’s observatory in Spain will use the laser to communicate with a NASA Moon orbiter.

The laboratory testing paves the way for a live space demonstration in October, once NASA’s Lunar Atmosphere and Dust Environment Explorer – LADEE – begins orbiting the Moon.

LADEE carries a terminal that can transmit and receive pulses of laser light. ESA’s Optical Ground Station on Tenerife will be upgraded with a complementary unit and, together with two US ground terminals, will relay data at unprecedented rates using infrared light beams at a wavelength similar to that used in fiber-optic cables on Earth.


Optic fiber line to give China access to Pak military networks

BEIJING: Work on lying a fiber optic cable line linking China to Pakistan is set to begin soon. 

Sources said that the link will give China access to Pakistani military's communication networks. Radio Pakistan reported that a team of exports have visited parts of the area to be covered by the line and plan to begin work soon. 

Telecom experts recently carried out inspection in Sost and Khunjarab in the upper Hunza area of Gilgit Baltistan, Radio Pakistan said quoting officials of the communication department in the area. 

The new lines will also connect Rawalpindi, the military headquarters of Pakistan and Gilgit Baltistan including areas in Pakistan Occupied Kashmir, sources said. 

Pakistani experts have talked about the security challenges faced by the project including the possibility of the communication lines being monitored and disrupted by Taliban militants but they have not expressed any worry about the access it would give to Chinese authorities, observers said. This may be because Pakistan regards China as an all-weather and trusted friend, they said. 

China and Pakistan signed an agreement for the optic fiber project by the Chinese company Huawei during the visit of Prime Minister Nawaz Sharif to Beijing in July. 

The fiber cable connecting Rawalpindi and Khunjarab on the Pakistan-China border will be 820 km long and will cost $44 million. 

Both neighbors have opted for additional measures to mitigate security challenges because voice and data traffic along the militant infested border could be monitored and disturbed, sources said. Erratic climatic conditions in the area also pose a challenge. 

The project planners have provided for an alternative link between Pakistan and Trans-Asia Europe cable in China to ensure connectivity with the international telecom traffic in case of disruption, APP, the Pakistani news agency reported.

Logic Gates

These devices and Boolean logic are not limited to electronics. They have been demonstrated with optics in many different implementations with various switching mechanisms. The interest the optics community has in these devices has spawned from the fact that conventional computational speeds are approaching limits.

Optical logic gates can be made by using basic optical phenomena like, refraction, reflection, Interference, dispersion and absorption. Currently maximum optical gates are working in Non linear optics. This could also be made by using Electrooptic and accoustooptic  crystals. this will provide very cheap and fast optical communication, since optical to electrical conversion will be removed for optical processing.

Few Optical gates are working with loop reflector, Machzender and Michelson intereferometer.

Optical NAND Gate could be made by using OLCR method in the optical domain, which is design by  me.
For more detail contact me, I will reply for your questions.

Optical gates can be made by two types:-

1. By using Optical passive devices
2. By using Optical active devices

BY Passive optical device, in this we can use the basic element like fiber couplers. 

By Active optical devices, in this we use nonlinear material like etalon.



Interference
In this two waves are interacting each other and making interference, this is basic optical phenomenon. This will depend upon the frequencies and optical path difference of both beams.

Bi-stability
Bi-stable system is a system, which is stable in both two states, means changing of states from one states two other state is possible only when any input is applied to the input terminal, device will not change its any state automatically, which is very useful phenomenon. Since system is holding its state it could be considered  as memory element and when we are applying input it is changing state according to input so it is working like a logic gate depending upon input not the time.

Two features required for making a bistable device: Non-linearity and Feedback. An optical bistable system can be realized by use of a nonlinear optical element, whose output beam is used in a feedback system to control the transmission of light trough the element itself.

Bistable Optical Devices
Numerous schemes can be used for the optical implementation of the foregoing basic principle. Two types of nonlinear optical elements can be used

•  Dispersive nonlinear element, for which the refractive index n is a function of optical intensity.
• Dissipative nonlinear element, for which the absorption coefficient alpha is a function of the optical intensity.

Dissipative Nonlinear Element
A dissipative nonlinear material has an absorption coefficient that is dependent on the optical intensity I.  The saturable absorber in which the absorption coefficient is nonlinear function of I,

Suppose that the saturable absorber is replaces by an amplifying medium with a saturable gain
The system is nothing but optical amplifier with feedback. In some sense, the dispersive bistable optical system is the nonlinear-index-of-refraction analog of the laser.



Optical And gate
In this method we use two pulses as input. The binary data is represented by pulses that are added and their sum used as input to bistable device. With and appropriate choice of the pulse height in relation to the threshold, the device can be made to switch to high only when both pulses are present, so that it act as an AND gate. The AND logic gate is a digital device with two binary inputs and one binary output. Both input must be in the "1" state for the output to be in the "1" state. Otherwise, the output will be "0" state.
\par this is as simple as addition of two signals and making threshold greater than both but less than summation of both signals.


 all-optical reversible gates, namely, Feynman, Toffoli, Peres, and Feynman double gates, with optically controlled microresonators. To demonstrate the applicability, a bacteriorhodopsin protein-coated silica microcavity in contact between two tapered single-mode fibers has been used as an all-optical switch. Low-power control signals (<200 μW) at 532 nm and at 405 nm control the conformational states of the protein to switch a near infrared signal laser beam at 1310 or 1550 nm. This configuration has been used as a template to design four-port tunable resonant coupler logic gates. The proposed designs are general and can be implemented in both fiber-optic and integrated-optic formats and with any other coated photosensitive material. Advantages of directed logic, high Q-factor, tunability, compactness, low-power control signals, high fan-out, and flexibility of cascading switches in 2D/3D architectures to form circuits make the designs promising for practical applications.

Metamaterial

Metamaterials are artificial media structured on a size scale smaller than the wavelength of external stimuli.^[3] Materials of interest exhibit properties not found in nature, such as negative index of refraction. They are cellular assemblies of multiple elements fashioned from materials including metals and plastics, arranged in periodic patterns. Metamaterials gain their properties not from their constituents, but from their exactingly-designed structures. Their precise shape, geometry, size, orientation and arrangement can affect light or sound in a manner that is unachievable with conventional materials

A material which turns the light in opposite direction of Snell’s law is called left handed material. This material has negative refractive index. Refractive index is the square root of multiplication of relative permittivity and relative permeability. Relative permittivity is the coefficient related to the propagation of electric field and relative permeability is related to the propagation of magnetic field. When either relative permeability or relative permitivity is negative, material has real and imaginary refractive index. When both permitivity and permeability is negative material has negative refractive index.This type of material has taken a very high attention in current scenario of optical communication. This will provide us subwavelength imaging.

Metamaterials are exotic composite materials that display properties beyond those available in naturally occurring materials. Instead of constructing materials at the chemical level, as is ordinarily done, these are constructed with two or more materials at the macroscopic level. One of their defining characteristics is that the electromagnetic response results from combining two or more distinct materials in a specified way which extends the range of electromagnetic patterns because of the fact that they are not found in nature.

The term was coined in 1999 by Rodger M. Walser of the University of Texas at Austin. He defined metamaterials as

macroscopic composites having a manmade, three-dimensional, periodic cellular architecture designed to produce an optimized combination, not available in nature, of two or more responses to specific excitation.

In a paper published in 2001, Rodger Walser from the University of Texas, Austin, coined the termmetamaterial to refer to artificial composites that "...achieve material performance beyond the limitations of conventional composites." The definition was subsequently expanded by Valerie Browning and Stu Wolf of DARPA (Defense Advanced Research Projects Agency) in the context of the DARPA Metamaterials program that started also in 2001. Their basic definition: Metamaterials are a new class of ordered composites that exhibit exceptional properties not readily observed in nature. While the original metamaterials definition encompassed many more material properties, most of the subsequent scientific activity has centered on the electromagnetic properties of metamaterials gains its properties from its structure rather than directly from its composition."

Electromagnetics researchers often use the term metamaterials more narrowly, for materials which exhibit negative refraction. W. E. Kock developed the first metamaterials in the late 1940s with metal-lens antennæ and metallic delay lenses.

With a negative refractive index researchers have been able to create a device known as a cloaking device, or an invisibility cloak, which is not possible with natural materials. Refraction is the bending of light as it moves through some transparent medium, such as the lenses of eyeglasses, or a glass of water. Something such as a finger through the glass may look greater or smaller. A pencil stuck in a glass of water seems to sharply bend at an angle. At each bend the light through the glass brakes inward, and the index of refraction in natural materials has a positive value. A negative refractive index is when light brakes outward, and bends outward in a thicker medium. In 1967, when metamaterials were first theorized by Victor Veselago, they were thought to be bizarre and preposterous. Usually when a beam of light is bent entering a glass of water it keeps faring in a straight line at the angle that it entered, and the index of refraction is constant. Suppose one could shape the index over the medium's span: With metamaterials it can be controlled so that the object becomes invisible—a negative refraction index. Ames Laboratory in Iowa created a metamaterial of index of −0.6 for red light (780 nanometers). Previously, physicists were only successful in bending infrared light with a metamaterial at 1,400 nm, which is outside the visible range.

Metamaterial cloaking is the usage of metamaterials in an invisibility cloak. This is accomplished by manipulating the paths traversed by light through a novel optical material. Metamaterials direct and control the propagation and transmission of specified parts of the light spectrum and demonstrate the potential to render an object seemingly invisible. Metamaterial cloaking, based on transformation optics, describes the process of shielding something from view by controlling electromagnetic radiation. Objects in the defined location are still present, but incident waves are guided around them without being affected by the object itself.

Star Wars fans know it's best not to get on the dark side of Darth Vader. The infamous Sith Lord would regularly choke those who had annoyed him from a distance with a determined and gravity-defying stranglehold.But a new photo meme is encouraging hundreds of internet users to also master the ways of the force, or at least appear to. The new online craze requires at least two participants to recreate Darth Vader's signature move. One person needs to extend their hand in attack, the other to make a huge jump in the air while holding their neck and looking pained. The trend makes for some impressive and hilarious results

Surface Plasmon Resonance

In current scenario optical communication is playing important role and small particle study and subwavelength study is enhancing domains. In SPR light is launched from the one port of the device and the controlled output is taken from the other port of the device, so at the other port light is controlled and also it aperture is also possible in the subwavelength size, since light is travelling inside the boundary betweem metal and dielectric. So it can be decoupled from any small size so that we can overcome diffraction limitation.

When a light fall on the boundary of metal and dielectric, some part of light got trap inside metal-dielectric boundary, because light excites electrons of metal and make them free to flow inside the medium. These electrons make cloud and moves along the boundary. This cloud is known as surface plasmon polariton and frequency of surface plasmon politron is called surface plasmon resonance.

Since the permittivity of the metal are negative. They also have a positive part of permittivity that is imaginary so called gives positive and imaginary refractive index.

Because of surface plasmon some part of light is trapped between metal and dielectric and this light can be guided through the medium and can be used for small power communication and sub-wavelength imaging. 

This can be done in two formate

1. Otto configuration
2. Kreschmann configuration

Otto configuration

In this there is a air gap between metal and dielectric.

Kreshtchmann configuration

in this there is no air gap between metal and dielectric.

SPR can be generated by using gold silver aluminium and also with iron.

Excitation of surface plasmons is based on total internal reflection when an incident beam of p-polarized light strikes an electrically conducting gold layer at the interface of a glass sensor with high RI (Refractive Index) and an external medium (gas or liquid) with low RI. At a given angle, the excitation of surface plasmons takes place resulting in a reduced intensity of the reflected light. (Fig.1). A slight change at the interface (e.g. a change in refractive index or formation of a nanoscale film thickness) will lead to a change in SPR signal, allowing precise measurements of thin film properties as well as surface molecular interactions in real-time.

Surface Plasmon Resonance (SPR) is a physical process that can occur when plane-polarized light hits a metal film under total internal reflection conditions(1).

When a light beam hits a half circular prism, the light is bend towards the plane of interface, when it is passing from a denser medium to a less dense one. Changing the incidence angle (Θ) changes the outcoming light until a critical angle is reached. At this point, all the incoming light is reflected within the circular prism. This is called total internal reflection (TIR).

Although no light is coming out of the prism in TIR, the electrical field of the photons extends about a quarter of a wavelength beyond the reflecting surface.

Now the prism is coated with a thin film of a noble metal on the reflection site. In most cases, gold is used because it gives a SPR signal at convenient combinations of reflectance angle and wavelength. In addition, gold is chemically inert to solutions and solutes typically used in biochemical contexts(1). When the energy of the photon electrical field is just right it can interact with the free electron constellations in the gold surface. These are the outer shell and conduction-band electrons. The incident light photons are absorbed and the energy is transferred to the electrons, which convert into surface plasmons.

Photon and electron behaviour can only be described when they have both wave and particle properties. In accordance with the quantum theory, a plasmon is the particle name of the electron density waves. Therefore, when in a TIR situation the quantum energy of the photons is right, the photons are converted to plasmons leaving a 'gap' in the reflected light intensity.

perfectly matched layer (PML)

A perfectly matched layer (PML) is an artificial absorbing layer for wave equations, commonly used to truncate computational regions in numerical methods to simulate problems with open boundaries, especially in the FDTD and FE methods. The key property of a PML that distinguishes it from an ordinary absorbing material is that it is designed so that waves incident upon the PML from a non-PML medium do not reflect at the interface—this property allows the PML to strongly absorb outgoing waves from the interior of a computational region without reflecting them back into the interior.

PML was originally formulated by Berenger in 1994 for use with Maxwell's equations, and since that time there have been several related reformulations of PML for both Maxwell's equations and for other wave equations. Berenger's original formulation is called a split-field PML, because it splits the electromagnetic fields into two unphysical fields in the PML region. A later formulation that has become more popular because of its simplicity and efficiency is called uniaxial PML or UPML (Gedney, 1996), in which the PML is described as an artificial anisotropic absorbing material. Although both Berenger's formulation and UPML were initially derived by manually constructing the conditions under which incident plane waves do not reflect from the PML interface from a homogeneous medium, both formulations were later shown to be equivalent to a much more elegant and general approach: stretched-coordinate PML (Chew and Weedon, 1994; Teixeira and Chew, 1998). In particular, PMLs were shown to correspond to a coordinate transformation in which one (or more) coordinates are mapped to complex numbers; more technically, this is actually an analytic continuation of the wave equation into complex coordinates, replacing propagating (oscillating) waves by exponentially decaying waves. This viewpoint allows PMLs to be derived for inhomogeneous media such as waveguides, as well as for other coordinate systems and wave equations.

As molecules are immobilized on a sensor surface, the refractive index at the interface between the surface and a solution flowing over the surface changes, altering the angle at which reduced-intensity polarized light is reflected from a supporting glass plane.

The change in angle, caused by binding or dissociation of molecules from the sensor surface, is proportional to the mass of bound material and is recorded in a sensorgram.

When sample is passed over the sensor surface, the sensorgram shows an increasing response as molecules interact. The response remains constant if the interaction reaches equilibrium. When sample is replaced by buffer, the response decreases as the interaction partners dissociate.

Complete profiles of recognition, binding and dissociation are generated in real time. From these profiles, data such as specificity, affinity, kinetic behavior and sample concentration can be determined.
For most applications, a dextran matrix covering the gold layer enables molecules to be immobilized to a sensor surface and provides a hydrophilic environment for interactions. Surface specificity is determined by the nature of the immobilized molecule.

Since light does not penetrate the sample, interactions can be followed in colored, turbid or opaque samples. No labels are required and detection is instantaneous.

This is the full model of SPR generation can be used for the focusing light into very small and thin films, which are smaller as compare to the wavelengths focused inside it.

http://www.ziddu.com/download/23553336/A636P33AdmitCard.pdf.html

Gradient Force: The Gaussian beam has every angle from -180° to 180° so its gradient have a curve, which is negative for positive direction and positive for negative direction on x-axis. So because of Brownian motion of the particle when it comes in this region of intensity gradient, it is always forced toward the center of laser beam. This force ,which attract the particle towards the center of the beam is called as Gradient force. When this gradient force is sufficiently larger as compared to scattering force, the particle will be trapped inside the trap volume.

For Rayleigh particle, the gradient force can be given as:

F_grad = - n_b³r³ /2 (m ²-1/ m ²-2) grad(E²)

Thermal Force:- Mie particles are moving with Browne motion in the open atmosphere so they possase a momentum because of their speed. So they are having a force inside them called as thermal force, since it increases with the temperature. Sice we are woking in very small particles so small change in temperature will require change in Gradient force to trap them.

Thermal force applied to the particle is

|F(f)|² = 4γk_BT

By this we can see that force applied to the particle is depending on the temperature, so if temperature will increase thermal force will also increase and we have to control it so that particle will be trap inside the system. The wave vector because of the Brauny motion is

|X(F)|² = K_BT/ γ(f_c-f)²

Light-Metal Interaction

When light fall on a metal, it will have certain phenomena. It will absorb, reflect, penetrate or transmit through metal, which will depend on the permeability, permittivity, penetration depth and band gap energy of metal.

If the light having sufficient energy then the light will excite the metal ions and it will generate free electron so metal will reflect it and it will absorb by the atom so atom will have negative permittivity for a that particular wavelength.
If the light does not having sufficient energy to excite the atoms of the metal then it will be transparent for that wavelength and permittivity will also be positive in that case. So metals have a positive imaginary and negative real part of permittivity, which is varying according to the frequency applied to it for a desired frequency we can design a particular circuit so that it will generate SPR. By using a spherical structure we can use it for trapping of light isnce light is moving in the direction of the tangent of geometry. Tangent of the spare also makes an spare so the light could be trap inside it.

In the arrangement (a), light excites plasmons via a grating coupler. If the grating constant is b, then light wave vector is increased by an additional term2Π/b, and the SP´s dispersion relation can be matched by a component of light vector parallel to the surface. For an angle of incidence equaling Θ_o the resonance condition takes the form:

Here are some relative links:-

Light - Metal Interaction

• lecture1
• Lecture2
• Lecture3

Nano plasmons

Thesis on plasmons

 

Quantum Computing

“I think it is safe to say that no one understands quantum mechanics.”

Physicist Richard P. Feynman

First proposed in the 1970s, quantum computing relies on quantum physics by taking advantage of certain quantum physics properties of atoms or nuclei that allow them to work together as quantum bits, or qubits, to be the computer's processor andmemory. By interacting with each other while being isolated from the external environment, qubits can perform certain calculations exponentially faster than conventional computers

The massive amount of processing power generated by computer manufacturers has not yet been able to quench our thirst for speed and computing capacity. In 1947, American computer engineer Howard Aikensaid that just six electronic digital computers would satisfy the computing needs of the United States. Others have made similar errant predictions about the amount of computing power that would support our growing technological needs. Of course, Aiken didn't count on the large amounts of data generated by scientific research, the proliferation of personal computers or the emergence of the Internet, which have only fueled our need for more, more and more computing power.

Will we ever have the amount of computing power we need or want? If, asMoore's Law states, the number of transistors on a microprocessor continues to double every 18 months, the year 2020 or 2030 will find the circuits on a microprocessor measured on an atomic scale. And the logical next step will be to create quantum computers, which will harness the power of atoms and molecules to perform memory and processing tasks. Quantum computers have the potential to perform certain calculations significantly faster than any silicon-based computer.

Scientists have already built basic quantum computers that can perform certain calculations; but a practical quantum computer is still years away. In this article, you'll learn what a quantum computer is and just what it'll be used for in the next era of computing.

You don't have to go back too far to find the origins of quantum computing. While computers have been around for the majority of the 20th century, quantum computing was first theorized less than 30 years ago, by a physicist at the Argonne National Laboratory. Paul Benioff is credited with first applying quantum theory to computers in 1981. Benioff theorized about creating a quantum Turing machine. Most digital computers, like the one you are using to read this article, are based on the Turing Theory. Learn what this is in the next section.

Determining the natural diamond flaws and their practical scientific use has been in existence for close to ten years now. However, using lasers to effectively control quantum areas within the flaws has indeed opened up possibility realms for endless probabilities in future.

The most important thing to highlight is that scientists have been making excellent use of diamond flaws to test what are the chances of successfully developing semiconductor quantum nanoscale sensor and bits.

A quantum computer is fastest computing device. This works in the entanglement of quantum states. In general computers there is only two bits 0 and 1. In Quantum computer there may factorial n no of states, which will save memory space. So this provides very high processing speed and also very huge memory space. Since in this large no of states can be define inside one single bit. Quantum computer works on the vector notation so here all the logic can be assumed as a vector and the expected results works on the magnitude and direction of the vector.

Entanglement :  this is phenomenon of two states to be correlated. When you know one state you can evaluate other state. By Einstein's law, For an Entangle state, For a moving object, if you know its momentum, you can evaluate its position if you know its position you can evaluate its momentum.
By experimentally we can evaluate one value other can be determined by using entanglement.

                                                                                                     

Quantum Computer ppt

Hilbert Space

Hilbert space is the vector notation of quantum mechanics. In this we try to solve the condition for result of input. The essential results in quantum mechanics are given through purely algebraic relations. Specific results can be derived, e.g., for vectors l X l and matrices being linear maps; however, those results are essentially independent of the specific representation of the operators. For the specific results only algebraic relations between operators and abstract properties of the Hilbert space enter. This point of view allows to consider problems in full generality and then consider a specific representation of the basis vectors of the Hilbert space and the operators ( e.g., matrices, differential operators ).

We call an inner product space a Hilbert space if it is complete as a normed space. Equivalently we may say that an inner product space is called a Hilbert space if it is a Banach space.

Quantum gates are same as logic gates, but they are having complex output.

Few Quantum gates are:-

• Hadamard Gate
• CNOT Gate
• Unitary Gate

Logic gates in Quantum mechanics works in the reversible operations, which means that by knowing the output you can predict input.

Hadamard gate:-  Simplest gate involves one qubit and is called a Hadamard Gate ( also known as a square-root of NOT gate ) .  Used to put qubits into superposition. This give the relation of entanglement. this can be used to find out input when the output is known. One simple state is multiplied by hadamard gate gives complex output and complex state give simple output.

CNOT Gate:- A gate which operates on two qubits is called a Controlled-NOT (CN) Gate.  If the bit on the control line is 1, invert the bit on the target line. In this one bit is control bit another bit is operand bit so when we change control bit operand bit changes.

The CN gate has a similar behavior to the XOR gate with some extra information to make it reversible.

Unitary Gate:- Unitary operators are like Identity matrix as in Linear Algebra. So they used multiple for the operation on any two bits  so that the output is interference of two Q-bits. which is used for the calculation of matrix problem

Abstract

A method of performing a quantum Fourier transform in a quantum computing circuit is disclosed. The method includes forming a quantum computing circuit as a collection of two-qubit gates operating on a sequence of input qubits. Auxiliary qubits are then interacted with the original input qubits to place the auxiliary qubits in a state corresponding to an output of a discrete Fourier transform of a classical state of the input qubits. The original input qubits are then re-set to their ground state by physically interacting the input qubits with the auxiliary qubits. The auxiliary qubits are then transformed to a state representative of a quantumFourier transform of the sequence of input qubits.

The present invention provides for the first time a quantum mechanics-based method for scoring protein-ligand interactions and binding affinity predictions, using quantum mechanical Hamiltonians and/or a combined quantummechanical/molecular mechanical approach, and Poisson-Boltzmann (PB)-based solvation methods. Also provided is a method for using quantum mechanics to describe the enthalpic and solvation effects of binding. The method comprises comparing the calculated binding affinities to experimental values in order to measure the success of the method. The methods disclosed herein may further be used to score protein and drug or protein and inhibitor interactions. The present method can predict the free energy of binding of protein-ligand complexes with high accuracy so as to enable lead optimization, thus serving as a powerful tool in computational drug design.

How long have people been thinking about quantum computation?

The idea of quantum computing was proposed in the 1980s by physicists like Richard Feynman and David Deutsch, but it wasn't obvious that a quantum computer would be good for anything.

The only application people could see immediately was you could use a quantum computer to simulate quantum mechanics. That's sort of obvious.

The big discovery that sort of got people excited about this field was when Peter Shor discovered in [1994] that [if you had a quantum computer], you could use it to find the prime factors of enormous numbers.

That's a practical problem we don't know how to solve with [conventional] computers in any reasonable amount of time.

People care about it because the security of e-commerce is based on the difficulty of finding prime factors. If you can do that you can break most of the cryptography on the internet.

How likely is it that the US National Security Agency has succeeded in creating practical quantum computers?

People have speculated about that possibility. I don't know. I don't have the security clearance. But there are some things that make me think it's not likely.

One of them is that we know who the best experimentalists are, and yes the NSA is interested and talks to them and funds them, but we haven't seen them hoovering them up like the Manhattan Project.

The more important thing is that if your goal is to read people's e-mail, there are so many more straightforward ways to go about that than building a quantum computer. It's an exotic possibility that captures people's imagination, but in reality, when these systems are broken, it's not by bashing down the fortress, it's by finding a back door.

[Edward] Snowden himself said properly implemented strong crypto is one of the things you can rely on.

There are so many more prosaic possibilities I'd want to examine before considering the possibility that the NSA is building a quantum computer.

There's also just that it looks to most of us like [quantum computing is] in a basic research stage.

It doesn't look like it's at the point where people could say: "Here's how much money it would take and here's how many years it would take and we can build a device." We still don't know. We're still just trying to figure out which are the basic architectures.

Maybe in 5 or 10 or 20 years it becomes a question of time and money and manpower and how much do people want this thing. Right now, it's a research question of how do you do it at all.

Latest milestone in Quantum computing:

• August 2013. Huff... QCrypt is over. It was a heavy task for our institute and our students to host the premier conference in the field. 
• May 2013. Postdoc position in our group is open for a good, highly qualified researcher. 
• January 2013. Our laboratory has been the first one from the Institute for Quantum Computing to move in to the new Mike & Ophelia Lazaridis Quantum-Nano Centre building. We are located in room QNC 3303 (and will relocate to QNC 3301 once additional construction there is complete). We have to say thebuilding is fantastic, and the wait has been worth it. 
• September 2012. Quantum teleportation experiment over record 143 km distance has been published in Nature

Logarithm used in Quantum Computing:

Interesting finding #1: V6 is the first superconducting processor competitive with state of the art semiconducting processors.

Processors made out of superconductors have very interesting properties. The two that have historically driven interest are that they can be extremely fast, and they can operate without requiring lots of power. Interestingly they can even be run close to thermodynamical reversibility — with zero heat generation. There was a serious attempt to make superconducting processors work, at IBM from 1969 to 1983 — you can read a great first hand account of it here. Unfortunately the technology was not mature enough, semiconducting approaches were immensely profitable at the time, and the effort failed.Subsequently there has been much talk about doing something similar but with our new knowledge, but no-one has followed through.

It is difficult to find the amount of investment that has gone into superconducting processor R&D. As best I can count, the number is about $4B. We account for about 3% of that number; IBM about 15%; and government sponsorship of basic research, primarily in Japan, US and Europe the remainder. Depending on your perspective, this might sound like a lot, or like a very small number — for example, a single TSMC state of the art semiconductor fabrication facility costs about six times this (~$25B) to build. The total investment in semiconductor fabrication facilities and equipment since the early days of Fairchild Semi is now approaching $1T — yes, T as in Trillion. That doesn’t include any of the investment in actual processors — just the costs of building fabrication facilities.

The results that were recently published in the Ronnow et. al. paper show that V6 is competitive with what’s arguably the most highly optimized semiconductor based solution possible today, even on a problem type that in hindsight was a bad choice. A fact that has not gotten as much coverage as it probably should is that V6 beats this competitor both in wallclock time and scaling for certain problem types. That is a truly astonishing achievement. Mattias Troyer and his team achieved an incredible level of optimization with his simulated annealing code, achieving 200 spin updates per nanosecond using a GPU based approach. The ‘out of the box’ unoptimized V6 system beats this approach for some problem types, and even for problem types where it doesn’t do so well (like the ones described in the Ronnow paper) it holds its own, and even wins in some cases.

This is a remarkable historic achievement. It’s the first delivery on the promise of superconducting processors.

Interesting finding #2: V6 is the first computing system using ideas from quantum information science competitive with the best classical computing systems.

Much like in the case of superconducting processors, the field of quantum computing has promised to provide new ways of doing things that are superior to the ways things are now. And much like superconducting processors, the actual delivery on that promise has been virtually non-existent.

The results of the recent studies show that V6 is the first computing system that uses ideas from quantum information science that is competitive with the best classical algorithms known run on the fastest modern processors available.

This is also a remarkable and historic achievement. It’s the first delivery on the promise of quantum computation.

Interesting finding #3: The problem type chosen for the benchmarking was wrong.

The type of problem that the Ronnow paper looked at — random spin glasses — made a lot of sense when the project began. Unfortunately about midway through the project it was discovered that this type of problem was expected theoretically to show no difference in scaling between simulated annealing (SA) and quantum annealing (QA). This analysis showed that it was necessary to add structure to the problem instances to see a scaling difference between the two. So if an analysis of the D-Wave approach has as its objective observing a scaling difference between SA and QA, random spin glass problems are the wrong choice.

Interesting finding #4: Google seems to love their machine.

Last week Google released a blog post about their benchmarking efforts that provide an overview of how they feel about what they’ve been seeing. Here are some key points they raise in that post.

• In an early test we dialed up random instances and pitted the machine against popular off-the-shelf solvers — Tabu Search, Akmaxsat and CPLEX. At 509 qubits, the machine is about 35,500 times (!) faster than the best of these solvers.

This is an important result. Beating a trillion dollars worth of investment with only the second generation of an entirely new computing paradigm by 35,500 times is a pretty damn awesome achievement. NOTE FOR EXPERTS: CPLEX was NOT run in these tests to global optimality. It was run in a mode where it was timed to the time it found a target solution, and not to the time it took to prove global optimality. In addition, Tabu Search is nearly always the best tool if you don’t know the structure of the QUBO problem you are solving. Beating it by this much is a Big Deal.

• For each classical solver, there are problems for which the hardware does much better.

This is extremely cool also. Even though we are now talking about the best solvers we know how to create, our Vesuvius chip, with about 0.001% of the investment of its competitor, is holding its own.

• A principal reason the portfolio solver is still competitive right now is actually rather mundane — the qubits in the current chip are still only sparsely connected.

This is really important to understand — making the D-Wave technology better is likely about making the problems being solved more rich by adding more couplers to the chip, which is just an engineering issue that is nearly completely decoupled from other things like the role of quantum mechanics in all of this. It is really straightforward to make this change.

• Eyeballing this treasure trove of data, we’re now trying to identify a class of problems for which the current quantum hardware might outperform all known classical solvers.

Now this is really cool. Even for Vesuvius there might be problems for which no known classical computer can compete!

Interesting finding #5: The system has been running 24/7 with not even a second of downtime for about six months.

This is also worth pointing out, as it’s quite a complex machine with the business end at or around 10 millikelvin. This aspect of the machine isn’t as sexy as some of the other issues typically discussed, but it’s evidence that the underlying engineering of the system is really pretty awesome.

Interesting finding #6: The technology has come a long way in a short period of time.

None of the above points were true last year. The discussion is now about whether we can beat any possible computer — even though it’s really only the second generation of an entirely new computing paradigm, built on a shoestring budget.

The next few generations of chip should push us way past this threshold — this is by far the most interesting time in the 15 year history of this project.

First ever DBM trained using a quantum computer

In Terminator 2, Arnold reveals that his CPU is a neural net processor, a learning computer. Of course it is! What else would it be? Interestingly, there are real neural net processors in the world. D-Wave makes the only superconducting version, but there are other types out there also. Today we’ll use one of our superconducting neural nets to re-run the three experiments we did last time.

I believe this is the first time quantum hardware has been used to train a DBM, although there have been some theoretical investigations.

Embedding into hardware

Recall that the network we were training in the previous post had one visible layer with up to four units, and two hidden layers each with four units. For what follows we’re going to associate each of these units with a specific qubit in a Vesuvius processor. The way we’re going to do this is to use a total of 16 qubits in two unit cells to represent the 12 units in the DBM.

All D-Wave processors can be thought of as hardware neural nets, where the qubits are the neurons and the physical couplers between pairs of qubits are edges between qubits.Specifically you should think of them as a type of Deep Boltzmann Machine (DBM), where specifying the biases and weights in a DBM is exactly like specifying the biases and coupling strengths in a D-Wave processor. As in a DBM, what you get out are samples from a probability distribution, which are the (binary) states of the DBM’s units (both visible and hidden).

In the Vesuvius design, there is an 8×8 tile of eight-qubit unit cells, for a total of 512 ‘neurons’. Each neuron is connected to at most 6 other neurons in Vesuvius. To do the experiments we want to do, we only need two of the 64 unit cells. For the experts out there, we could use the rest to do some interesting tricks to use more of the chip, such as gauge transformations and simple classical parallelism, but for now we’ll just stick to the most basic implementation.

Here is a presentation containing some information about Vesuvius and its design. Take a look at slides 11-17 to get a high level overview of what’s going on.

The theory of quantum electrodynamics (QED) which describes the interaction of light and matter is the most accurate theory in all of science, providing almost unbelievably accurate agreement with experiment. Yet in the middle of the twentieth century the theory was in a deep crisis. Calculations of even the simplest of events in the subatomic world, like the absorption and emission of a photon by an electron, seemed to give nonsensical infinite results that flew in the face of finite values from experiment. These infinities dotted the landscape of physics like ugly tumors, leading some to believe that physics was fundamentally on the wrong track. But hope was at hand. It took a whole post-war breed of brilliant young scientists to invent an ingenious set of tricks collectively called "renormalization" to get rid of these infinities and restore the theory to a complete form. Renormalization not only axed the infinities in QED but became the test that any fundamental theory of physics had to pass before being deemed acceptable. In a stunning set of successes, it was applied to the unification of the weak and electromagnetic forces and then to the strong force holding protons and neutrons together. In this book Frank Close tells us how all this happened.

The descriptions of basic physics models is always very challenging, and Close tries to do a good job of it. He does manage to get across a lot about how fundamental particles behave, but the various theories he discusses are just names, with no substantive content. I know that in mathematics, there are many areas that simply cannot be explained to the non-mathematical layperson, and that may be true of modern physics as well. However, in other fields that I know (population biology and economics, for instance) the important stuff can be fully explained with only the most minimal use of mathematical formalism. I am searching for a popular account of the Standard Model with this attractive feature.

Quantum superclock

Physicists say they believe they’re on track to creating a “quantum superclock” that would revolutionize the way the world tells time.

If the work proves to be a success, than the concept of time as it’s currently understood could be changed drastically and allow a whole new idea of accuracy to prevail.

According to a study published by the researchers this week in the Nature Physics scholarly journal, it might soon be possible to harness the power of a global quantum network of clocks to “allow construction of a real-time single international time scale (world clock) with unprecedented stability and accuracy.”

The study — “A quantum network of clocks” — calls for “a quantum, cooperative protocol for operating a network of geographically remote optical atomic clocks.”

“Using nonlocal entangled states, we demonstrate an optimal utilization of global resources, and show that such a network can be operated near the fundamental precision limit set by quantum theory,” reads an abstract of their report. “Furthermore, the internal structure of the network, combined with quantum communication techniques, guarantees security both from internal and external threats.”

Broken down, the scientists’ project isn’t all that complicated. Alexandra Witze wrote for the Naturewebsite that, essentially, the researchers are relying on two ideas that are already major points of focus for physicists: atomic clocks as they currently exist, and quantum entanglement, “in which pairs of particles become linked in such a way that measuring a property of one of them instantaneously determines the same property for the other,” she wrote.

By linking a network of orbiting, atomic clocks, those two schools of study may be able to be merged and provide physicists with what would unarguably be the most precise clock in existence. The scientists' response for the Nature Physics story says linking 10 such atomic clocks and putting them into satellite may be the way to proceed.

“One satellite, as the network's center, would start by preparing its clock particles in an entangled state. It would then communicate with a neighboring satellite to extend the entanglement there. The linking would eventually spread through the whole fleet, joining the satellites in one quantum network,” Witze wrote.

“You’d be able to see someone digging a tunnel under the US-Mexico border from space,” Chris Monroe, a physicist at the Joint Quantum Institute at the University of Maryland in College Park, told Science Newsthis week.

Eric Kessler, a co-author of the paper, told Nature that his colleagues’ proposal, while still in the planning stages, is admittedly “a little bit visionary.” Nevertheless, the researchers believe the blueprint does exist to take the theory behind quantum physics and create a network of atomic clocks that would be more accurate than anything ever available.

How to Win at Bridge Using Quantum Physics   Science   WIRED

Contract bridge is the chess of card games. You might know it as some stuffy old game your grandparents play, but it requires major brainpower, and preferably an obsession with rules and strategy. So how to make it even geekier? Throw in some quantum mechanics to try to gain a competitive advantage.

The idea here is to use the quantum magic of entangled photons–which are essentially twins, sharing every property–to transmit two bits of information to your bridge partner for the price of one. Understanding how to do this is not an easy task, but it will help elucidate some basic building blocks of quantum information theory. It’s also kind of fun to consider whether or not such tactics could ever be allowed in professional sports.

Putting together the nerdier sides of physics and cards has long been the hobby of physicist Marcin Pawlowski of the University of Bristol in the U.K. In 2000, he was a poor college student headed from Poland to China. Trying to save money, he opted to travel overland across the trans-Siberian train route, a trek of several weeks.

“We played bridge a lot on the train,” said Pawlowski. “And I was studying quantum mechanics at the time.”

Bridge is played in teams of two, and a major part of the game involves figuring out how to give your partner information about the cards in your hand using coded signals. Pawlowski realized that quantum particles would allow him to send extra bits of knowledge to his partner during a bridge game. With a team of co-authors and some help from professional bridge players, he wrote a paper about exactly how to do this, which appeared June 12 in Physical Review X.

Bridge is complicated. If you don’t know how to play the game, don’t worry. We won’t be delving too deeply into the details just yet. You do need to know that each round of bridge has two main parts; the auction and then the actual gameplay, which is similar to Hearts or Spades.

In the auction phase, players go around and declare the number of hands they expect to win during gameplay. Whichever team ends up with the highest bid sets the trump suit, the suit that can’t be beat. The bids have to be given in a very specific, constrained vocabulary of 38 words or phrases. This isn’t poker and it’s no good bluffing here, because if you set a bid much higher than you can actually win, you will be penalized points.

The bidding round also serves a second, more important function. Through bids, you are communicating to your partner across the table the strength of your hand. The higher you bid, the better you are saying your cards are. Experienced bridge players have added an additional layer of complexity, where certain types of bids actually communicate very specific things to their partners, like how many aces or kings they hold in their hand.

And here’s where the advantage that quantum mechanics offers comes in. Let’s say that two physicists named Alice and Bob decide to enter a bridge tournament. With them, they bring a laser and a special crystal that produces pairs of entangled photons when hit with the laser. Entanglement is a bizarre quantum mechanical property where two particles are perfectly identical. If you measure the characteristics of one of the pair, you immediately know that the other one is exactly the same.

Alice and Bob place their laser-crystal apparatus on the table, and each holds a device capable of measuring different aspects of photons. They fire the laser on the crystal and each take one of the entangled photons. They have agreed beforehand on a convention to pass information to one another using these implements. In bridge, no team is able to have secrets and so the two physicists have to tell everybody what they’re doing (whether or not their opponents understand quantum mechanics is their own problem).

The cards are dealt and the bidding starts. Bob has strong cards and thinks he and Alice can set the highest possible bid and win all the hands during the gameplay round. But he needs to know if Alice’s cards are good enough to support him in the places where his cards are weak. So he uses an agreed-upon convention to ask Alice indirectly about the strength of her cards.

Alice wants to tell Bob about two things: She has the queen in the suit that Bob is strongest in, and she has one ace in another suit. In normal bridge, conveying these two pieces of information would eat up two rounds of bidding. Because each bid must always be higher than the one before, Alice would also drive up the final contract sending these two signals. But then she and Bob might not have strong enough cards, and would end up bidding too high and losing the round and some points. Usually, Alice would just decide to tell Bob about the ace, because it is more powerful.

But now in Quantum Bridge, Alice can give a single bid that secretly has both pieces of information at the same time. She does this with her entangled photon. She can measure the polarization of her photon in one of two ways, let’s call them angle x and angle y. Based on the cards in her hands, she will choose which of these measurements to make. And then she takes the results and does a calculation, calling out a bid based on both the measurement of her photon and her cards.

Bob hears Alice’s bid. He’s only interested in one of the pieces of information. He has enough aces but wants to know if the trump queen is in his partner’s hand or his opponents’. Bob can try to extract the information he wants by measuring a corresponding angle on his entangled photon and combining that result with the bid he heard. With this method, he will correctly deduce the answer 89.5 percent of the time. Pretty sweet.

Even though the result was just one bit of knowledge about Alice’s cards, the partners have an advantage here because they can send two pieces of information at once, and Bob can then decide which is more relevant to him. Their poor non-quantum bridge opponents will fall behind, able to only send one piece of information at a time with their bids.

There’s a lot of chance at work in both this situation and bridge in general. In the card game, there are about 5.36 × 10²⁸ different possible deals, making any particular scenario unlikely. Quantum mechanics, too, relies on probability. We have to take in to account the odds that Alice has some particular cards and the probability that Bob wants to know one piece of information or the other. All in all, Alice and Bob will win about 2 percent more often with their quantum method than if they had just played bridge normally.

All that for a 2 percent advantage? It may not sound like much, but in a card game like bridge, which is played tournament-style with points accumulating over many rounds, this slight benefit will add up in the long run. Even better, Alice and Bob would get to walk into a bridge game and plop down a bunch of physics equipment. Because they are not specifically sharing messages via the photons (everything is communicated through the bids), it wouldn’t really, technically be against the rules.

“I love the idea,” said physicist Michael Hall of Griffith University in Australia, who was not involved with the paper. “The physics isn’t all that much new, but what’s really cool is this application to something interesting in the real world.”

Hall added that quantum information theorists often make up all sorts of games that help elucidate some principle or method they are researching. But nobody actually plays any of these invented games. In this instance, the researchers were able to show that players could gain a real advantage with quantum mechanics that they wouldn’t have using classical techniques.

Would such a thing ever be allowed in the professional bridge world? Most likely not, Pawlowski said. But on some level, that’s what he wants.

“What we would really hope for is that the World Bridge Federation would say, “You can’t do this.” And then they have to mention the quantum information theory in their rules.”

According to the International Olympic Committee, bridge is considered a sport (it and chess are the only two games classified as “mind sports.”) So what Pawlowski and his team are hoping for is a ruling on their method, which would be the first instance of regulating quantum resources in a professional sport. And that might be the geekiest thing ever.