The electrical and electronic engineers that have design and develop Central Microprocessing Units (CPUs) know that if anyone had a single repeatable function that was required to be computed by the CPU, it may perform its job much quicker if the CPU went on a “physics” diet. i.e. slim it down, throw it all out in the garbage, clean out the attic and downsize the house; reduced instruction sets, optimized on chip memory and so on. Well all of the three companies have done that. Either for routing purposes or a hardwired ticker plant, companies are going “hard” wired for EPROMs, Gate Arrays, and custom ICs.

More to Come…

• scalable physically to increase the # of qubits
• qubits can be initialized to arbitrary values
• quantum gates faster than decoherence time
• Turing-complete gate set
• qubits can be read easily

There are a number of practical difficulties in building a quantum computer, and thus far quantum computers have only solved trivial problems. One major problem is keeping the components of the computer in a mixed state as the slightest interaction with the external world would cause the system to decohere.

• Superconductor-based quantum computers
• ” Nuclear magnetic resonance on molecules in solution“-based
• ” quantum dot on surface”-based
• ” laser acting on floating ions (in vacuum)”-based ( Ion trapping )
• ” Cavity quantum electrodynamics ” ( CQED )-based
• molecular magnet-based
• SQUID-based
• the solid state NMR Kane quantum computer

This section surveys what is currently known mathematically about the power of quantum computers. It describes the known results from computational complexity theory and the theory of computation dealing with quantum computers.

The class of problems that can be efficiently solved by quantum computers is called BQP, for “bounded error, quantum, polynomial time”. Quantum computers only run randomized algorithms, so BQP on quantum computers is the counterpart of BPP on classical computers. It is defined as the set of problems solvable with a polynomial-time algorithm, whose probability of error is bounded away from one half. A quantum computer is said to “solve” a problem if, for every instance, its answer will be right with high probability. If that solution runs in polynomial time, then that problem is in BQP.

BQP is suspected to be disjoint from NP-complete and a strict superset of P, but that is not known. Both integer factorization and discrete log are in BQP. Both of these problems are NP problems suspected to be outside P. Both are suspected to not be NP-complete. There is a common misconception that quantum computers can solve NP-complete problems in polynomial time. That is not known to be true, and is generally suspected to be false.

An operator for a quantum computer can be thought of as changing a vector by multiplying it with a particular matrix. Multiplication by a matrix is a linear operation. It has been shown that if a quantum computer could be designed with nonlinear operators, then it could solve NP-complete problems in polynomial time. It could even do so for #P-complete problems. It is not yet known whether such a machine is possible.

Although quantum computers are sometimes faster than classical computers, they can’t solve any problems that classical computers can’t solve, given enough time and memory. A Turing machine can simulate a quantum computer, so a quantum computer could never solve an undecidable problem like the halting problem. The existence of quantum computers does not disprove the Church-Turing thesis.

Many cognitive studies have demonstrated convincingly that human cognition relies more heavily on visual than numeric stimuli. People absorb and process large amounts of visual data using the visual cortex, a specialized area of the brain, every second. Despite this fact, the most common basis for presenting and analyzing quantitative research in financial engineering is still numerical, e.g., spreadsheets and tables. Some have argued that visualization is less achievable for financial applications because of the high dimensionality of the problems. These arguments have been refuted dramatically in other highly quantitative disciplines such as fluid dynamics, electrical engineering, mechanical engineering, molecular biology, and meteorology, in which visualization has come to play a central role in both basic research and industry applications. 

Over the past decade our understanding of how we precive data and process it has improved and so has the corresponding computer science field of information visualization. It has developed and grown over the last few decades, enabled by the capability of economically massive storage, powerful 64-bit processors, GPUs with capabilities sometimes more impressive than their CPU, and new methods to manipulate the data using high performance vector and Hilbert-based databases. Information visualization hinges on the idea that data can be visually represented in useful and insightful ways that enhance our understanding of the information. The flip side is that complex data can often be grasped quickly and intuitively when rendered visually. An effective approach to realizing theses innovative visualization techniques is to bring to bear the multiple disciplines of cognitive science, graphic design, computer science and, of course, Finance.  

Admittedly, there have been financial companies in the data visualization space for a sometime now. The heat-maps visualizations are perhaps the most popular on trading desks. A popular one found on smartmoney.com uses a large rectangle to represent the market capitalization of an entire industry. Within the industry rectangle contain smaller rectangles that represent sectors within that industries market capitalization. Further inside the sectors are rectangles that represent the market capitalization of individual companies. The sizes of these rectangles are dynamic and change in size relative to the price changes of the individual stocks in real-time. All the rectangles sizes are normalized so they continue to fit into the larger rectangle perfectly.  Companies that are down in market capitalization are shaded red and ones that are up are shaded green. This goes for the sectors as well. One gets an intuitive understanding of the state of the market quickly and easily. The value of this simple tool is impressive when one considers that you are only utilizing two of René Descartes Cartesian coordinates, several shades of color, and some careful thought.

Treemapping is a method for displaying information about entities with a hierarchical relationship, in a “space-constrained” environment (such as a computer monitor).

 –Wikipedia

Treemaps can be used to track the performance of portfolios or a desk’s risk exposure more quickly and seamlessly than existing alternatives. Users can track the relative performance of, say, 1,000 stocks in real time and drill down to get more detailed information, instead of looking at those 1,000 stocks in a 30-page spreadsheet. JPMorgan uses heat-mapping toolkit to produce Credit Map, a visualization product that enables the bank’s institutional customers to visualize real-time developments in the credit markets.

Now, to the award winning product: Fractal:Edge. Fractal:Edge’s visualization is vaguely similar to the heat-map’s with some notable improvements. In essence it uses the moments of fractals to represent varying market concepts. In the figure below, for example, the company’s real-time chart of the global equities market is represented by a large circle with progressively smaller ones contained inside, akin to a Venn diagram. In this depiction, the regions of the world are shown as large circles. Within those circles are rings containing what look like smaller spheres. The rings represent indexes in that region and the spheres within each of them depict the sectors within that index. Each circle, ring and sphere is color-coded based on performance, and a viewer can drill down from a global level to the individual stock level in moments.

Fractal:Edges’ Fratal Map

Less know, but more impressive is work done by W. Bradford Paley, professor at Columbia University that has both sides of his brain functioning in, undeniably, perfect unison, creating innovative visualization methods intuitively. Out of several impressive visualization techniques he has created one stands out for me; it is TextArc. First, it converts temporal data into a Euclidian space with vector features. How it works is that a time-series of data is “rolled out”, line by line around in an oval outline. Secondly, an inner arc is drawn by analyzing the unique elements in the outer arc. When a new data element is discovered in the outside arc, its datum is set where it was found. The method then continues to parse the outside arc searching for the same data element, when it finds another instant it “pulls” the original instant towards the new instance in a vector type manner, some finite distance. This process continues until the out side arc is exhausted and the method moves on to the next unique element. The original element might have been “pulled” in many different directions resulting in its ending state being almost anywhere within the oval. Paley then labels the data element with its real value and shows the array of vectors emanating form the element, like rays of light from a star, some small finite distance. The result is astounding. Paley has worked in the finance space for several years now and I’m hoping to see some real impressive applications to his work.

TextArc by W. Bradford Paley

Finally, let’s look at enabling technologies for visualization: and let’s keep our feet on the ground and shelve the “Holo-deck for today”. A few years ago I encounter a very interesting piece of hardware at an SIA show that I have not seen since. It was a monitor akin to a simple double-glazing window found in your home. The first panel was, seemly, a normal LCD panel, the second panel, which was laid, directly over the first was a translucent panel. That was it, the rest we leave to Newton and his description of the properties of “Opticks”. You see the magic of this device simply lies in the properties of geometry and stereoscopic vision that creates a profound visual effect that is actually quite normal and performed by our eye ever few seconds.

One way to describe this physical behavior is the use of a term called  Depth of Field and is described as the following:

In optics, particularly film and photography, the depth of field (DOF) is the distance in front of and behind the subject which appears to be in focus. For any given lens setting, there is only one distance at which a subject is precisely in focus, but focus falls off gradually on either side of that distance, so there is a region in which the blurring is tolerable. This region is greater behind the point of focus than it is in front, as the angle of the light rays change more rapidly; they approach being parallel with increasing distance.

–Wikipedia

You can imagine that this new two paneled monitor uses DOF to its advantage. With its distance from your face at only 12” to 24”, and with a normally symmetrical human operator’s eyes being 2” to 3” apart, creates a 12 degree horizontal field of view. Ignoring the math for now this yields a very small and precise DOF of around ¼ of an inch. This DOF is more than enough to be able to focus on the back or front panel only, and eliminating the unfocused panel within your field of view. The demonstration I saw had both panels with Excel sheets filled with a massive amount of numbers; it was very easy to read one panel or the other. Imaging the power of this technology coupled with some real innovative visualization techniques; one can only think.

Another why to describe this physical behavior of the dual-panel monitor is the use of the more formal phyiscs field of stereopsis. Depth from stereopsis arises from the slightly different positions each eye occupies on the head, a form of parallax, as described above. A stereoscopeis a device by which each eye can be presented with different images, allowing stereopsis to be stimulated with two pictures, one for each eye. This has lead to various crazesfor stereopsis, usually prompted by new sorts of stereoscopes. Stereopsis appears to be processed in the visual cortex in binocular cells having receptive fields in different horizontal positions in the two eyes. Such a cell is active only when its preferred stimulus is in the correct position in the left eye and in the correct position in the right eye, making it a disparity detector. When a person stares at an object, the two eyes converge so that the object appears at the center of the retina in both eyes. Other objects around the main object appear shifted in relation to the main object. In the following example, whereas the main object remains in the center of the two images in the two eyes, the cube is shifted to the right in the left eye’s image and is shifted to the left when in the right eye’s image. Because each eye is in a different horizontal position, each has a slightly different perspective on a scene yielding different retinal images. Normally two images are not observed, but rather a single view of the scene, a phenomenon known as singleness of vision. If the images are very different (such as by going cross-eyed, or by presenting different images in a stereoscope) then one image at a time may be seen, a phenomenon known as binocular rivalry.

Regardless of which description helps you understand this application the simple fact remains that the monitor is very innovative and impressive.

With profound advances in enabling technologies and a “renaissance” in thought process, data visualization is starting to gain traction in the financial services industry. As this happens, the adoption of visualization tools is likely to be rapid, particularly as automated and electronic trading takes off and market data, like Level II depth, become more accessible.

First, a very quick background: In the early 1980s, renowned physicist Richard Feynman began to investigate the possibility of having a quantum computing machine that could simulate quantum systems as conventional computers simulate classical physical processes. He considered the “representation of binary numbers in relation to the quantum states of two-state quantum systems”. While classical computers of the mid 20th century utilized as their basic unit of information the “bit”, which could represent at any one time either “0″ or “1″, a quantum bit, or “qubit”, would harness the power of quantum mechanics in order to represent “0″, “1″, or a superposition of both. Thus a quantum computer would be able to simulate quantum mechanical processes that classical computers take too long to do or are entirely unable to handle.

Because of its speed and versatility, it seems likely that the search aspect of quantum computers will be one of the more important applications of a quantum computer. By the laws of quantum physics, specifically the Superposition Principle, atoms can be in several different energy states at once. The enormous potential of quantum computing is derived from the fact that this principle could allow for the creation of a computing device able to act on all its possible states simultaneously, carrying out numerous computations in parallel. Quantum computers are able to perform non-classical logic operations and can be used to solve computationally intractable problems that cannot be solved by conventional massively parallel supercomputers.

A classic nonlinear problem is that of the “Traveling Salesman,” which tries to find the shortest route between X number of cities the vendor must visit. As the value of X increases, the problem gets exponentially harder. Finding the best route without testing every possible route against each other, one by one, and assessing results, is the holy grail of information technology. That is the conundrum for quantum computers; the emergence of such a powerful tool comes with relatively few real-world applications. Most people would never see or use a quantum computer. This is not one of those things which will replace all computers. There are already products on the market using quantum mechanics. When they become more powerful the banking space will have endless applications to this new computational paradigm:

• Used to calculate Enterprise Risk Positions intra-day if not real-time
• Used to search massive networks of liquity for Pair trading opportunities
• Massively improve analytics for real-time pricing of exotic products
• Conduct analysis, i.e. Monte Carlo, in 1/1000 of the time frame
• and many more…

So where are we: Teams consisting of scientists and practitioners around the world are succeeded in creating very small quantum computers at the tail end of the 20th century. The first quantum computer consisted of two qubits and was demonstrated by a team of researchers led by Isaac Chuang at the University of California-Berkeley in 1998. Chuang and his colleagues then demonstrated the first three-qubit quantum computer the following year at the IBM-Almaden research facility in Silicon Valley. This one was able to carry out Grover’s database-search algorithm. In 2000 the same people demonstrated order-finding on a five-qubit computer and in 2001 they were able to construct a seven-qubit computer that carried out Shor’s integer-factoring algorithm. The latter of these was built with 1018 molecules, each consisting of the nuclei from five fluorine and two carbon atoms. The molecules interacted with one another as qubits, were “programmed by radio frequency pulses and… detected by nuclear magnetic resonance (NMR) instruments similar to those commonly used in hospitals and chemistry labs” (IBM, 2001). Using Shor’s algorithm, the computer correctly identified 3 and 5 as the factors of the integer 15.

The future of quantum computing is bright and getting near, with applications in many fields and quantum physics modeling on the horizon and further computational work in the distance. There are some notable obstacles as well, including the various forms of error correction and the reverse salient of software development. We have some why to go but the prize is to large to miss the target.

More to come…

Many mutual fund holders also suffer from being over-diversified. Some funds, especially the larger ones, have so many assets (i.e. cash to invest) that they have to hold literally hundreds of stocks and consequently, so are you. In some cases this makes it nearly impossible for the fund to outperform indexes – the whole reason you invested in the fund and are paying the fund manager a management fee. As the sage words of the “Oracle of Omaha”, Warren Buffett: “wide diversification is only required when investors do not understand what they are doing”.

When analyzing investment performance, statistical measures are often used to compare ‘funds’. These statistical measures are often reduced to a single figure representing an aspect of past performance. Alpha represents the fund’s return when the benchmark‘s return is 0. This shows the funds performance relative to the benchmark and can demonstrate the value added by the fund manager; the higher the ‘alpha’ the better the manager. Alpha investment strategies tend to favor stock selection methods to achieve growth.  Beta represents an estimate of how much the fund will move if its benchmark moves by 1 unit. This shows the fund’s sensitivity to changes in the market. Beta investment strategies tend to favor asset allocation models to achieve out performance.  R-squared is a measure of the association between a fund and it’s benchmark. Values are between 0 and 1. 1 indicates a perfect correlation and 0 indicates no correlation. This measure is useful in determining if the fund manager is adding value in their investment choices or acting as a closet tracker mirroring the market and making little difference.  Standard deviation is a measure of volatility of the fund’s performance over a period of time; the higher the figure the greater the variability of the funds performance. High volatility is an indicator of increased investment risk in a fund.

A large Fund of funds has so much capital to put to work, efficacy becomes the defining bottle neck. In other words at some point of capital placement each incremental new placement does not improve the overall return and in a lot of cases diminishes the returns. Fund to funds conduct large complicated, recursive algorithms on each placement, and each position in each placement, to look at the alpha or beta of the scenario.

It may be interesting to model the Fund to Funds world as a network and determine if it is a well structured network or not. This may lead to less computationally intense ways to find capital placement opportunities and improve the efficacy of large funds.