Papers by Andrei Soklakov
Physical Review A, Sep 15, 2006
We investigate the problem of Bayesian updating of a probability distribution encoded in the quan... more We investigate the problem of Bayesian updating of a probability distribution encoded in the quantum state of n qubits. The updating procedure takes the form of a quantum algorithm that prepares the quantum register in the state representing the posterior distribution. Depending on how the prior distribution is given, we describe two implementations, one probabilistic and one deterministic, of such an algorithm in the standard model of a quantum computer.
Physical Review A, Mar 13, 2003
A common experimental setup in cavity quantum electrodynamics (QED) consists of a single twolevel... more A common experimental setup in cavity quantum electrodynamics (QED) consists of a single twolevel atom interacting with a single mode of the electromagnetic field inside an optical cavity. The cavity is externally driven and the output is continuously monitored via homodyne measurements. We derive formulas for the optimal rates at which these measurements provide information about (i) the quantum state of the system composed of atom and electromagnetic field, and (ii) the coupling strength between atom and field. We find that the two information rates are anticorrelated.
arXiv (Cornell University), Sep 7, 2000
We introduce the principle of Occam's Razor in a form which can be used as a basis for economical... more We introduce the principle of Occam's Razor in a form which can be used as a basis for economical formulations of physics. This allows us to explain the general structure of the Lagrangian for a composite physical system, as well as some other artificial postulates behind the variational formulations of physical laws. As an example, we derive Hamilton's principle of stationary action together with the Lagrangians for the cases of Newtonian mechanics, relativistic mechanics and a relativistic particle in an external gravitational field.
The European Symposium on Artificial Neural Networks, 2005
There has recently been numerous applications of kernel methods in the field of bioinformatics. I... more There has recently been numerous applications of kernel methods in the field of bioinformatics. In particular, the problem of protein homology has served as a benchmark for the performance of many new kernels which operate directly on strings (such as amino-acid sequences). Several new kernels have been developed and successfully applied to this type of data, including spectrum, string, mismatch, and profile kernels. In this paper we introduce a general probabilistic framework for stringtype kernels which uses the fisher-kernel approach and includes spectrum, mismatch and profile kernels, among others, as special cases. The use of a probabilistic model however provides additional flexibility both in definition and for the re-weighting of features through feature selection methods, prior knowledge or semi-supervised approaches which use data repositories such as BLAST. We give details of the framework, place wellknown kernels in the framework and give preliminary experimental results which show some effects of using the probabilistic approach. * The first and third author thank the EPSRC for their support through grant no GR/S22301/01 ("Development and Application of String-Type Kernels")
Physical Review A, Jan 9, 2006
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum com... more We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably bounded amplitudes, the algorithm requires resources that are polynomial in the number of qubits. Such sequences of states occur naturally in the problem of encoding a classical probability distribution in a quantum register.
arXiv (Cornell University), Apr 28, 2013
Quantitative structuring is a rigorous framework for the design of financial products. We show ho... more Quantitative structuring is a rigorous framework for the design of financial products. We show how it incorporates traditional investment ideas while supporting a more accurate expression of clients' views. We touch upon adjacent topics regarding the safety of financial derivatives and the role of pricing models in product design.
arXiv (Cornell University), Apr 26, 2001
We consider a typical setup of cavity QED consisting of a two-level atom interacting with a singl... more We consider a typical setup of cavity QED consisting of a two-level atom interacting with a single resonant electromagnetic field mode inside a cavity. The cavity is resonantly driven and the output undergoes continuous homodyne measurements. We derive an analytic expression for the state of the system conditional on a discrete photocount record. This expression takes a particularly simple form if the system is initially in the steady state. As a byproduct, we derive a general formula for the steady state that had been conjectured before in the strong driving limit.
Physical Review A, 2006
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum com... more We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably bounded amplitudes, the algorithm requires resources that are polynomial in the number of qubits. Such sequences of states occur naturally in the problem of encoding a classical probability distribution in a quantum register.
arXiv (Cornell University), Sep 5, 2000
Given a reference computer, Kolmogorov complexity is a well defined function on all binary string... more Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the reference computer. We argue that this approach can be more useful if it is refined to include an important practical case of simple binary strings. Kolmogorov complexity calculus may be developed for this case if we restrict the class of available reference computers. The interesting problem is to define a class of computers which is restricted in a natural way modeling the real-life situation where only a limited class of computers is physically available to us. We give an example of what such a natural restriction might look like mathematically, and show that under such restrictions some error terms, even logarithmic in complexity, can disappear from the standard complexity calculus.
arXiv (Cornell University), Apr 28, 2013
Financial derivatives have often been criticized as casino-style betting instruments. It turns ou... more Financial derivatives have often been criticized as casino-style betting instruments. It turns out that many naive ways of making them are indeed equivalent to gambling. Fortunately, this inadvertent effect can be understood and prevented. We present a theory of product design which achieves that.
arXiv (Cornell University), Jun 15, 2011
The recent crisis and the following flight to simplicity put most derivative businesses around th... more The recent crisis and the following flight to simplicity put most derivative businesses around the world under considerable pressure. We argue that the traditional modeling techniques must be extended to include product design. We propose a quantitative framework for creating products which meet the challenge of being optimal from the investors point of view while remaining relatively simple and transparent. * Date of the original submission to RISK Magazine. and, conversely, how to imply investors beliefs from the payoff structures they use. This gives us tools for tailoring new products as well as checking implicit assumptions behind existing positions. Most people would agree that complex products can be dangerous. What is less obvious is that simple products can also be pretty far from ideal. We find that investment products can be very easily oversimplified to the point when they can no longer reflect any rational view. Paraphrasing the famous observation about physical theories, investments should be made as simple as possible but not simpler. Two fundamental features distinguish investment from speculation: the use of in-depth research and attention to safety. The above caution on oversimplification is related to the ability of products to accommodate results of in-depth research. Thinking about safety, we show how one can use the technology of derivatives to stabilize raw investment strategies. This line of thinking leads us to a class of derivatives which, in terms of their complexity, lie between vanillas and exotics. Consider a random variable representing an observable market parameter: stock price, index value, interest rate, etc. Everything we know about the variable can be summarized using probability distributions. The ability of probability distributions to summarize the knowledge about random variables does not depend on whether this knowledge is factually true or not. This powerful feature of probability-based descriptions left its mark on most modern fields of human knowledge: from foundations of quantum mechanics to artificial intelligence. It is certainly very important for describing the world of finance where both hard data and investors' beliefs have material impact. Interplay between reality and beliefs is at the heart of every investment. We set the stage by introducing distinct concepts of market-implied, investor-believed and actual realized distributions -all of which refer to the same market variable. These distributions play three distinct roles which can be outlined as follows. Market-implied distribution, m(), represents the market view. The reader is almost certainly familiar with deriving such distributions from the relevant market prices. The investor's view is given by the believed distribution, b(). The form of this distribution is entirely up to the investor and we do not make any assumptions regarding b(). Realized distribution, p(), represents the reality that both the market and the investor are trying to predict. In practice, realized distribution can be very difficult to estimate leading to the use of proxies such as realized mean and realized variance. We use m(), b() and p() as auxiliary concepts -as thinking tools -refining the definitions along the way as required. We shall see, however, that these concepts have very real and easily accessible (often visualizable) meaning. In hindsight, it is not surprising to find products which already use the language of distributions in their intuition. Futures and variance swaps, for example, compare the mean and the variance of the market-implied and realized distributions. Exotics, such as barriers, suggest that there might be more to trading distributions than using a few of their leading moments. This is indeed the case. Imagine, for example, that you have strong opinions on both the mean and the variance of some market variable. How would
arXiv (Cornell University), Jul 26, 2015
Quality-designed products are easy to recognize. Wouldn't it be great if the quality of financial... more Quality-designed products are easy to recognize. Wouldn't it be great if the quality of financial products became just as apparent? This paper is addressed to financial practitioners. It provides an informal introduction to Quantitative Structuring -a technology of manufacturing quality financial products. The presentation is arranged in three parts: the main text assumes no prior knowledge of the topic; important detailed discussions are arranged as a set of appendices; finally, a list of references provides further details including applications beyond product design: from model risk to economics.
Physical Review A, Dec 5, 2001
We consider a typical setup of cavity QED consisting of a two-level atom interacting strongly wit... more We consider a typical setup of cavity QED consisting of a two-level atom interacting strongly with a single resonant electromagnetic field mode inside a cavity. The cavity is resonantly driven and the output undergoes continuous homodyne measurements. We derive an explicit expression for the state of the system conditional on a discrete photocount record. This expression takes a particularly simple form if the system is initially in the steady state. As a byproduct, we derive a general formula for the steady state that had been conjectured before in the strong driving limit.
and linear entropy increase in the quantum baker’s map
Feedback and Information Gain in Single Atom
Conversion of Mathematical Statements
Physical Review D, 2006
We investigate how classical predictability of the coarse-grained evolution of the quantum baker'... more We investigate how classical predictability of the coarse-grained evolution of the quantum baker's map depends on the character of the coarse-graining. Our analysis extends earlier work by Brun and Hartle [Phys. Rev. D 60, 123503 (1999)] to the case of a chaotic map. To quantify predictability, we compare the rate of entropy increase for a family of coarse-grainings in the decoherent histories formalism. We find that the rate of entropy increase is dominated by the number of scales characterising the coarse-graining.
Physical Review A, 2003
A common experimental setup in cavity quantum electrodynamics (QED) consists of a single twolevel... more A common experimental setup in cavity quantum electrodynamics (QED) consists of a single twolevel atom interacting with a single mode of the electromagnetic field inside an optical cavity. The cavity is externally driven and the output is continuously monitored via homodyne measurements. We derive formulas for the optimal rates at which these measurements provide information about (i) the quantum state of the system composed of atom and electromagnetic field, and (ii) the coupling strength between atom and field. We find that the two information rates are anticorrelated.
Physical Review A, 2001
We consider a typical setup of cavity QED consisting of a two-level atom interacting strongly wit... more We consider a typical setup of cavity QED consisting of a two-level atom interacting strongly with a single resonant electromagnetic field mode inside a cavity. The cavity is resonantly driven and the output undergoes continuous homodyne measurements. We derive an explicit expression for the state of the system conditional on a discrete photocount record. This expression takes a particularly simple form if the system is initially in the steady state. As a byproduct, we derive a general formula for the steady state that had been conjectured before in the strong driving limit.
Physical Review A, 2006
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum com... more We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably bounded amplitudes, the algorithm requires resources that are polynomial in the number of qubits. Such sequences of states occur naturally in the problem of encoding a classical probability distribution in a quantum register.
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Papers by Andrei Soklakov