Mystic's Physics

Updated: Aug 26, 2019

Authored by Alastair Poole


Here be Dragons

During the medieval period, the world was uncertain and unexplored; whispers of knowledgeable women mistaken for magical, or a cheeky cartographer sketching dragons in the recesses of a map sent people puzzling furiously over an imagined threat.

It is difficult to think that even the mighty Genghis Khan so grounded in the world of his making was taken in by conjurors visiting court, how he felt panic at simple magic-circle material- but how in others it ignited the spark of inquisitive adventure.



More recently we have had our fair share of fantastic tales and their respective monsters; keeping wraith-like weapons of quantum destruction chained to our will, escaping the end of the universe via black hole, and dealing with a redefining of what it means to merely have mass- not easy news to take before breakfast.


While we ourselves are shadowed by the quantum leviathan, are our worlds really so distant?


Taking Maxwell’s Hammer to Thermodynamics

Maxwell’s demon was originally a thought experiment by James Clerk Maxwell of electromagnetic fame, where a mixed-energy gas is observed by an intelligent demon that filters particles of different energies into separate containers, extracting work from a system to a degree not allowed by the second law of thermodynamics- quite problematic for the field of thermal physics.


This facet of the demon was explained in 1961 by Rolf Landauer with the Landauer principle describing the entry of external energy sources and conversion into an increase in order within the gas.


In its purest form, Landauer’s principle may be more remarkable; since the second law of thermodynamics is not a prerequisite, the latter may be a consequence of the former[1].


Feeling the quantum creep, this year an international research team including Dr Janet Anders based at Exeter university heralded a way to bring Maxwell’s demon to life.


Trapping ions, particles with a net electric charge, within a magnetic saddle-potential oscillating six million times per second scientists can then expose them to carefully controlled light beams, simultaneously to stop excitations of the ion from its lowest energy state through induced energy emission, and to superimpose the ion’s states, states that then acts as the memory of the demon[2].


Rotating magnetic-potential trap ions similarly to how rotating saddles can trap balls- as long as the ball doesn't hit an edge! Source: published on youtube, Video Credit: Harvard NatSci Demonstrations dep.


As the machine measures the energy of the gas particles, it stores information about the particle, information then destroyed to maintain Landauer’s principle.

Almost uniquely this offers us a deep view into the relation between energy and order.


Riding the Quantum Demon

While a long way off, the positive difference such an application would make is monumental; super efficient fridges and ovens, potentiating a future of effective quantum containers and computers, and this isn’t the first case of quantum oddness competing with classical normality in our day to day lives.


The pioneers of application is undoubtably google labs, seeking to breed a host of quantum chimera from the inert mathematics. Powered by this behemoth, Quantum computers have been shown to vastly outrank classical computers in modelling quantum phenomena like spin glass and now fermions, representing complex networks, and less abstractly in answering discrete optimisation problems such as finding the fastest way home from a night out.


From a company that has revolutionised our understanding of linguistic networks and developed evolving algorithms designed to optimise themselves, the speed, scope and depth of quantum infiltration seem even less certain. 


One such upcoming effect of quantum computing will be the potential destruction, and the restoration of online security.


For almost 40 years internet security has been backed by Public Key Cryptography[3], a standardised method encoding information with a published list of functions and ‘public keys’ open for anyone to securely transmit data over the internet. This system operates on a recipe of complex functions, called ‘trap door functions’; and the vastness of the public key, a composite number of two very large primes that give clues as to Bob and Alice’s private key, allowing them to read all of your online information.


By harnessing the ability for particles to be in many states simultaneously, quantum computers can calculate factorisations in a fraction of the time to a high degree of certainty by completing a series of unitary (reversible) transformations on those states before a measurement ascertains the answer.


Increased efficiency in prime decomposition means that, when viable, quantum computers will take an axe to the trap door.


Faust's Order

Two prongs in quantum computing's trident are hidden in the algebra; by firstly placing the answers at the hindmost, and secondly as a shift in the algebra we use that allows it to generalise from simple yes no states presented by classical Turing machines, to an infinite shade of maybe.


Classical computing is predicated on finding the yes, no answer to problems by a series of reversible steps. You are presented with an engine complemented by a finite list of internal states, command and inputs. The programmer breaks down a question into a set of more fine truth statements. 


This method works by changing the output of the Turing machine by analyzing the truth states of the input with respect to the internal state, a concept tied to Boolean logic and distilling computations into a series of fundamental questions that form a full and truthful answer.


Contrastingly, quantum algorithms operate on the same level as the matrix-Heisenberg (C*) algebra of quantum mechanics more generally. This means that instead of a series of open and shut gates, inputs and outputs are represented by a particle's overlapping of yes and no, and can be tied together through entanglement, a handy quirk of matrix mechanics of unitary operators, to represent more complex systems.


In other words, while the basic aim of Quantum computing remains the same as Classical, because of its matrix algebra quantum computers can represent vastly more complex systems and equations, allowing quanta to interact with each other in a controlled setting to formulate an answer that tends to be right.


Tending to an answer, though not wholly satisfatory, is excusible given the relative speed up in algorithms when switching from the classic to the quantum and is enough to make quantum error detection a very lucrative field.


The different algebraic structure is more powerful yet; on classical machines we are able to read off the truth values of the input directly, as they appear on the output. In quantum computing, to read the values off every time an operation was done to the state, we would have to collapse the wavefunction time and again, losing all its peculiar properties that make these computations work, and we would have no proper answers. This is solved again by a quirk of what measurement is to a quantum system, which is restricting the possible space of answers. If you were to require a measurement and then complete an operation, by reordering the two you let the restricted space of answers evolve with the operation, and then refine the state to the originally desired one.


Quantum computing takes advantage of uncertainty in the system, and in speeding up computations it sacrifices our knowledge of the system, revealed later by the devil who has taken the hindmost.

Devils Advocate

Studying most legends and fairy tales, you often find the villain has an excuse; the pied piper was wronged by the beleaguered townsfolk, and even in the Grimm edition of Hansel and Gretel the witch was suffering a famine

The principle of quantum teleportation may be the excuse to its effect on our security.

Hidden deep within textbooks, found among the matrices is the no-cloning principle. This states that you cannot make an identical copy of a quantum particle without measuring it, which would collapse the wave function and so any mixed state, and the information it carried, is lost. Simply put, if someone wishes to open your mail they will destroy the message by opening it, opening up a realm of possibility in uncrackable communication. Before even now quantum mechanics has shown both of its two-faces. Science of decay and radiation used to terminate at Hiroshima and Nagasaki is now used to kill tumours.


Even quantum tunnelling, a phenomena that limits the size of classic circuits by redefining what is an unsurpassable barrier facilitates touch screen technology today.


Much like the witch at the corner of a village, quantum tech can bring many boons, or be a mighty enemy.


A fuzzy feeling

It seems Quantum tentacles appear to envelope us in light shadows of upcoming technology, and also reveal fantastic opportunities in health, communication. These stretch to background tasks that would make life incomparably easier, if the trend is true, by first making it harder.

Like twelfth century squires, sitting around the campfire wondering at the stories of knights who fought off dragons, we day-dream of how the quantum beast can lift us soaring above the clouds or drag us into regression.


But it is by the work of researchers and professors touched by curiosity, departments like Durham Maths spearheading quantum computing education, that allow us to root out the map’s corners, and happily bring uncertainty to our lives.


References;

[1] An improved Landauer principle with finite-size corrections, David Reeb and Michael Wolf, published Oct. 2014 in New Journal of Physics, Vol. 16. DOI: https://doi.org/10.1088/1367-2630/16/10/103011, License (creative commons)

[2] Introduction to Ion Trap Quantum Computing, Andrew Steane, (date of origin unknown) as part of Oxford University Ion Trap Quantum Computing Group. https://www2.physics.ox.ac.uk/research/ion-trap-quantum-computing-group/intro-to-ion-trap-qc#- for educational purposes only.

[3] Cryptography/A Basic Public Key Example, Wikibooks Contributors, last updated 31/08/2017 on Wikibooks, the Free Textbook Project. https://en.wikibooks.org/w/index.php?title=Cryptography/A_Basic_Public_Key_Example&oldid=3287989 License.

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