by Majvell Kay G. Odarve

A quantum computer is device for computation that uses the phenomena of quantum mechanics to perform operations on data. Because of the quantum mechanical phenomena, such as entanglement and superposition of states, quantum computers have great offers in the field of computations and data handling. The distinctive feature of a quantum computer lies on its ability to store and process superposition of numbers.  This potential for parallel computing points out that some problems can be efficiently solved using quantum computers compared to the classical one. Shor’s algorithm, for example, which solves the problem that ‘Given an integer N, find its prime factors’, shows that quantum computer should be able to efficiently factor large numbers. The field appears to be of great interest since most data encryption schemes (in cryptography-science of information security) relies on the inability of the classical computers to factor large numbers.

To have an experimental realization of a quantum computer, there is a requirement of an isolated quantum system which will act as qubits and the presence of controlled unitary interactions between the qubits that allow construction of a controlled-NOT (CN) quantum logic gate. Quantum logic gates are building blocks of quantum circuits which operate on small numbers of quantum bits (qubits).  Quantum logic gates, unlike the classical logic gates, are reversible.  A CN quantum logic gate is one of the commonly used logic gates which operate on two qubits (we label the qubits as and ).   The CN gate transforms the state of the two qubits from to where is an addition modulo 2. The CN gate represents a computation at the most fundamental level, that is, a certain ‘target’ qubit is flipped depending on the state of a ‘control’ qubit .

Christopher Monroe and his team from National Institute of Standards and Technology (NIST) Laboratory in Boulder, Colorado, who are working on ion-trapped quantum computers, have been able to demonstrate the operation of a two-bit controlled-NOT quantum logic gate operating on prepared quantum states.  In their experiment, the two qubits comprise two internal (hyperfine) states and two external (quantized motional harmonic oscillator) states of a single trapped atom using a single beryllium ion (Be⁺). The trapped ions are first laser cooled to zero-point energy for them to stay in the ground state.   In the trapped-ion architecture, the qubits are associated with the internal states of the ions and information is transferred between the qubits through a shared motional degree of freedom. With this configuration, decoherence can be small so it will be easier to extend the idea to large registers and the qubit readout will have a nearly unit efficiency.

To realize the CN gate, three sequential pulses of the Raman beams is applied to the ion, namely the π/2 pulse applied to the carrier transition, a 2π pulse applied on the blue side band transition and a π/2 pulse applied to the carrier transition with a π phase shift relative to the first pulse. The truth table for a CN gate operation is given as:

Input State            Output State

In their experiment, the key features of the CN gate was demonstrated by verifying that the populations of the register follow the truth table and by demonstrating the conditional quantum dynamics associated with the CN operation. On the results of the experiments of Monroe, et. al., decoherence were still present. The decoherence were caused by instabilities of the laser beam power, the position of the ions relative to the laser beams, the fluctuation of external magnetic fields, instabilities in the trap drive frequency and voltage amplitude, dissipation of the ion motion and some spontaneous emission caused by off-resonant transitions. The single ion quantum register in the experiment comprises only two qubit which is not useful for computations. The next step of the researchers then is to apply their operation techniques to many ions cooled at a state of collective motion for the possibility of implementing computations on larger quantum registers.

Reference:

1. C. Monroe, D.M. Meekhof, B.E. King, W.M. Itano, and D.J. Wineland, Physical Review Letters, Vol. 75, Num. 25, December 1995.

Patrick Alvin M. Alcantara

Einstein maintained that quantum mechanics entails “spooky actions at a distance” (the interaction of two objects which are separated in space with no known mediator of the interaction); experiments have now shown that what bothered Einstein is not a debatable point but the observed behavior of the real world. He called this “spooky action at a distance” because he didn’t know about decoherence, so it seemed spooky to him.

In May 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published the EPR Paper, an argument that quantum mechanics fails to provide a complete description of physical reality. The theoretical and experimental work it inspired remain remarkable for the vivid illustration they provide of one of the most bizarre aspects of the world revealed to us by the quantum theory. Their work describes a situation ingeniously to force the quantum theory into asserting that properties in space-time region B are the result of an act of measurement in another region A; so far from B that there is no possibility of the measurement in A exerting an influence on region B by any known dynamical mechanism. Under these conditions, Einstein maintained that the properties in A must have existed all along. The fundamental result that they were trying to show in their paper was not that quantum mechanics is wrong. They did, in fact, acknowledge that quantum mechanics could be used to make highly accurate statistical predictions about experiments. They were interested mainly in what the fundamental properties of reality are.

Their paper involves a paradox — a thought experiment which challenged long-held ideas about the relation between the observed values of physical quantities and the values that can be accounted for by a physical theory. According to its authors the EPR experiment yields a dichotomy. Either:

1. The result of a measurement performed on one part A of a quantum system has a non-local effect on the physical reality of another distant part B, in the sense that quantum mechanics can predict outcomes of some measurements carried out at B.
2. Quantum mechanics is incomplete in the sense that some element of physical reality corresponding to B cannot be accounted for by quantum mechanics (that is, some extra variable is needed to account for it).

An enormous set of data, generated out from the apparatus used in the said experiment, by many, many runs. Thus, as Einstein partly said on his letter to Max Born: “…I am therefore inclined to believe that the description of quantum mechanics…has to be regarded as an incomplete and indirect description of reality…”

Hananish Joy G. Odarve

Paul Adrien Maurice Dirac was born on 8th August, 1902, at Bristol, England. He was educated at the Merchant Venturer’s Secondary School, Bristol, and then went on to Bristol University where he studied and obtained B.Sc. in Electrical Engineering degree. He also studied mathematics for two years at Bristol University, later going on to St. John’s College, Cambridge, as a research student in mathematics. He received his Ph.D. degree in 1926. He became a Fellow of St. John’s College and also held the position Lucasian Professor of Mathematics at Cambridge. Dirac was given The Nobel Prize in Physics 1933 together with Erwin Schrödinger for their discovery of new productive forms of atomic theory. He then gave a lecture regarding matter and antimatter specifically on electrons and protons on the Nobel Lecture he delivered on December 12, 1933.

In his lecture, Dirac emphasizes that the procedure he came up with is successful in the case of electrons and positrons and that he hoped that in the future some such procedure will be found for the case of the other particles. He considered the electron and positron because in their case, the theory has been developed further. He outline the method for electrons and positrons, showing how one can deduce the spin properties of the electron, and then how one can infer the existence of positrons with similar spin properties and with the possibility of being annihilated in collisions with electrons.

The general quantum mechanics at Dirac’s time describe the motion of any kind of particle, no matter what their properties are. However, it is only valid when the particles have small velocities and fail when the effect of relativity comes in. Basically, Dirac started with an equation connecting the kinetic energy and momentum and let this act on a wave function since we can view and as operators. The equation is not linear in the kinetic energy and momentum. Now, according to the general requirement of quantum mechanics, the wave equation should be linear in the operator and in order that the equation may have relativistic invariance, it must also be linear in . Thus, new variables where introduced which give rise to the spin of the electron and give rise to some rather unexpected phenomena concerning the motion of the electron. In practice, the kinetic energy of a particle is always positive however the equation allows two kinds of motion. Only one motion is familiar. The other corresponds to electrons with a very peculiar motion. The faster they move, the less energy they have, and one must put energy into them to bring them to rest called the positron which corresponds to the motion of an electron with a positive charge instead of the usual negative one. We can then look at the process of annihilation where an ordinary electron, with positive energy, drops into a hole, fill up this hole and electromagnetic radiation is liberated. On the other hand, creation of an electron and a positron from electromagnetic radiation should also be observed.

Also, he added that if we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of Nature, we can also get negative protons. However, the process will be more rigorous since protons are more complicated and the theory would require reliable basis which was not yet discovered at that time.

Liza Marie T. Dangkulos

This article contains a summary of Max Born’s Nobel lecture entitled, “The statistical interpretation of quantum mechanics”.

In 1926, shortly after the formulation of the Schrodinger’s equation, Max Born studied the scattering of a beam of electrons and was led to his interpretation of the wave function in the said equation.

Born’s statistical interpretation states that:
The probability of finding an electron, described by the wave function, Ψ (x,t), in the region lying between x and x+dx is given by:

where

is the complex square or Ψ*Ψ[1]

He, therefore, introduced the statistical point of view into modern physics.[2] For this invaluable contribution in the field of quantum mechanics, Born was awarded the Nobel Prize in Physics in 1954.

During his Nobel lecture, Born accounted the developments in the field of quantum mechanics that led him to his statistical interpretation. He mentioned that in 1925, he and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. Wolfgang Pauli consequently calculated the stationary energy values of hydrogen atom by means of the matrix method and from this moment onwards, there could no longer be any doubt about the correctness of the theory.

In 1926, Louis de Broglie formulated the de Broglie hypothesis claiming that all matter, has a wave-like nature. He related wavelength (denoted by λ) and momentum (denoted by p) as:

λ=h/p

where h is the Planck’s constant

Schrodinger, following de Broglie’s wave-particle duality theory of matter, constructed his famous equation that describes how the quantum state of a physical system changes in time. This equation can be mathematically transformed into matrix mechanics.

Not long after, Born developed his statistical interpretation. Not only was it developed from Schrodinger’s equation but from Einstein’s idea as well. Einstein interpreted the square of the optical wave amplitudes as the probability density for the occurrence of photons. For Born, this concept could be carried over to the Ψ-function.  Ψ*Ψ represents the probability density for electrons.

Furthermore, Born also emphasized that the indeterministic statistical interpretation should be accepted despite the strong oppositions of some respected physicists like Erwin Schrodinger, Louis de Broglie and Albert Einstein. He believed that Heisenberg’s uncertainty principle contributed to the swift acceptance of the statistical interpretation of the Ψ-function.

Uncertainty principle states that certain pairs of physical properties cannot both be known to arbitrary precision. Its meaning, according to Heisenberg, is that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle with any great degree of accuracy. With this, Born had this to say, “Can absolute prediction really be made for all the time on the basis of the classical equations of motion?”

Towards the end of his lecture, Born made these two statements: “Classical physics cannot be used as an objection to the essentially indeterministic statistical interpretation of quantum mechanics” and that “I am emphatically in favour of the retention of the particle idea.”[3]

Through his statistical interpretation, Max Born showed that the solution of the Schrodinger equation has a physical significance.

[1] Stephen Gasiorowics. Quantum Physics, 3rd ed. (John Wiley and Sons, Inc., 2003) p. 28.
[2] Walter Greiner. Quantum Mechanics: An Introduction, 4th ed. (Springer-Verlag, Berlin) p.65
[3] Max Born. The Statistical Interpretation of Quantum Mechanics. Nobel Lecture, 1954.

John Paul J. Aseniero

Computers today are now fundamental part of people’s lives. It is used in a lot of applications such as in business, communication, security systems, sciences and etc. Developing fast classical computer has come to its fundamental limitation and aiming this type of computer would rely on making the device smaller to make chips’ transistor switch faster. However, when they begin to approach 10 nanometers, electrons will start revealing their quantum nature and very strange things will happen. When transistors reach those infinitesimal dimensions and electrons start showing their true colors, this will be the start of vast new frontiers for computing which is based on quantum computers.

Finding something to act as quantum bit or qubit whose quantum state can be read and manipulated is the first thing to remember in building a quantum computer. However, quantum state is a frail thing for it can easily be changed by just a fluctuation of magnetic field or a strong-willed photon interaction. By then, two physicists from Austria’s University of Innsbruck, Juan Ignacio Cirac and Peter Zoller, theorized that a string of ions held fast in a vacuum by an electromagnetic field and cooled to within a few thousandths of a degree above absolute zero could act as stable qubits and form the basis of a quantum computer. There are also research group in NIST that had lot of experience in trapping and cooling ions from their work of atomic clock and one example of their work is trapping beryllium ion as qubit to perform logic operations which is the main key in running a quantum computer.

Even before, physicists have come up with at least half a dozen ways to do quantum computation. This includes using atomic nuclei in organic compounds as qubits and manipulating electrons within superconducting loop. However, it’s hard to handle more than a dozen of qubits which will never lead to an efficient quantum computer that requires hundreds if not thousands. It’s hard to create a full scale ion trap big enough to accommodate that many qubits. Therefore, the only way to build quantum computer is to build the equivalent of quantum integrated circuits. Trap technique is the best way to create these quantum transistors that work the same way like to shrink them down enough and put many of them of the same piece of semiconductor.

Quantum computers could one day replace silicon chips, just like the transistor once replaced the vacuum tube. But for now, the technology required to develop such a quantum computer is beyond our reach. Most research in quantum computing is still very theoretical. There is difficulty in some aspect of building this quantum computer because an equivalent of very large scale integration would require handling the control circuitry just to move the ions around. Five thousand ions would need many dozens of lasers for cooling, detection, and gate operations which should be precisely controlled in coordination with the ions’ motion in the trap. Therefore, this needs a great deal of infrastructure, including a powerful classical computer, to run a useful quantum computer. The most advanced quantum computers have not gone beyond manipulating more than 16 qubits, meaning that they are a far cry from practical application. However, the potential remains that quantum computers one day could perform, quickly and easily, calculations that are incredibly time-consuming on conventional computers. But there is still hope since scientists are running today and plan to run in the near future will almost certainly lead to insights that could make full-scale quantum computing.