Quantum Computing – Computers with Quantum Mechanics

Although quantum computing is a relatively new field of study, it has the potential to revolutionize humanity’s relationship with information, just as classical computers did in the last century. This revolution is still a long way off. As Richard Feynman first observed, “if you want to make a simulation of nature, you’d better make it quantum mechanical.” This highlights the fact that in order to effectively understand and simulate the behavior of the universe, a quantum mechanical device would be best. With the ever-increasing role of computers in society, quantum computing is its logical and perhaps most powerful evolution. Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is a theory which, at its core, is very different from classical mechanics, yet it provides very accurate predictions for a staggeringly diverse range of phenomena. Because much of this phenomena, given time, can be modeled by a quantum computer, quantum mechanics is an invaluable resource for the future of computing. By harnessing the distinct laws of quantum mechanics to build a computer, quantum computing is able to solve certain problems in significantly less time than classical computing.

1. Current Applications of Quantum Computing and Limitations

High expectations of quantum computing are associated with the development of quantum algorithms for optimization problems. The most famous example of a quantum optimization algorithm is the adiabatic algorithm; a direct quantum analogue of simulated annealing. A promising result was the quantum adiabatic factorization algorithm (QAFA) which, using 4 qubits, was able to outperform the best-known classical algorithms for a particularly hard integer factorization problem. Along similar lines, quantum algorithms have been developed for search problems which can quadratically outperform the best-known classical algorithms. These results bode well for the future of quantum optimization; however, the Holy Grail is developing a fault-tolerant quantum algorithm for the optimization of any NP complete problem. While quantum computing has shown great potential for simulating quantum systems, the same cannot be said of implementing quantum error correction. The efficacy of quantum error correction is highly dependent on the existence of a large number of physical qubits which behave akin to idealized logical qubits. At present, quantum error correction is largely unfeasible in a system of less than several hundred qubits due to the high probability of erroneous physical operations.

Quantum computing has greatly evolved in the past few years, generating a heightened interest from a wide variety of technological sectors as well as growing interest from the academic space. In particular, it is the application of quantum simulation which has garnered a lot of attention. Quantum simulators are designed to understand how interacting quantum systems behave, as classical computers cannot effectively model them. An example of this was demonstrated by a group of scientists, where they implemented a quantum simulator using 4 superconducting qubits to mimic the energy bands of an H2 molecule. By mapping the quantum wave function of the molecule to the ground states of the qubits, they were able to simulate the electronic state of the H2 molecule and find its energy using the variational method. This is highly significant as understanding molecules on a quantum level can lead to discovering more efficient syntheses of rare earth materials or more efficient drugs. In addition to this, quantum simulation has far-reaching consequences in the field of condensed matter physics and materials science, where highly entangled quantum systems can often behave in ways which are counterintuitive and unfeasible to simulate classically. A quantum simulator could be designed to shed light on these behaviors and substantially increase our knowledge of the subject. These are relatively small-scale examples, but the dream of simulating complex quantum systems has a wide array of applications which at present we can only imagine.

2. Advancements and Potential Impacts of Quantum Computing

The second part of the Article, “Advancements and Potential Impact,” is a comprehensive report about advancements that have been made in the field of QC, and possible future impacts of these advancements. This Article compares the evolution of classical computers to that of quantum computers. Looking at the time it took for classical computers to progress from their initial conception to their present state, it is assumed that it will be several decades before quantum computers are developed. This may not be the case, however, as due to rapidly advancing technology, the time between discovery and implementation of new technology has steadily decreased. An example given is of the classical electromechanical computer, and how it was quickly replaced by the vacuum-tube computer. This then paved the way for the much faster transistor computer. If further advancements and refinements to quantum computers can quickly replace the previous model, we may see an exponential growth in the speed of development. Comparing the size and speed of these computers, it is likely that future quantum computers will be many times faster and smaller than those of today. As of now, the largest quantum computers are composed of only a few dozen qubits and are often prone to errors. As future research designs better algorithms and methods of error correction, computers will become both faster and more reliable. A study (cited in the National Academy of Sciences) compared the processing speed of a quantum simulation to that of a classical supercomputer. Although the simulation was slow and the quantum computer used for it was large, it showed that the algorithm used was more efficient. The study extrapolated from this and estimated that with further development, a similar simulation could be run on a computer with only a few thousand qubits that would vastly surpass the speed of any available supercomputer.

3. Challenges and Ethical Considerations

The magnitude of the difficulty in building a large scale quantum computer can’t be overstated. Mustering a broad coalition of scientists and engineers from different disciplines, government policymakers and industrial support to work on the fundamental issues now and into the next century may be the biggest long term challenge. In the nearer term, industry support of 10-15 years is necessary to develop the low level implementation of a quantum computer. With the increasing pace of life in the developed world, over a 15 year period it’s possible that a government or industrial funding agency may lose the will for a project as speculative as quantum computing and scramble for quick fixes to currently feasible problems. High public expectations about quantum computers can be a double edged sword. Whilst it helps to raise the level of funding and awareness of the field, even a hint that the field is not living up to its promise, or that a quantum computer might fail in some way, could lead to a premature termination of funding. Recently a possible example of this has been seen with NASA’s interest in quantum computing.

To date, the most striking algorithms developed by Shor and Grover have raised the hope that some problems might be vastly more tractable on a quantum computer. Grover’s algorithm, for example, can search an unsorted database of N items in O(square root of N) time, as opposed to the O(N) time of the classical algorithm. Similarly, Shor’s algorithm shows that the prime factorization of an integer N can be solved on a quantum computer in O((log N)^2) time, compared to the best known classical methods which take O(exp((log N)(1/3)(log logN)(2/3))) time using the general number field sieve. Note, however, that these quantum algorithms only give us an asymptotic speed-up. No one knows how hard it will be to build a quantum computer that can execute these algorithms.

Although it is true that quantum computers may be able to solve certain problems much faster than today’s classical computers, don’t believe the hype. Let’s have a look at the main problems.

4. Conclusion and Future Possibilities

Our constant acceleration towards the future will hopefully lead us to answering Leibniz’s question as to “why is there something rather than nothing.” If that something is the existence of our universe, then answering this question consists of finding an explanation for the laws which govern our universe. Richard Feynman in The Character of Physical Law believes that “it is the task of physics to search for general laws of such a kind that the knowledge of them should enable us to predict with exactness the subsequent phenomena.” If we take this as the mission statement for physics, we are still a long way off achieving our goal in the field of quantum physics. By taking into account quantum theory in our quest for understanding, we hope to use the computer to simulate quantum systems and examine their behavior. With understanding the laws of quantum mechanics, it is hoped that we can at last manipulate and control the outcomes of quantum processes. Our ultimate goal is to build a quantum computer which can solve problems about the behavior of nature, problems which are currently impossible to solve with today’s Turing machine-based computers. This venture into the future presents a new dawn for computer science and indeed physics. Weiler believes that quantum computing represents a new branch in the quest for human knowledge. He likens it to the exploration and colonization of new continents by our ancestors with the conquest of the land being equivalent to the discovery of new principles in nature. With the potential to change the day-to-day life of ordinary people, the development of quantum computing will be a journey worth taking.