Quantum Age

Abstract

Current technology is able to produce computers, a powerful tool in creating methods and algorithms to make daily life more convenient. However, technology is only progressing and it is only a matter of time before current common computing becomes a thing of the past. The next milestone of progression to be made, is the achievement of attaining optimized quantum computing. Once quantum computing is established as a stable and reliable tool, the question of how quantum computing could potentially change the world of computer science and its applications arises. This question is vital to the development of quantum computers due to the fear of the unknown capabilities of quantum computers. As quantum computing is still in the very early stages of development, only the very basics of the hardware can be explained. Consequently, there are many theories, hardware functionalities, fundamental algorithms, and other aspects to be explored. After conducting thorough research from recent sources and quantum algorithms dating back to the late 1900’s, this paper will cover and explain how a quantum computer differs from a classical computer, how a quantum computer functions, applications of algorithms in a quantum computer, and theorized future impacts of quantum computers.

Quantum Age

Before computers were invented, all calculations were done by humans. As tools, people would use manual instruments such as an abacus, slide rule, or mathematical tables. However, humans are not always perfect and a lot of errors would reside within their algorithms and problem solving. As a result, many scientists began to create ideas and invent tools that would later build into our modern day computer. Some famous inventors to name would be Gottfried Leibniz, who created the idea of binary numbers, and George Bool with his idea of boolean expressions. The first ever “complete computer” was created by an amazing mathematician, Alan Turing, who invented the Turing machine which utilized a moving central processing unit (CPU) to store information into the machine itself (Bennett et al. 5). These innovators all made it possible for the classical computers in which we heavily rely on today, to be created. Some might be frustrated with the fact that we may be too reliant on machines and computers to do the work for humans, computers are significant tools that were created to make life easier.

Essentially, computers are machines that work with zeroes and ones, a two dimensional concept of coding. However, quantum computers use a multi-dimensional concept of coding; consequently creating vast methods of reaching solutions to a problem. To thoroughly explain, Steane says “[the] significant feature of quantum theory for our purpose is not the precise details of the equations of motion, but the fact that they treat quantum amplitudes, or state vectors in a Hilbert space, rather than classical variables” (7). It is not a linear way of achieving answers like how classical computing would function, but rather analyzes all possible solutions and finds the most optimal or probable solution. With the possibility of finding probable answers or solutions, some major concerns are brought upon cyber security and other applications of quantum computing. Within this paper, the hardware of a quantum computer, how a quantum computer functions, and applications of quantum computing will be examined to answer the question of “how can quantum computing potentially change the world of computer science and its applications?”

Currently, classical computers, which are commonly used today, are built with microscopic transistors, resistors, capacitors, logic gates, and others of the like. As a result, it is physically impossible to create a more effective and efficient computer while maintaining the current size. If scientists were able to pursue this feat, the computer parts would have to be physically smaller than the size of an atom. To explain the functionality of classical computers, the computer’s main component, also referred to as the brains of the computer, is called a central processing unit (CPU). Working with the CPU is another component called an input/output controller (IOC). The CPU retrieves binary instructions from the random access memory (RAM) by interfacing with the IOC, processes the information within the CPU, and further outputs the processed information from the CPU back into its respective location within the RAM (Krylov 6431). Classical computing has a fairly easy flow of processing to understand, whereas quantum computers use multiple complex hardware that functions in a completely different manner than classical computers.

Just like many other innovations, quantum computing started off as a concept. However, modern technology recently acquired the ability and technology to build the hardware of quantum computers. Differing from regular bits of zeroes and ones, quantum computers undergo a unique process via quantum bits, qubits for short, to further process information. With these qubits, it is possible to go through three possible quantum properties: superposition, entanglement, and interference.

Superposition is one of the three quantum properties used in quantum computers. Qubits come into play with superposition by taking the qubits, essentially spinning the polarity of the qubits, and eventually sets the qubit into a zero or one. To further demonstrate, Steffen explains:

When the laws of quantum mechanics apply, the overall state of a qubit may be
written as a linear combination of the states, … the system behaves like a classical
bit. For all other values, the system is in a quantum superposition with no classical
analog. Extending this to multiple qubits, it can be easily shown that an n-qubit
system is described by requiring [ 2^n - 1] complex numbers to describe the full
quantum mechanical system. (2)

In classical computers, a bit can represent to be either false/off or true/on. However, with superposition coming into play, a qubit arbitrarily spins until reaching a superposition of a number between zero and one. While the qubit is “spins,” it is immeasurable for that qubit to be either a zero or one until finally setting after processing an answer.

Entanglement is the next of the three quantum properties. Taking the concept of superposition, qubits still undergo the spinning of polarization. However, the major difference between superposition and entanglement is that entanglement “entangles” two qubits together. While a qubit is paired together, the magnetic field between the two causes the rotating polarization of both qubits. Consequently, Entanglement is a very powerful quantum property. As Steffen claims, “[over] the years, it became clear that it is not quantum superposition itself but rather entanglement that is a necessary ingredient for speeding up quantum algorithms” (2). When pairs of qubits are entangled, depending on the amount of qubits that quantum computer has, the probability effectiveness and success rate increases exponentially. It is heavily examined that entanglement is the key to improving the speed efficiency of computation; thus, entanglement is a key function in discovering the possibilities of quantum computing.

The remaining quantum property that a quantum computer uses is interference. Similar to noise canceling headphones and earbuds, waves that are out of phase with each other will ultimately cancel each-other out. Gisin, a member of a physics group in the University of Geneva, states “[the] two-state protocol can also be implemented using an interference between a macroscopic bright pulse and a dim pulse with less than one photon on average” (9). For interference regarding quantum computers, qubits go into a superposition of many states which will have a phase on each of the states when being used in problem solving. The phases of each superposition state will then continue to amplify each other or cancel each other out, until a probable solution has been reached (Gisin 24).

Being previously analyzed, classical computers use bits that read as either zeros or ones, on or off, or true or false. Due to this, the capabilities in finding solutions to problems is limited to trial and error until solutions are found, even with billions of bits embedded into the hardware (Bova et al. 6). After examining the quantum properties that the quantum computer’s hardware is capable of, we are able to explore the differences between classical and quantum computer’s capabilities. In quantum computers, the amount of qubits correlates with the performance of the computer, just as the amount of bits correlates to a classical computer’s performance and capabilities. For qubits, the amount of pathways and qubits are represented by the formula 2^n. For example, 1 qubit is 2 pathways, 5 qubits would be 32 pathways, and 50 qubits would be 4294967296 capable pathways. The amount of qubits exponentially increases the performance and capabilities; despite this fact, this does not mean that a quantum computer will function at an accelerated pace than a classical computer (Wallden 123). With the pathways of the qubits representing the amount of possibilities in finding the solution to a problem, taking the superposition and entanglement of many qubits will bring light unto more different possible solutions to a program. Consequently, the interference between the superpositioned qubits will cancel out more unlikely answers. As a result of more qubits, the error rate within this process decreases as well.

Error rates are a significant aspect when it comes to computing, which is why classical computers are near perfect in their effectiveness with a near 0% error rate. As previously stated, quantum computers are still in the very early stages of development. Bennett et al., researchers with IBM Research in New York, found that

[the] photomultipliers have quantum efficiency approximately 9%, with dark
count rates of about 200 per second, or about 10 -4 per 500 ns time window.
When using pulses of 0.1 expected photon per pulse, with about 0.05 expected
photon arriving within the 500 ns time window, this dark count rate would yield a
bit error rate around 2%; the actual error rate, about 4%, was due also to imperfect
alignment of the Pockels cells. (13)

There are a lot of variables that could affect the error rate of a quantum computer. Some might argue to add more qubits to create a more accurate quantum computer. However, the achilles heel to this idea is that adding more qubits will add more noise, sound, and vibrations into the vacuums of the hardware, ultimately causing an up-rise in error rates (Perdomo-Ortiz 5).

Although error rates and overall development is still in its early stages, quantum computing experiments have showcased promising applications and possibilities for the future of quantum computing. Applying to businesses, all fields of science, and any instances possible, quantum computers are able to create simulations of these instances to answer questions that classical computing is incapable of solving (Wang 38). With the use of simulation via quantum computing, Egger, an IBM Quantum research scientist, found that “[simulation] focuses on creating scenarios of potential outcomes, such as the impact of volatility on risk, evaluating asset values for pricing, or monitoring economic system impacts in the market” (4). Being able to simulate scenarios connected to real-world scenarios makes quantum computing a very powerful tool. Another way of effectively using quantum simulation is by creating simulations between atoms and chemicals. Not only would scientists be able to discover new probable ways that atoms can interact with each other, but also discover new effects of atoms. Within time, it would be possible to find major probable causes and cures for diseases. Quantum computers hold astonishing potential for technological progression.

As a result of change due to the innovation of quantum computing, there are some people who will be naturally afraid of the quantum computing upbringing. One of the major fears is towards the subject of cyber security. A fundamental algorithm, pertaining to cyber security, is Shor’s Algorithm. To better understand Shor’s Algorithm, Politi explains that “Shor’s quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method a task that lies at the heart of modern information security, particularly on the internet. This algorithm requires a quantum computer a device which harnesses the ‘massive parallelism’ afforded by quantum superposition and entanglement of [qubits]” (1). In other words, Shor’s algorithm is an algorithm that has been mathematically proven being able to solve base factors used in RSA encryption algorithms, given that the quantum computer is powerful enough. In response to the development quantum computing and encryption, Chen et al., officials in the National Institute of Standards and Technology, believe that:

The need for stronger cryptography is driven by advances in both classical and
quantum computing technologies. To maintain security against classical attacks,
NIST has already recommended transitions from key sizes and algorithms that
provide 80 bits of security, to key sizes and algorithms that provide 112 or 128
bits of security [SP 800-131A]. To provide security against quantum attacks,
NIST will have to facilitate a more difficult transition, to new post-quantum
cryptosystems. (6)

However, their theory does not seem to be full-proof against decrypting with a quantum computer. After further development and implementation of qubits, it is highly possible for a quantum computer to utilize Shor’s algorithm in breaking, ideally, all encryptions; therefore, cyber security would be rendered ineffective in the age of quantum computing. While it is possible to break through encryptions, the success of Shor’s Algorithm being used to its full potential is far from being achieved. With that being said, it is too early to determine what quantum computing is capable or incapable of doing.

Technology is advancing at an incredible rate. Within the next few decades, quantum computing may become fully developed and ready to use for programmers, cryptologists, and all other fields of computer science. The sheer potential of quantum computers far surpasses the capabilities of classical computers; however, this does not mean that classical computing will not be used in the event of quantum computers being released. Classical computers are still effective and efficient for everyday use, while quantum computers would be a means for research and discovery. Through the use of superposition, entanglement, and interference, quantum computers are able to simulate a multitude of different instances and find results that classical computers are incapable of doing. Not only programmers and businesses will benefit from quantum computing, but also researchers in all departments of science will benefit for the development of humanity.

Works Cited

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Chen, Lily, et al. Report on post-quantum cryptography. Vol. 12. US Department of Commerce, National Institute of Standards and Technology, 2016.

Egger, Daniel J., et al. “Quantum computing for Finance: state of the art and future prospects.” IEEE Transactions on Quantum Engineering (2020).

Gisin, Nicolas, et al. “Quantum cryptography.” Reviews of modern physics 74.1 (2002): 145. Krylov, Anna I., et al. Quantum Computing and Quantum Information Storage. 11 Mar. 2021, pp. 6341–6343.

Perdomo-Ortiz, Alejandro, et al. “Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers.” Quantum Science and Technology 3.3 (2018): 030502.

Politi, Alberto, Jonathan CF Matthews, and Jeremy L. O’brien. “Shor’s quantum factoring algorithm on a photonic chip.” Science 325.5945 (2009): 1221-1221. Steane, Andrew. “Quantum computing.” Reports on Progress in Physics 61.2 (1998): 117.

Steffen, Matthias, et al. “Quantum computing: An IBM perspective.” IBM Journal of Research and Development 55.5 (2011): 13-1.

Wallden, Petros, and Elham Kashefi. “Cyber security in the quantum era.” Communications of the ACM 62.4 (2019): 120-120.

Wang, Shuangbao, Matthew Rohde, and Amjad Ali. “Quantum cryptography and simulation: Tools and techniques.” Proceedings of the 2020 4th International Conference on Cryptography, Security and Privacy. 2020.