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4. Quantum Background: In a nutshell
Introduction:
Learning quantum science concepts is meant to be intuitive. There's been several books published now trying to make it more accessible for this exact reason with works such as Quantum Computing for Babies, Quantum Computing for Everyone, and even Quantum Computing for Dogs. We've been societally educated on a paradigm for so long that learning another one takes approaching this training from a completely blank slate, which is often why digital or conventional computation is referred to as “classical” computation similar to being in a classical age. Now that the technology is advancing, it is indicative of an era that intuitively welcomes a new population of those well-immersed in rather natural quantum-informed concepts and requires, in some ways, to let go of what one was taught from before.
While the in-depth full education on quantum mechanics & quantum computer science is outside the scope of this paper, a brief background is necessary in order to move forward into development and understanding the powerful use-cases! The essential fundamentals in quantum mechanics which are then applied to quantum computers must first be understood to begin. This will further prepare learners in order to understand and implement the goals discussed in the introduction.While having those fully versed in a complete quantum mechanics/mathematics/computer science PhD level is certainly important and necessary on a quantum application team as a subject matter expert, this does not help anyone in gaining a standard understanding of what is happening behind the scenes. A universal essential summary of concepts is much more necessary for the entire team, and that is exactly within the scope of this paper.
Having this as a reference or guide is important as it meets one of the largest problems the industry currently has -- the lack of interdisciplinary collaboration in attempting to understand essential concepts in the quantum technology field. The purpose of this paper is to attempt for furthering collective quantum development rather than the rapid development by a few (and puts less pressure on those PhDs too to bear the burden to collaborate, develop, as well as to constantly re-explain! ). Although each of these concepts can have entire books of their own, a quick overview is all that's needed and if you're curious you can dig deeper to understand more when the case comes up.
Central quantum mechanics concepts:
Hilbert space: This is the set of mathematical space that a quantum computer typically computes upon.
A value in this space is multidimensional, allowing for more information to be returned (in contrast to the space we classically compute upon, which is in Euclidean or cartesian space ie, [x] or [y]). This goes outside of the realm of what we have classically computed upon since it can take a value that has more than one dimension for examples [x1,x2, x3….] all as one value or [y1, y2, y3,...]. So a single input going into this space would typically be a matrix, or a set of multiple values.
Entanglement: the quantum mechanical property stating that when particles or objects are generated or share spatial proximity with each other, the quantum state of the objects cannot be described independently of each other, no matter how far the distance.
Objects will share some common information between each other when entangled and so entanglement is a key feature incorporated into quantum computers. This is not the case in classical technology, which relied on Newtonian physics and seeks to compute upon separate entities and separate properties without assuming entanglement. Yet in the real world, particles are naturally entangled. Quantum computers generate quantum objects assuming that entanglement of the system will take place, and it is the information extracted from this entanglement that we are trying to compute.
Measurement: an active process that alters the system being measured.
More specifically, any measurement of an object’s properties results in an irreversible wave function collapse of that object and changes the original quantum state (and affects the quantum system as a whole). This is where Schrodinger’s cat analogy comes into play! A cat exhibits the states of both dead and alive in the property of Life. Yet when you look at the cat to measure for this property, what results is the irreversible wave function collapse resulting in one answer.
Superposition: Any two or more quantum states added together will result in another valid quantum state.
We can often observe superpositions with photons or flashlights as a simple example, as one beam on top of another beam which will result in a different type of light beam that we observe to not be the original two beams which we can then perform measurement on, despite the new beam actually being a result from the existence of both beams flashing at the same time. With quantum computers, superposition is a fundamental operation which preserves the wave function collapse of the entangled objects that we pass through. .
Decoherence: the instability of a quantum state
As Heisenberg’s uncertainty principle holds, this explains that any quantum measurement that is attempted will not be stable for long due to interference & further entangled communication from external factors. This is why quantum computations have to be processed in very isolated environments for best results, as they are very sensitive to all interacting objects surrounding them, also known as quantum noise.
Error correction: An operation necessary in real-time quantum computers to fine-tune the output state.
This is done in order to protect quantum information from errors due to decoherence and other quantum noise. This is a necessary step following superposition so that the desired output from the quantum system does not decohere. There are both hardware designs and software-incorporated approaches to take that allow for efficient error correction on a quantum computation.