Quantum Perception and Quantum Computation

Abstract

Quantum theory has led to the development of quantum technology and also advances in quantum technology further enhance our understanding of quantum theory. Among these technologies, quantum computing holds special importance as it is based on the quantum states concept, known as qubits or qudits. To advance quantum computation, it is crucial to deepen our understanding of quantum field theory. In this letter, we define quantum understanding as the first step towards this goal. Transitioning from classical to quantum perception is essential, as maintaining a classical viewpoint introduces numerous challenges in building a quantum computer. However, adopting quantum thinking mitigates these difficulties. This letter will first introduce quantum perception by examining the process of classical understanding and how this new approach to thinking transforms our perspective of nature. We will discuss how this shift in thinking provides a better conceptual understanding of the realization of quantum technology and quantum computing.

Introduction

The classical perception of a physical system is based on the reality observation of physical systems by the observer. The process of classical understanding and learning in humans is widely applied to the advancement of artificial intelligence and machine learning. Artificial Intelligence (AI), particularly in the form of machine learning, is based on finding patterns, making predictions, and improving through data-driven feedback. Traditional AI is typically limited by classical computational capabilities, especially for large datasets or highly complex problems.

Recently, scientists have been exploring Quantum Machine Learning (QML), an emerging field that combines quantum computing [], with machine learning, through a process of trial and error []. QML aims to process and analyze massive datasets more efficiently than classical computers by using quantum algorithms, potentially enabling AI to make faster and more complex decisions. By integrating QML, AI systems may become exponentially more powerful, as quantum computers can process certain calculations far more quickly than classical ones. Quantum algorithms can handle high-dimensional spaces and complex probability distributions [], which could enable more sophisticated pattern recognition, feature extraction, and optimization. Some useful technical methods and quantum algorithms for quantum computation have been introduced recently [].

While we have some knowledge of classical understanding and learning in humans, we know very little about quantum perception and quantum learning. In this paper, we define the quantum perception of a physical system, which is based on its quantum state. The quantum state exists prior to observation and can be used for quantum computation since its evolution is unitary []. In the next section, we review the classical framework, followed by a definition of quantum perception in Section 3. Section 4 is dedicated to examining the impact of quantum perception on quantum computation. Finally, we present concluding remarks in Section 5.

Classical perception

The process of thinking and reaching perception in classical physics is inextricably intertwined with the observation and reality of physical systems, which are two of the most challenging topics in quantum theory. The reality of physical systems is understood through observation, and in classical theory, it exists independently of observation. In classical physics, the fundamental physical systems consist of matter, waves, and spacetime. Matter is composed of fundamental particles, and waves are described by tensor or spinor fields. In general relativity, spacetime is also explained by a rank-2 symmetric metric tensor field ????_mn, which, in the linear approximation, plays the role of gravitational waves [].

Fundamental particles are localized in a point in spacetime and mathematically represented by position vectors as functions of time, ????^®(????), while waves are spread through spacetime and modeled by tensor (or spinor) fields in spacetime, Φ(????,_????^®). These functions are embedded in, and evolve within, spacetime []. All information about the physical system, such as energy, momentum, angular momentum, frequency, wavelength, polarization, etc., is encoded in these mathematical functions, upon which classical perception can be extracted. These mathematical functions can be determined by the principles and laws of classical physics if we have the boundary or initial conditions, which are obtained through observation. Classical thinking is based on these functions and classical logic, which leads to a classical perception, i.e., an understanding of reality with certainty.

It is important to note that the classical perception is achieved in the spacetime. The spacetime in the small velocity and very small gravitational field can be modeled by the Galilean relativity. Time, space, and matter-waves are independent of each other in this model. The time can be modeled with the real number IR and space with IR³, which are the Euclidian geometry. In Special Relativity, space and time are not independent; instead, they are interwoven into a single continuum known as 4-dimensional (4-d) spacetime. They are independent of matterwaves. Spacetime is a flat manifold, represented as ???? = ℝ × ℝ³, and is known as Minkowski spacetime. A point of spacetime is presented by a four-vector ???????? ≡ (????,????,????,????) ≡ (????,????^®). In General Relativity, the matter-waves are the source of the spacetime and in the presence of the source, the spacetime is a curved manifold M_C, which can be described by a rank-2 symmetric tensor field ????_µν (????????^®). It can be obtained from the solution of the Einstein field equation []. In Riemannian geometry, a curved spacetime manifold can be described by the metric ????_µν (????????^®) (satisfying the metric-compatibility condition) and can be visualized as a 4-dimensional hypersurface embedded in a flat spacetime of more than four dimensions [].

In summary, classical perception arises from observation and determines the reality of the physical system. According to the principles of classical physics, by applying measurement error correction, the observed reality is exactly the same as the truth of the physical system before observation, i.e., reality and truth are the same.

Quantum perception

What is the fundamental concept in quantum theory? In quantum theory, the fundamental classical concepts of particles and waves lead to the particle-wave duality problem, making them inapplicable in this context; thus, they must be replaced with alternative concepts. There are various equivalent models for constructing quantum field theory []; to better align with quantum computation, we use the quantum state formalism and Dirac’s Bra-Ket notation. In this framework, the physical system is represented by a quantum state |????,????⟩, immersed in Hilbert space, H, and evolving within it. The Hilbert space and quantum state replace the concepts of spacetime and particle-wave, respectively, and quantum understanding must be built on these concepts.

The Hilbert space can be constructed using the principles of quantum field theory and the algebra of observable operators; for more details, see []. In quantum theory, including quantum geometry (qg), the quantum space of state is H???????? ≡ H×KG, where KGis the quantum space of states of spacetime geometry and His Hilbert space of the matter-radiation fields, for more details, see []. In the limit of the classical geometry (cg), which is used in the quantum technology and laboratory frame we obtain the Fock space bundle H???????? ≡ H×????, i.e. the quantum space KG is replaced with spacetime manifold ????. It is the quantum field theory in curved or flat spacetime. The Hilbert space can be considered the "fiber" of a bundle over the base spacetime manifold ???? []. ???? can be considered as the laboratory frame and His the Hilbert space of the physical system in the lab, which is defined at every point of spacetime. Conversely, at every point in Hilbert space, one can imagine all of spacetime, which can explain tunneling in space and time.

In a laboratory frame or Minkowski spacetime, by using the principles of quantum theory and having the initial conditions, |????,????0⟩, the quantum state can be determined with certainty at any time. This determinism over the quantum state is expressed through the unitarity principle:

|????,????⟩ = ???? (????,????0;????)|????,????0⟩, ???????? ^† = ???? ^†???? = I,                     (1)

Where ???? is the Hamiltonian operator of the physical system, ???? is the unitary evolution operator and I is the identity operator in Hilbert space H.

In quantum theory, the act of observation or external interaction with the physical system causes the quantum state |????,????⟩ to collapse into the new state |????,????⟩, which depends on the Hamiltonian detector, ????????, of the observer. We define |????,????⟩ as the reality of the physical system for the observer and |????,????⟩ as the truth of the physical system, which is different from the reality of the physical system. The reality depends on the observer and their chosen Hamiltonian detector ????????, but the truth depends on the Hamiltonian of the physical system, ????, and the initial conditions |????,????0⟩. It is important to remember that |????,????⟩ is independent of the observer and exists before observation []. Due to the collapse of the quantum state, the truth is inaccessible to the observer. This reminds us of Feynman’s famous saying: "I think I can safely say that nobody understands quantum mechanics".

Now, if we rename the collapse quantum state |????,????⟩ as the initial state of our new system.

|????,????0⟩, then by using the unitary evolution operator ????, one can obtain and understand the quantum state |????,????⟩ with certainty. Therefore the understanding of this quantum state is called the quantum perception, which can be used in quantum technology and quantum computation []. The quantum state vector can be written in terms of the integral and sum over the quantum number ???? and ????, where ???? and ???? are the set of continuous and discrete quantum numbers respectively. They are labeled the eigenvalue and eigenvector of the set of commutative operator algebras of the physical system, which determine the Hilbert space H [].

It is important to note that the trajectory of a particle ????^®(????), the classical field Φ(????,????^®), and the quantum state |????⟩ all of them are mathematical quantities used to explain physical systems. If our minds have difficulty grasping the quantum state, it is because the quantum state is a relatively new concept, whereas we are more accustomed to the concepts of a particle’s trajectory and the field function distribution. However, all these quantities are abstract mathematical concepts, and within the microscopic domain, the quantum state provides a better explanation of our physical system than the particle and wave.

In summary, the classical approach aims to understand and predict the future behavior of particles and waves, while the quantum approach seeks to determine the quantum state and its evolution. The first results in classical perception and the second in quantum perception. According to the principles of quantum theory, reality is different from the truth of the physical system.

Quantum computation

Quantum technology, and especially quantum computation, is performed at infinitesimal scales. At this level, what are the fundamental physical systems? Honestly, I’m not sure of the answer, and it seems no one is certain. Classical theories generally describe these systems as particles and waves (either tensor or spinor fields), but this framework doesn’t account for all the phenomena we observe. In quantum theory, however, physical systems are represented by quantum states, which offer a more comprehensive explanation of our observations than classical particles and waves. The concept of a quantum state integrates the characteristics of both particles and waves, presenting a unified view that is crucial in quantum computing [].

Then we assume that the fundamental system at this level is a quantum state. The process of developing quantum technology or quantum computation with this assumption involves three key steps: The first step is constructing an appropriate initial quantum state |????,????????⟩, which includes the registration and readout of qubits or qudits []. The second step involves determining the time evolution of the system
|????⟩ = ???? |????,????????⟩, akin to implementing gates to perform calculations. The final step is the deterministic detection and output of calculation results

|????,????????????⟩.

The basic processing unit in quantum computing is the quantum state. In this case, classical bits are replaced by quantum states and classical gates by unitary transformations. Calculations are conducted using quantum algorithms instead of classical ones, which are based on principles of quantum theory []. However, quantum computation faces several significant technical challenges, some of them are:

Isolating quantum states (qubits or qudits), since the microscopic and macroscopic worlds interfere with each other in the process of recording and reading the information.

Quantum state collapse during qubit registration and readout, various techniques leveraging entanglement properties allow for deterministic readouts of qubit states in quantum theory [].

Implementation of quantum gates, since in the microscopic world inherent quantum fluctuation appears, which must be mitigated by using quantum properties such as entanglement and superposition.

Controlling unintended entanglements as the number of quantum qubits increases can be achieved by using anti-entanglement properties, which may be provided by applying a quantum scalar field to the set of qubits.

Finally, it is important to note that the quantum state perspective in the quantum field theory permits us to visualize a quantum state, which propagates in the Fock space bundle H???????? ≡ H×????, i.e. background field method. His defined at any point in spacetime and it can be considered the fiber of a bundle over the base spacetime manifold ????. The Wightman two-point function provides a correlation function between two different points in spacetime and their corresponding Hilbert spaces [], which played a central role in quantum telecommunication.

Conclusion

In classical physics, perception emerges from observation and defines the reality of a physical system, where reality and truth are viewed as synonymous. However, in quantum theory, the physical system is represented by a quantum state, whose determination and evolution lead to what can be described as a quantum perception. Here, reality diverges from the underlying truth of the physical system. Embracing this perspective on quantum theory may facilitate the development of quantum technologies and quantum computing. A comprehensive exploration of the relationship between theoretical physics concepts, such as quantum states, and quantum computing elements, like qubits and qudits, can enhance our understanding of unresolved challenges in quantum computing. By highlighting the parallels between challenges in theoretical physics and computer science, we aim to apply techniques from theoretical physics to address issues in computer science, which will be discussed in the following paper.

Acknowledgment

The author wishes to express particular thanks to A.M. Djafari, A. Djannati-Atai, and S. Rouhani for their discussions. The author would like to thank Collège de France, Université Paris Cité, and Laboratorie APC for their hospitality.

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Takook M. Quantum Perception and Quantum Computation. IgMin Res. . October 18, 2024; 2(10): 818-821. IgMin ID: igmin253; DOI:10.61927/igmin253; Available at: igmin.link/p253

• DOI10.61927/igmin253

09 Oct, 2024

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17 Oct, 2024

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18 Oct, 2024

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