Prerpints.org logo
Preprint
Article

Complements to Existing Implementations of Quantum Information Processing

Altmetrics

Downloads

92

Views

17

Comments

0

This version is not peer-reviewed

Submitted:

21 August 2024

Posted:

24 August 2024

You are already at the latest version

Alerts
Abstract
Two approaches are being proposed to complements existing practical implementations of quantum information processing; (a) Multiplexed Michelson interferometry for Linear Optical quantum computation which should in principle split further an initially split beam to yield new sets of beams which are scalable to multiple interferometric outputs beyond just the dual output in Mach Zehnder interferometry. Generally Interferometry is applied in quantum computation particularly linear optical quantum computation schemes such as K.L.M protocol using the Mach-Zehnder interferometer, however a multiplexed Michelson interferometry enables the production of scalable cross-correlated beams making it suitable for optical multi-qubit operations. (b) Coupled LDR Circuits for Quantum emulation which can model cross correlation and probabilistic qubit states to enable parallelization and Gating on Classical electrical circuits. The system is to be designed as a network of electrical circuits coupled to each other using electrical coupling elements and are equipped with a light dependent resistor (LDR) alternatively referred to as photo-resistor to provide variable resistance in response to varied intensity of incident light. The maximum threshold current state which is being defined for the circuit and a minimum current state corresponds to 1 and 0 binary states respectively, however an intermediate current state models a superposition of 1 & 0. Likewise varying the intermediate current values closer to either 1 or 0 is akin to a probability rotation of the qubit states which is achieved by varying resistance using the LDR where the multi-circuit coupling interaction helps emulates cross-correlation of multi-qubit systems. The proposed system can be useful at least as a tool for informative applications in a classical framework.
Keywords: 
Subject: Physical Sciences  -   Quantum Science and Technology

Introduction

Michelson interferometer [3,4] has found several applications in the field of instrumentation, especially for practicals and experiments requiring the detection of small changes and micro-scale effects. It is also applied in astronomical observations such as in LIGO (laser interferometer gravitational wave observatory) [5,6,7] in one personally written article, a prospect on the improvement of the laser interferometer gravitational wave observatory based on the application of Colloidal Quantum dots films for enhanced photo detection has also been discussed [26]. The Michelson interferometer is known to detect a single interference pattern/ fringes. But advances in interferometry led to the development of an interferometer that allowed the detection of two interference patterns, which is now known as the Mach Zehnder interferometer [8,9]. The fact that the Mach-Zehnder interferometer can generate dual interferometric outputs made it suitable for applications involving entangled states [10,11,12,13]. It is also considered for its potentials in quantum computation [14,15,16], particularly in optical quantum computation [17,18] schemes such as the KLM protocol [25].While the Mach Zehnder interferometer is useful for the cross correlation of two qubit system, applying to multi-qubit cross correlation akin to multi-partite entanglement doesn’t appear to be a straight forward possibility using a typical Mach-Zehnder interferometer. With the intention to develop an interferometric device with multiple detectable interference patterns, a potential interferometer design based on the modification of the Michelson interferometer is being presented. The diagram below illustrates the principle of operation of a regular Michelson interferometer.
Preprints 115936 g001
Figure 1. Caption.
Figure 1. Caption.
Preprints 115936 g001
Alternatively an Electrical system can be designed and developed to emulate quantum properties of superposition and parallelism to model artificial qubit systems. The proposed electrical system has unique features and elements such as its use of Light dependent resistors leveraging quantized photoelectric effects for varied resistance.
However it should be noted that this System is largely for emulating quantum states and for mimicking Quantum computational Operations. It can be considered a very useful and accessible informative tool but remains classical in every respect thus we can consider it a Classical quantum emulator.

Quantum Information Processing via the Mach Zehnder Interferometer

The Mach Zehnder interferometer has unique differences in its design when compared to the michelson interferometer, in that it employs a closed geometry in the configauration of its beam paths, and also has dual interferometric ouputs. The merit of this configauration for Quantum information processing is that it provides a means to practically cross-correlate two Optical qubit systems. The polarization state of light beams are considered to be a suitable representation of qubit states, and by implementing phase shifts to the light beam the polarization states which allows both probability rotation of states and gating operations to the qubit states. But applying these operations to two-qubit systems seemed made viable through the dual output beams in the mach zender inteferometer.
Preprints 115936 g002
Figure 2. Caption.
Figure 2. Caption.
Preprints 115936 g002
The superposed quantum states for both optical paths are given by;
ψ 1 = | 0 ± 1 2 … … p a t h   1       a n d       ψ 2 = | 0 ± 1 2 … … ( p a t h   2 )
Where the state “1” is represnted by vertical polarization of the light and “0” is represnted by the horizontal polarization of state.
Lineary the states are defined as;
| 0 = 1 0             | 1 = 0 1
A linear transformtion [23,24] applied on these states would yield an output, depending on the particular transformation matrix corresponding to a given quantum gate. The use of interferometers in quantum information processing and computational falls under the general umbrella of linear optical quantum computing (LOQC).
LOQC is one out of the many approaches in the development of a true universal quantum computer. LOQC involves the use of photons as carriers of quantum information, which can be manipulated using optical instruments like wave plates, mirrors, beam splitters etc. as ways of processing these informations.
In optical quantum computation, photon represents a qubit state which is a superposition of quantum states representing informations. Just as classical computation utilizes bits to represent informations, quantum computation also uses a superposition of two or more bits represented by quantum mechanical states to represent information. In optics the quantum states are represented by the polarization states
Qubits can be processed through quantum gates, such as the CNOT-gate, CPHASE-gate, and Toffoli-gate etc. in optical quantum computations these gates are implemented using wave-plates that alters the polarization states of the light beams, thereby applying a transformation to the information and eventually yield an output.
These operations can be carried out with a Mach Zehnder interferometer, and even more the Mach Zehnder interferometer performs the operations for entangled system (the two coherent light beams to be precise) with their quantum state being detected by the photodetectors. This makes the Mach Zehnder interferometer very suitable for processing two qubit systems.

Multiplexed Michelson Interferometer

Although the Mach Zehnder interferometer detects two fringes, an alternative interferometric system which may detect higher number of fringes is being proposed in this section, one which may be considered a modification of the michelson interferometer. Such that the michelson interferometer will detect more than just one or two fringes. Two digrams are given illustrating possible configaurations for the proposed device.
In Figure 3 it can be seen that the first beam splitter just after the light source splits the incoming beams from the source into two beams in perpendicular paths. Let one path be referred to as an x1 path; this is the path on vertical axis of the diagram, and the other path referred to as an x2 path on the horizontal axis of the diagram.
Additional beam splitters in array are introduced between the beam splitter and the mirror in the x2 path, the number of beam splitters that can be added is not limited. But for the simplicity of the diagram only two additional beam splitters are used. The additional beam splitters may require adjustments of the distance between the first beam splitter and the mirror, likewise the gaps between the beam-splitters in the array would also have to be considered.
Each additional beam splitters is splitting the beam in the x2 path further, and just like the first beam splitter, the additional beam splitters will also split the beams perpendicularly, into more x1 and x2 paths. All the beams in the x2 path will overlap in the same direction and still remain a single beam, but the new sets of x1 paths will be parallel to each other.
Like the Michelson interferometer, the beams in the x1 path will each be directed towards the mirrors in their paths, which then reflects them to their respective detectors. But before each of them must have intersected with the x2 beam leading to interference that will generate individual fringes for each interference which will be detected using the photo-detectors.
The phase difference for a single interference between two beams is typically given as;
Figure 4 is another configuration but based on the same principle, the first beam splitter also splits the beams into two paths x1 and x2. However the additional beam splitters are on the x1 path, unlike the previous configuration where it’s on the x2 path. This leads to an overlapping of all the x1 beams in form of a single beam, and a parallel set of x2 beams, with mirrors and detectors for each x2 that would interfere with the x1 beam.
It is seen that both configurations still modifies the Michelson interferometer in the same manner but with different setups. These configurations would allow us to have multiple detectable fringes, providing separate patterns of interference that can be compared and analyzed, which may reveal more details of the interference, and may enhance sensitivity. It also gives us multiple choices of reference beams, or even allow us to have more than one reference beams at the same time.

Merits of Multiplexed Michelson Interferometry for Instrumentation

The proposed interferometer would be an improvement to interferometry as instrumentation device, because with more number of beams all interfering with the beam in the x2 direction one would record significant difference in optical path length between the n-number of beams thus enhancing the interferometers sensitivity.
The interferometer also allows relative detection of fringes, as individual detectors would be detecting respective interferometric patterns. This way a parameter or sample can be studied or measured from different paths and perspectives. This is very useful for analysis as one can compare the data gotten from each detectors, revealing useful informations about the system.
Instrumentation involves measurement, detection and control of parameters, and the proposed interferometric system can been used to serve these purposes with greater capacity [19,20,21], particularly in terms of detection with high level of sensitivity and precision. It also has analytical advantage and freedom to vary the number of fringes according to experimental or practical needs, which is a level of control over the instrumentation system.

Scalability as a Quantum Computational Advantage of the Multiplexed Michelson Interferometer

In previous sections it was stated that the proposed interferometric system modifies the Michelson interferometer to extend the number of coherent beams and interference patterns, and that more than one fringes can be detected. The number of cross-correlated beams and interference output that can be generated are limited to two in a Mach-Zender interferometer, however they are not directly limited in the case of the proposed multiplexed Michelson interferometer as the number of beams only depends on the specific practical requirements. Making it possible to have scalable number of beams.
This implies that the proposed modification may enable multi-qubit system. Implementing quantum gates and transformations may be possible through the use of similar linear optical elements used with the Mach-Zehnder interferometer to alter the polarization states of the beams, such as the wave plate mentioned earlier. This is clearly an advantage in the field of quantum computation, indicating that the proposed interferometer to be just as useful as a Mach-Zehnder interferometer for quantum computation but with advantage of scalability.

Coupled Ldr Circuits

A quantum emulator can be developed using electrical circuits equipped with light dependent resistors, otherwise known as photoresistors which is meant to vary resistance on the circuit in response to the intensity of incident light. The response of the photoresistors which to some extent introduces some quantum mechanical effect to the system.
The proposed system consists of multiple electric circuits designed to perform parallel co-related operations through electrical coupling that allows both circuits to interact and influence each other’s states. But this is not entirely new as circuit coupling as a means of modelling entanglement is already a common notion. However the element of originality in this proposed system the use of partial on and off states of an electric circuit to represent a classical analog of qubit superposition which as stated previously is achieved by means of variable resistance made possible using light dependent resistors.
An LDR for concise formal definition in this article is a resistor whose resistance decreases with increasing incident light and increases with decreasing incident light. This characterization makes LDRs ideal for having a range of continuous current values.
To mimic superposition states using this circuit, intermediate current values between the highest and lowest current state is applied as the resistance is varied. The natural current value in the circuit is the minimum current value corresponding to ground state, but as we set a threshold for higher current values we define that threshold current as the maximum current value. The maximum threshold current can then be defined as the current state attained when the maximum intensity of incident light is attained. Mathematically this Analog superposition state is given in the following form.
  ψ = | I m i n ± I m a x 2
The closest thing to a gating operation that can be performed with this coupled LDR circuit is the use of a single or multiple light sources to either set the initial current state of the circuit or induce a change of current state. For example an emulation of the Hadamard gate can be implemented by adjusting parameters, intensities and frequency of the light sources such that the circuit’s current value would go from being at exactly maximum or minimum values to being at 50% of its maximum threshold current value, and this can be mapped on the Bloch-sphere as a probability rotation and a superposition state. As already stated the circuits are cross correlated via coupling using shared electrical components. There are various forms of electrical coupling such as Resistive coupling, Capacitative coupling, Diode coupling, Direct coupling etc. This allows the circuits to interact and is crucial for parallel processing, as it enables the circuits to operate in parallel. The circuit below illustrates two coupled circuit with light dependent variable resistors, which can emulate two qubit systems.

Quantum Emulation

Quantum emulation [1,2] is an interesting paradigm in the field of quantum computation and theoretical physics. At its core quantum emulation involves the simulation of quantum systems and quantum algorithms using classical or other quantum computational methods. This complex and multi-faceted subject spans a broad range of topics including computational techniques, theoretical principles and practical applications.
To define quantum emulation we state that it is the process of using classical computers to simulate the behavior and characteristics of quantum systems that are either too complex to study directly or are not yet accessible with current quantum hardware.
The main goals of quantum emulation includes gaining understanding of quantum systems which helps researchers and students to model the how complex quantum phenomena behave under different conditions. Enabling the development, testing and refining of quantum algorithms in a controlled environment before deploying them on actual quantum hardware. This is particularly important given the current limitations of accessibility of actual quantum hardware to institutions where quantum information processing is studied.
By emulating quantum systems, one can predict the outcomes of experiments and theoretical models. This predictive capability can guide experimentalists in interpreting actual quantum behaviors.
Quantum emulations can be performed using software based simulations that can be performed on classical digital computers, likewise one can develop classical hardware based emulations of quantum systems such as the proposed coupled LDR circuit which can simulate model quantum informations and quantum interactions.
As advancements in quantum computing continues, the ability to emulate increasingly complex quantum phenomena will improve. The developments of more powerful classical and quantum computing resources, along with innovations in quantum simulation algorithms will drive computational progress.
More ways can be explored in the future improve the use classical systems in modelling quantum behavior and interactions, making them more accurate leading to new understanding of quantum phenomena.
In summary quantum emulation can be a very informative tool to leverage classical electrical elements for gaining understanding on the behavior of quantum systems and also simulate quantum computational operations. It would not be wrong to say that quantum emulation schemes including the coupled LDR circuit has a potential of evolving to a much more legitimate and accepted approach for quantum inspired parallel computation.

Annealing

Annealing is a special computational technique for solving optimization problems which involves finding the optimal solution from a range of possible solutions to a particular problem, the optimal solution is that which best satisfies the problem conditions. It starts by defining the worst but known solution to the problem and continues to generate more improved solutions until it the best solution is attained.
Normally a simulated thermal annealing algorithm can be developed to model an actual physical annealing process which involves heating up a metal to a certain temperature and allowing it to cool until it reaches a temperature which satisfies the condition for malleability of the metal. As an algorithm a range of solutions are being generated such that solutions associated with the raised temperature corresponds to the worst solution and as it cools down the lower temperatures would correspond to optimized or improved solutions, until a solution is reached that satisfies the problem condition.
However an approach to annealing also exist that applies quantum mechanical principles this is known as quantum annealing. In quantum annealing temperature is not used to represent solutions, but instead the ground state and excited states are being used. Quantum annealing works by exciting the quantum system first to a certain energy level then allow it to gradually fall to lower excitation states approaching ground state till a state is reached that satisfies a problem condition.
The coupled LDR can also perform similar annealing operations but would function as a classical annealer to achieve this we start by introducing a light source which would be incident on the LDR where we raise the light intensity to certain level which would then decrease the resistance and raise the current value, then we allow the light intensity to gradually decrease leading to increased resistance and effectively a decreased current value. The range of decreasing current values are associated with possible solutions from the worst solution to more improved and optimized solutions, till an optimal solution is reached that would satisfy certain problems.

Conclusion

The proposed multiplexed Michelson interferometer which multiplies light beams and produces multiple interference outputs may serve well as a scalable linear optical quantum computational system with additional merits as an instrumentation device, given the enhancements it provides to the sensitivity and the multiplicity of interferometric data. Further research and development may be necessary to take the proposed interferometer from a simple stage of conceptualization to reality, it would be interesting to see it function in real time as there might be other merits it may have.
Likewise the emulation of quantum mechanical systems and quantum computational operations using classical elements such as a coupled LDR (light dependent resistor) circuit can be of informative and pedagogical value providing a simple, accessible, and cost effective means of leveraging both quantum mechanical principle (such as parallelism and superposition) and classical electric circuit elements for modelling gating operations and annealing.

DECLARATIONS

I hereby declare that this article, titled; “Complements to Existing implementations of Quantum information processing”.
  • Is written with no conflicting interest, neither is there any existing or pre-existing affiliation with any institution.
  • No prior funds is received by the author from any organization, individual or institution.
  • The content of the article is written with respect to ethics.
  • The content of the article does not involve experimentation with human and/or animal subjects.
  • Data-availability; no data, table or software prepared by an external body or institution is directly applicable to this article.

References

  1. Thomas Haner et-al, High performance Emulation of Quantum circuits, arXiv: 1604.06460, (2016).
  2. Sharan Mourya, Emulation of Quantum algorithms Using CMOS analog circuits, IEEE transactions on Quantum engineering, vol.4, pp.1-16, (2023). [CrossRef]
  3. J. Lawal and E. Kessler, Michelson interferometry with 10pm accuracy, Review of Scientific Instruments, 71(7), 2669-2676, (2000).
  4. M. Ikram and G. Hussain, Michelson interferometer for precision angle measurements, Applied Optics, 38(1), 113-120, (1999). [CrossRef]
  5. Alex Abramovici et-al, LIGO the Laser interferometer gravitational wave observatory, Science, 256(5055), 325-333, (1992).
  6. Junaid Aasi, Thomas abbot et-al, Advanced LIGO, Classical and quantum gravity, 32(7), 074001, (2015).
  7. Gregory. M. Harry Advanced LIGO: the next generational wave detectors, Classical and quantum gravity, 27(8), 084006, (2010). [CrossRef]
  8. S.F. Adams et-al. How does a Mach-Zender interferometer work? Physics Education, 35(1), 46, (2000).
  9. JG Rarity et-al, Two photon interference in a Mach-Zender interferometer, Physical review letters, 65(11), 1348, (1990).
  10. Ryzard Horodecki et-al, Quantum entanglement, Review of modern physics, 81(2), 865, (2009).
  11. Karol Zyczkowski et-al, Dynamics of quantum entanglement, Physical Review ‘A’, 65(1), 012101, (2001).
  12. Vlatko Vedral, Quantum entanglement, Nature physics, 10(4), 256-258, (2014).
  13. Barbara M Terhal, Detecting quantum entanglement, Theoretical computer science 287(1), 313-335, (2002).
  14. Vlatko Vedral and Martin. B. Pleino, Basics of quantum computation, Progress in quantum electronics, 22(1), 1-39, (1998).
  15. Chris Bernhardt, Quantum computing for everyone, MIT Press, (2020).
  16. Robert. S. Sutor, Dancing with qubits; how quantum computing works and how it can change the world, Packt Publishing, (2019).
  17. Tim. C. Ralph, and Geoff. J. Pryde, Optical quantum computing, Progress in Optics, 54, 209-269, (2010).
  18. Jeremy. L. O’Brien, Optical quantum computing, Science, 318(5856), 1567-1570, (2007).
  19. Shuming-Yang and Guofeng Zhang, A review of interferometry for geometric measurement, Measurement and science technology, 29(10), 102001, (2018). [CrossRef]
  20. Silvano Donati, Developing self-mixing interferometry for instrumentation and measurements, Laser & Photonics reviews, 6(3), 393-417, (2012). [CrossRef]
  21. Nicusor. V. iftima et-al. A portable low coherence interferometry based instrument for fine needle aspiration biopsy guidance, Review of scientific instruments, 76(6), (2005). [CrossRef]
  22. Wikipedia.org. https://en.m.wikipedia.org/wiki/Optical-coherence-tomography-(OCT).
  23. Charles. G. Cullen, Matrices and linear transformation, Courier-Corporation, (2012). [CrossRef]
  24. Daniel. T. Finkbeiner, Introduction to matrices and transformations, Courier-Corporation, (2013).
  25. Emmanuel Knill et-al, A Scheme for efficient quantum computation with linear optics, nature, 409(6816), 46-52, (2001).
  26. Adegbite Inioluwa Precious, Prospect of Quantum Dots for Photo detection in LIGO and other interferometric Gravitational Experiments, Preprints.org, Doi:10.29944/preprints202408.0181.v1, (2024).
Preprints 115936 g003
Figure 3. Caption.
Figure 3. Caption.
Preprints 115936 g003
Preprints 115936 g004
Figure 4. Caption.
Figure 4. Caption.
Preprints 115936 g004
Preprints 115936 g005
Figure 4. Caption.
Figure 4. Caption.
Preprints 115936 g005
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
Prerpints.org logo

Preprints.org is a free preprint server supported by MDPI in Basel, Switzerland.

facebook logotwitter logolinkedin logo
MDPI Initiatives
Important Links
Subscribe

Disclaimer

Terms of Use

Privacy Policy

© 2024 MDPI (Basel, Switzerland) unless otherwise stated