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American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

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Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

We are pleased to announce that submissions are now being accepted for peer review for all the journals across all our subject areas in SciEP.

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Label_Title

Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

We are pleased to announce that submissions are now being accepted for peer review for all the journals across all our subject areas in SciEP.

Please submit your manuscript via our online submission system:
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Qudits of Multi-Single Slits, Multi-Double Slits and Multi-Triple Slits --- Corresponding to Octal System, Decimal System, Duodecimal System, Hexadecimal System

Hui Peng*, James L. Peng

James Peng Lab, Fremont, CA USA

Abstract: One of tasks of quantum computing research is to reduce the components utilized for reaching certain computation power. To significantly reduce the components, we propose four kinds of Qudits of higher-dimension, multi-folds higher than the two-dimension of the qubits, which are respectively formed by: (1) multi-single-slits; (2) multi-double-slits (multi-Qubits); (3) multi-triple-slits (multi-Qutrits); and (4) combination of above. The further advantage is that the so formed Qudits may adopt Octal Number System, Decimal Number System, Duodecimal Number System, and Hexadecimal Number System, respectively.

Keywords: qudits, qubits, qutrits, single slit, double slit, triple slits, Octal system, Decimal system, Duodecimal system, Hexadecimal system

Received February 15, 2024; Revised March 17, 2024; Accepted March 24, 2024

Citation: Hui Peng, James L. Peng, Qudits of Multi-Single Slits, Multi-Double Slits and Multi-Triple Slits --- Corresponding to Octal System, Decimal System, Duodecimal System, Hexadecimal System. International Journal of Physics, 12 (2). 65-67. January 2024. doi:10.12691/ijp-12-2-1

1. Introduction

The quantum mechanics and the digital computer are the significant theory and the powerful technology respectively. In 1980s, Feynman [1] suggest that quantum theory might be applied in computer technology. In 2019, Google-NASA build a 54-qubit quantum computer [2]. IBM introduced IBM Q quantum computer in 2020 [3].

Recent developments in the quantum computation are: (1)

the entanglement of individual molecules is achieved, which may have significant applications in quantum computing Figure 4; (2) "quantum circuits" were created that correct errors more efficiently [5,6].

To achieve certain computing power, one of tasks of quantum computing research is to reduce the components.

The n qubits have the computing power of 2n [7]. One double slit has two slits and 2 basic states. The double slit experiment paves the way toward a novel strategy for quantum computing [8]. One triple slit has three slits and 3 quantum states. The n qutrits have the power of 3n [9,10].

Qudits can encodes more than three states. Qudits computer can reach more computing power than the qubit computer with less Qudits components.

In this article, we propose the higher dimension Qudits system formed by utilizing multi-single slits, multi-double slits, multi-triple slits and combination of above, respectively. We utilize the notation Qudits-x/y to present a qudits that contains x slit and y basic states, where x = 1, 2, 3 and 1-2-3 stands for that the Qudit is formed by multi-single slits, multi-double slits, multi-triple slits and combination of above, respectively. The “y” is the states.

The proposed Qudits not only have more basic states, much higher dimension, to reduce the number of the Qudits utilized for reaching certain computation power, but also can adopt the number systems beyond the binary system: Qudits-1/8 and Qudits-2/8 correspond to Octal number system, respectively. Qudits-1/10 and Qudits-2/10 correspond to Decimal number system, respectively. Qudits-1/12, Qudits-2/12 and Qudits-3/12 correspond to Duodecimal number system, respectively. Qudits-1/16 and Qudits-2/16 correspond to Hexadecimal number system, respectively.

2. Qudits-1/y System

Now let us consider several examples of Qudits-1/y, which is formed by multi-single slits (Figure 1).

Qudits-1/8 system has eight single slits and thus, 8 states,

= α₀|0⟩ + α₁|1⟩ + …+ α₇|7⟩. Where = 1. To get power (8)m = 2¹⁰⁰⁰, we need 334 of qudits-1/8, which would be able to perform as many operations as 1000 qubits.

Qudits-1/16 system has 16 single-slit and 16 states. To get power (16)m = 2¹⁰⁰⁰, we need 250 of qudits-1/16.

Qudits-1/24 system has 24 single slits and 24 states. To get power (24)m = 2¹⁰⁰⁰, we need 219 of qudits-1/24.

Qudits-1/36 system has 36 single slits and 36 states. To get power (36)m = 2¹⁰⁰⁰, we need 194 of qudits-1/36, namely 194 of qudits-1/36 would be able to perform as many operations as 1000 qubits.

Figure 1. Multi-single slits

Figure 2 shows how many Qudits formed by different number of single slits are needed for reaching power of 2¹⁰⁰⁰.

Figure 2. Qudits (multi-single slits) vs qubits

The more single slits a Qudit contains, the less Qudits are needed to reach the power of 2¹⁰⁰⁰.

Another feature of Qudits is that Qudits-1/8 can form Octal number system. Qudits-1/10 can form Decimal system. Qudits-1/12 can form Duodecimal number system. Qudits-1/16 can form Hexadecimal number system.

3. Qudits-2/y System

Now let us consider several examples of Qudits-2/y formed by multi-double-slits (multi-Qubits) (Figure 3).

Figure 3. Qudits of multi-double slits

Qudits-2/4 system has two double slit and 4 states,

= α₀|0⟩ + α₁|1⟩ + α₂|2⟩ + α₃|3⟩. Where = 1. To get the computing power of 1000 Qubits, 4m = 2¹⁰⁰⁰, we need 500 of qudits-2/4.

Qudits-2/8 system has Four double slit and 8 states. The red circle shows the area the photons land, so photons have the equal probability going through each slit. To get the power 8m = 2¹⁰⁰⁰, we need 334 of qudits-2/8.

Qudits-2/10 system has Five double slit and 10 states. To get power 10m = 2¹⁰⁰⁰, we need 302 of qudits-2/10.

Qudits-2/12 system has Six double slit and 12 states. To get power 12m = 2¹⁰⁰⁰, we need 279 of qudits-2/12.

Qudits-2/16 system has Eight double slits and 16 states. To get power 16m = 2¹⁰⁰⁰, we need 250 of qudits-2/16.

Figure 4 shows how many Qudits formed by different number of the double slits are needed for reaching power of 2¹⁰⁰⁰.

Figure 4. Qudits (multi-double slit) vs qubits

Qudits-2/8, Qudits-2/10, Qudits-2/12 and Qudits-2/16 can form Octal number system, Decimal number system, Duodecimal number system and Hexadecimal number system, respectively.

4. Qudits-3/y System

Now let us consider several examples of Qudits-3/y (Figure 5), formed by multi-triple-slits (multi-Qutrits).

Figure 5. Qutrits of Multi-triple slits

Qutrits-3/6 system has two triple-slit and 6 states. To get power (6)m = 2¹⁰⁰⁰, we need 387 qutrits-3/6.

Qudits-3/12 system has four triple-slits and 12 states. To get power (12)m = 2¹⁰⁰⁰, we need 279 qudits-3/12.

Qudits-3/27 system has nine triple-slits and 27 states. To get power (27)m = 2¹⁰⁰⁰, we need 211 qudits-3/27.

Figure 6 shows how many Qudits formed by different number of the triple slits are needed for reaching power of 2¹⁰⁰⁰.

Qudits-3/12 can form Duodecimal number system.

Figure 6. Qudits (multi-triple slits) vs qubits

5. Qudits-1-2-3/y System

Now let us consider two examples of Qudits-1-2-3/y, combination of single slit, double slits and triple slit (Figure 7).

Figure 7. Combination of single slit, double slit and triple slits

Qudits-1-2-3/8 system has one single slit, two double slit and one triple slit and total 8 states. To get the power

8m = 2¹⁰⁰⁰, we need 334 of qudits-1-2-3/8.

Qudits-1-2-3/12 system has two single slits, two double slits and two triple slits and total 12 states. To get the power of 12m = 2¹⁰⁰⁰, we need 279 of qudits-1-2-3/12.

6. Summary

We show several examples of Qudits systems formed respectively by (1) multi-single-slits; (2) multi-double-slits; (3) multi-triple-slits; and (4) combination of single slit, double-slits, and triple-slits.

The above Qudits have higher dimensions that are multi-folds of that of the qubits.

The advantage of the so formed Qudits is to significantly reduce the number of Qudits needed for certain computation power (Figure 2, Figure 4, Figure 6, Figure 8).

Another advantage of the so formed Qudits is to be able to adopt the number systems other than the binary number system into quantum computing. Qudits-1/8, Qudits-2/8 and Qudits-1-2-3/8 can form Octal number system, respectively. Qudits-1/10 and Qudits-2/10 can form Decimal system, respectively. Qudits-1/12, Qudits-2/12, Qudits-3/12 and Qudits-1-2-3/12 can form Duodecimal number system, respectively. Qudits-1/16 and Qudits-2/16 can form Hexadecimal system, respectively.

The Qudits system can be modularized.

Figure 8. Qudits (combination) vs qubits

ACKNOWLEDGEMENT

The authors thank Mr. Paul Sorich and Mr. Paul Miloglav for making the diaphragms of slits.

References

[1]   | R. Feynman, “Simulating physics with computer”, Inter. J. of Theor. Phys. 21(6/7) 467-488, (1982).
[2]   | Frank Arute, et al. "Quantum supremacy using a programmable superconducting processor". Nature. 574 (7779): 505–510 (2019).
[3]   | N. Schwaller, er.al., “Evidence of the entanglement constraint on wave-particle duality using the IBM Q quantum computer”. Phys. Rev. A 103, 022409.
[4]   | Staff, "Physicists 'entangle' individual molecules for the first time, hastening possibilities for quantum computing". Phys.org. Archived from the original on 8 December 2023.
[5]   | Bluvstein, Dolev, et al., "Logical quantum processor based on reconfigurable atom arrays". arXiv:2312.03982.
[6]   | Jr, Sydney J. Freedberg. "'Off to the races': DARPA, Harvard breakthrough brings quantum computing years closer". Breaking Defense. Retrieved 9 December 2023.
[7]   | M. A. Nielsen and I. Chuang, “Quantum Computation and Quantum Information. Cambridge University Press. p. 13. ISBN 978-1-107-00217-3. (2010)
[8]   | U. Sinha, “Quantum Slits Open New Doors”, Scientific American, Jan.1 (2020).
[9]   | P.B. R. Nisbet-Jones, “Photonic qubits, qutrits and ququads accurately prepared and delivered on demand”, arXiv:1203.5614.
[10]   | G. Rengaraj et.al., “Measuring Deviation from superpositionprinciple in interference experiments”, New Journal of Physics, 20 Article #063049 (2018).