🕷️ Crawler Inspector

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Direct Parameter Lookup

Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 77 (from laksa015)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa077.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://medium.com/@anjanakrishnan3100/superposition-beyond-the-misconceptions-b1a722b41027\')), getAhrefsUnparsedNoserviceFromURL(\'https://medium.com/@anjanakrishnan3100/superposition-beyond-the-misconceptions-b1a722b41027\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/medium.com\/@anjanakrishnan3100\/superposition-beyond-the-misconceptions-b1a722b41027","crawl_time":1770942421,"first_indexed_time":0,"http_code":200,"src_unparsed":"com,medium!\/@anjanakrishnan3100\/superposition-beyond-the-misconceptions-b1a722b41027 s443","src_root_hash":"13179037029838926277","history_drop_reason":null,"meta_title":"Superposition - Beyond the Misconceptions | by Anjanakrishnan | Medium","meta_descriptions":["Superposition - Beyond the Misconceptions Day 5- Quantum30 challenge As we approach the end of the first week of QuantumComputingIndia’s #Quantum30 challenge, it’s essential to explore the …"],"attrs_boilerpipe_text":"4 min read\nAug 5, 2023\nDay 5- Quantum30 challenge\nAs we approach the end of the first week of\n’s #Quantum30 challenge, it’s essential to explore the concept of ‘Superposition’ in quantum physics. This article provides more of a mathematical interpretation of the term.\nSuperposition.\nWhenever you search for this word in the context of Quantum Mechanics, the general and most common answer you get is\n‘Superposition is the ability of a (quantum) particle to exist in multiple states at the same time until its measured’\nThis is the definition that I got when I Googled the term. Though for a beginner, this is good and enough, this definition can be misleading at times. Let’s refine our understanding of this concept and clarify any misconceptions that might arise from preconceived notions. In yesterday’s post, we defined a wave function as a\nmathematical\ntool to represent a particle. So obviously, there is some abstract mathematics involved.\nThe Basis of Superposition: Linear Algebra and Vector Spaces\nTo comprehend superposition fully, we must first explore its mathematical foundations. In linear algebra, we encounter vector spaces and basis.\nTo keep it simple, if I have the color spectrum and the three primary colors — red, blue, and yellow, then the spectrum is the vector space while the primary colors are the basis. Here, we also have to understand that all these primary colors are completely distinct and independent, which in mathematical terms is known as ‘linearly independent’.\nA linear combination is just the addition of basis vectors with a scalar. So for the color green, we get a linear combination\nPress enter or click to view image in full size\nTo get a clearer understanding of these concepts you can refer 3Blue1Brown videos on the fundamentals of linear algebra.\nWave Function and Its Role in Superposition\nIn the context of quantum mechanics, we use the wave function to represent quantum particles. The wave function is a linear combination of basis states, much like mixing primary colors to create different shades. Each basis state corresponds to a specific quantum state, and the coefficients in the linear combination represent the probability amplitudes associated with each state.\nUnderstanding Quantum Superposition\nSuperposition in quantum mechanics is not a simultaneous existence of a particle in multiple positions. Instead, it denotes that the quantum particle exists in a combination of possible states, each with an associated probability amplitude. Until measured or observed, the particle’s exact state remains uncertain.\nGet Anjanakrishnan’s stories in your inbox\nJoin Medium for free to get updates from this writer.\nMathematically, for a quantum system described by a wave function |ψ⟩, it can be in a superposition of basis vectors, which is called basics states in quantum physics, represented as:\nThe Φ’s represent the basis states and a’s represent a complex number and the corresponding basis state’s probability amplitude\nBut doesn’t it look like simultaneously being in multiple states? Let’s take an example where I will consider position coordinates, for simplicity.\nImagine a particle described by a wave function |ψ⟩ = α|0⟩ + β|1⟩, where |0⟩ and |1⟩ represent two possible states. It may initially seem as if the particle exists simultaneously in both states, much like a body at the position 5x + 3y might appear to be at both 5x and 3y coordinates simultaneously. However, this is not the case.\nIn reality, the position 5x + 3y merely represents a point between the linearly independent x and y axes. Similarly, the wave function |ψ⟩ = α|0⟩ + β|1⟩ signifies that the quantum particle exists in a coherent combination of the states |0⟩ and |1⟩ until a measurement is made.\nJust as the body’s position is determined by proportions (5 and 3) along the x and y axes, the quantum particle’s state is determined by the complex probability amplitudes α and β associated with each basis state. These amplitudes represent the probabilities of finding the particle in states |0⟩ and |1⟩ upon measurement.\nThe crucial distinction between classical and quantum systems lies in the measurement process. In classical cases, the function representing a body’s position remains unchanged. However, in quantum mechanics, upon measurement, the wave function collapses to one of the basis states, with probabilities given by the squared magnitudes of the probability amplitudes. This collapse is a fundamental property of quantum mechanics and leads to specific outcomes when measurements are performed.\nIn summary, the analogy with position coordinates clarifies that superposition does not imply simultaneous existence in multiple states. Instead, it denotes a combination of possible states described by the wave function, with a definitive state emerging only upon measurement. coordinates for simplicity.\nPhew!!! That was a lot of math.\nConclusion\nQuantum superposition, a truly intriguing phenomenon, serves as the bedrock for the swiftly evolving Quantum Industry. It forms the backbone of Quantum Computing, which harnesses this enigmatic property to achieve remarkable advancements in various fields.\nIf you want to know a bit about the weird behavior exhibited by particles due to superposition, check out the video by Up and Atom\nAnd if you have more time, you can watch the 1-hour long version of the above video\nReferences","attrs_markdown":"[Sitemap](https:\/\/medium.com\/sitemap\/sitemap.xml)\n\n[Open in app](https:\/\/play.google.com\/store\/apps\/details?id=com.medium.reader&referrer=utm_source%3DmobileNavBar&source=post_page---top_nav_layout_nav-----------------------------------------)\n\nSign up\n\n[Sign in](https:\/\/medium.com\/m\/signin?operation=login&redirect=https%3A%2F%2Fmedium.com%2F%40anjanakrishnan3100%2Fsuperposition-beyond-the-misconceptions-b1a722b41027&source=post_page---top_nav_layout_nav-----------------------global_nav------------------)\n\n[Medium Logo](https:\/\/medium.com\/?source=post_page---top_nav_layout_nav-----------------------------------------)\n\n[Write](https:\/\/medium.com\/m\/signin?operation=register&redirect=https%3A%2F%2Fmedium.com%2Fnew-story&source=---top_nav_layout_nav-----------------------new_post_topnav------------------)\n\n[Search](https:\/\/medium.com\/search?source=post_page---top_nav_layout_nav-----------------------------------------)\n\nSign up\n\n[Sign in](https:\/\/medium.com\/m\/signin?operation=login&redirect=https%3A%2F%2Fmedium.com%2F%40anjanakrishnan3100%2Fsuperposition-beyond-the-misconceptions-b1a722b41027&source=post_page---top_nav_layout_nav-----------------------global_nav------------------)\n\n![](https:\/\/miro.medium.com\/v2\/resize:fill:32:32\/1*dmbNkD5D-u45r44go_cf0g.png)\n\n# Superposition - Beyond the Misconceptions\n[![Anjanakrishnan](https:\/\/miro.medium.com\/v2\/da:true\/resize:fill:32:32\/0*u9mqhRhRykwAenMf)](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---byline--b1a722b41027---------------------------------------)\n\n[Anjanakrishnan](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---byline--b1a722b41027---------------------------------------)\n\nFollow\n\n4 min read\n\n·\n\nAug 5, 2023\n\n21\n\n1\n\n[Listen](https:\/\/medium.com\/m\/signin?actionUrl=https%3A%2F%2Fmedium.com%2Fplans%3Fdimension%3Dpost_audio_button%26postId%3Db1a722b41027&operation=register&redirect=https%3A%2F%2Fmedium.com%2F%40anjanakrishnan3100%2Fsuperposition-beyond-the-misconceptions-b1a722b41027&source=---header_actions--b1a722b41027---------------------post_audio_button------------------)\n\nShare\n\nDay 5- Quantum30 challenge\n\nAs we approach the end of the first week of\n\n[QuantumComputingIndia](https:\/\/medium.com\/u\/1b400b39fb87?source=post_page---user_mention--b1a722b41027---------------------------------------)\n\n’s \\#Quantum30 challenge, it’s essential to explore the concept of ‘Superposition’ in quantum physics. This article provides more of a mathematical interpretation of the term.\n\n**Superposition.** Whenever you search for this word in the context of Quantum Mechanics, the general and most common answer you get is\n\n> ‘Superposition is the ability of a (quantum) particle to exist in multiple states at the same time until its measured’\n\nThis is the definition that I got when I Googled the term. Though for a beginner, this is good and enough, this definition can be misleading at times. Let’s refine our understanding of this concept and clarify any misconceptions that might arise from preconceived notions. In yesterday’s post, we defined a wave function as a **mathematical** tool to represent a particle. So obviously, there is some abstract mathematics involved.\n\n## The Basis of Superposition: Linear Algebra and Vector Spaces\nTo comprehend superposition fully, we must first explore its mathematical foundations. In linear algebra, we encounter vector spaces and basis.\n\nTo keep it simple, if I have the color spectrum and the three primary colors — red, blue, and yellow, then the spectrum is the vector space while the primary colors are the basis. Here, we also have to understand that all these primary colors are completely distinct and independent, which in mathematical terms is known as ‘linearly independent’.\n\nA linear combination is just the addition of basis vectors with a scalar. So for the color green, we get a linear combination\n\nPress enter or click to view image in full size\n\n![](https:\/\/miro.medium.com\/v2\/resize:fit:700\/1*Lmeicn9Eff0ZtbdmlKRmFg.png)\n\nTo get a clearer understanding of these concepts you can refer 3Blue1Brown videos on the fundamentals of linear algebra.\n\n## Wave Function and Its Role in Superposition\nIn the context of quantum mechanics, we use the wave function to represent quantum particles. The wave function is a linear combination of basis states, much like mixing primary colors to create different shades. Each basis state corresponds to a specific quantum state, and the coefficients in the linear combination represent the probability amplitudes associated with each state.\n\n## Understanding Quantum Superposition\nSuperposition in quantum mechanics is not a simultaneous existence of a particle in multiple positions. Instead, it denotes that the quantum particle exists in a combination of possible states, each with an associated probability amplitude. Until measured or observed, the particle’s exact state remains uncertain.\n\n## Get Anjanakrishnan’s stories in your inbox\nJoin Medium for free to get updates from this writer.\n\nSubscribe\n\nSubscribe\n\nMathematically, for a quantum system described by a wave function \\|ψ⟩, it can be in a superposition of basis vectors, which is called basics states in quantum physics, represented as:\n\n![Here, all the Φ’s represent the basics states and a’s represent the corresponding](https:\/\/miro.medium.com\/v2\/resize:fit:578\/1*tA3Y_cKMJjsxhwUZ6F9s5Q.png)\n\nThe Φ’s represent the basis states and a’s represent a complex number and the corresponding basis state’s probability amplitude\n\nBut doesn’t it look like simultaneously being in multiple states? Let’s take an example where I will consider position coordinates, for simplicity.\n\nImagine a particle described by a wave function \\|ψ⟩ = α\\|0⟩ + β\\|1⟩, where \\|0⟩ and \\|1⟩ represent two possible states. It may initially seem as if the particle exists simultaneously in both states, much like a body at the position 5x + 3y might appear to be at both 5x and 3y coordinates simultaneously. However, this is not the case.\n\nIn reality, the position 5x + 3y merely represents a point between the linearly independent x and y axes. Similarly, the wave function \\|ψ⟩ = α\\|0⟩ + β\\|1⟩ signifies that the quantum particle exists in a coherent combination of the states \\|0⟩ and \\|1⟩ until a measurement is made.\n\nJust as the body’s position is determined by proportions (5 and 3) along the x and y axes, the quantum particle’s state is determined by the complex probability amplitudes α and β associated with each basis state. These amplitudes represent the probabilities of finding the particle in states \\|0⟩ and \\|1⟩ upon measurement.\n\nThe crucial distinction between classical and quantum systems lies in the measurement process. In classical cases, the function representing a body’s position remains unchanged. However, in quantum mechanics, upon measurement, the wave function collapses to one of the basis states, with probabilities given by the squared magnitudes of the probability amplitudes. This collapse is a fundamental property of quantum mechanics and leads to specific outcomes when measurements are performed.\n\nIn summary, the analogy with position coordinates clarifies that superposition does not imply simultaneous existence in multiple states. Instead, it denotes a combination of possible states described by the wave function, with a definitive state emerging only upon measurement. coordinates for simplicity.\n\nPhew!!! That was a lot of math.\n\n## Conclusion\nQuantum superposition, a truly intriguing phenomenon, serves as the bedrock for the swiftly evolving Quantum Industry. It forms the backbone of Quantum Computing, which harnesses this enigmatic property to achieve remarkable advancements in various fields.\n\nIf you want to know a bit about the weird behavior exhibited by particles due to superposition, check out the video by Up and Atom\n\nAnd if you have more time, you can watch the 1-hour long version of the above video\n\n## References\n\n[Quantum Physics](https:\/\/medium.com\/tag\/quantum-physics?source=post_page-----b1a722b41027---------------------------------------)\n\n[Quantum Superposition](https:\/\/medium.com\/tag\/quantum-superposition?source=post_page-----b1a722b41027---------------------------------------)\n\n[Quantum Mechanics](https:\/\/medium.com\/tag\/quantum-mechanics?source=post_page-----b1a722b41027---------------------------------------)\n\n[Linear Algebra](https:\/\/medium.com\/tag\/linear-algebra?source=post_page-----b1a722b41027---------------------------------------)\n\n[Quantum Computing](https:\/\/medium.com\/tag\/quantum-computing?source=post_page-----b1a722b41027---------------------------------------)\n\n21\n\n21\n\n1\n\n[![Anjanakrishnan](https:\/\/miro.medium.com\/v2\/resize:fill:48:48\/0*u9mqhRhRykwAenMf)](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---post_author_info--b1a722b41027---------------------------------------)\n\n[![Anjanakrishnan](https:\/\/miro.medium.com\/v2\/resize:fill:64:64\/0*u9mqhRhRykwAenMf)](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---post_author_info--b1a722b41027---------------------------------------)\n\nFollow\n\n[Written by Anjanakrishnan](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---post_author_info--b1a722b41027---------------------------------------)\n\n[160 followers](https:\/\/medium.com\/@anjanakrishnan3100\/followers?source=post_page---post_author_info--b1a722b41027---------------------------------------)\n\n·[28 following](https:\/\/medium.com\/@anjanakrishnan3100\/following?source=post_page---post_author_info--b1a722b41027---------------------------------------)\n\nA curious learner.\n\nFollow\n\n## Responses (1)\n![](https:\/\/miro.medium.com\/v2\/resize:fill:32:32\/1*dmbNkD5D-u45r44go_cf0g.png)\n\nWrite a response\n\n[What are your thoughts?](https:\/\/medium.com\/m\/signin?operation=register&redirect=https%3A%2F%2Fmedium.com%2F%40anjanakrishnan3100%2Fsuperposition-beyond-the-misconceptions-b1a722b41027&source=---post_responses--b1a722b41027---------------------respond_sidebar------------------)\n\nCancel\n\nRespond\n\n[![Kshitij Gurumoorthy](https:\/\/miro.medium.com\/v2\/resize:fill:32:32\/1*_IY38QkJ4aqg_VlD-ZmZ1A.jpeg)](https:\/\/medium.com\/@kshitijguru256?source=post_page---post_responses--b1a722b41027----0-----------------------------------)\n\n[Kshitij Gurumoorthy](https:\/\/medium.com\/@kshitijguru256?source=post_page---post_responses--b1a722b41027----0-----------------------------------)\n\n[Aug 5, 2023 (edited)](https:\/\/medium.com\/@kshitijguru256\/greatly-written-ab62923f7989?source=post_page---post_responses--b1a722b41027----0-----------------------------------)\n```\nGreatly written. Took time to understand, had to do some Google searches to finally come to the conclusion that this quantum superposition is directly related to Young's double-slit experiment (or at least conceptually). Correct me if I'm wrong :D1… more\n```\n1 reply\n\nReply\n\n## More from Anjanakrishnan\n![Quantum Annealing for absolute beginners](https:\/\/miro.medium.com\/v2\/resize:fit:679\/format:webp\/0*T_UUcH2HHZhVEl3E.png)\n\n[![Anjanakrishnan](https:\/\/miro.medium.com\/v2\/resize:fill:20:20\/0*u9mqhRhRykwAenMf)](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----0---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n[Anjanakrishnan](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----0---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n[Quantum Annealing for absolute beginnersDay 14 — Quantum30 Challenge](https:\/\/medium.com\/@anjanakrishnan3100\/quantum-annealing-for-absolute-beginners-d38c51ac2b3f?source=post_page---author_recirc--b1a722b41027----0---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\nAug 14, 2023\n\n[A clap icon 9](https:\/\/medium.com\/@anjanakrishnan3100\/quantum-annealing-for-absolute-beginners-d38c51ac2b3f?source=post_page---author_recirc--b1a722b41027----0---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n![Quantum Cryptography for absolute beginners](https:\/\/miro.medium.com\/v2\/resize:fit:679\/format:webp\/0*5j12taJOYyYSDrtk.png)\n\n[![Anjanakrishnan](https:\/\/miro.medium.com\/v2\/resize:fill:20:20\/0*u9mqhRhRykwAenMf)](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----1---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n[Anjanakrishnan](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----1---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n[Quantum Cryptography for absolute beginnersDay 16 — Quantum30 Challenge](https:\/\/medium.com\/@anjanakrishnan3100\/quantum-cryptography-for-absolute-beginners-5e74b09401d?source=post_page---author_recirc--b1a722b41027----1---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\nAug 16, 2023\n\n[A clap icon 23](https:\/\/medium.com\/@anjanakrishnan3100\/quantum-cryptography-for-absolute-beginners-5e74b09401d?source=post_page---author_recirc--b1a722b41027----1---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n![DiVincenzo's Criteria for absolute beginners](https:\/\/miro.medium.com\/v2\/resize:fit:679\/format:webp\/0*j2jR00umx3hAiny6.png)\n\n[![Anjanakrishnan](https:\/\/miro.medium.com\/v2\/resize:fill:20:20\/0*u9mqhRhRykwAenMf)](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----2---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n[Anjanakrishnan](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----2---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n[DiVincenzo's Criteria for absolute beginnersDay 13 — Quantum30 Challenge](https:\/\/medium.com\/@anjanakrishnan3100\/divincenzos-criteria-for-absolute-beginners-f7f40a45bdb7?source=post_page---author_recirc--b1a722b41027----2---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\nAug 13, 2023\n\n[A clap icon 6](https:\/\/medium.com\/@anjanakrishnan3100\/divincenzos-criteria-for-absolute-beginners-f7f40a45bdb7?source=post_page---author_recirc--b1a722b41027----2---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n![QNN — A beginner’s overview and breakdown of code](https:\/\/miro.medium.com\/v2\/resize:fit:679\/format:webp\/1*ddYL8602tdtWB3fQngfT3Q.png)\n\n[![Anjanakrishnan](https:\/\/miro.medium.com\/v2\/resize:fill:20:20\/0*u9mqhRhRykwAenMf)](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----3---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n[Anjanakrishnan](https:\/\/medium.com\/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----3---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------)\n\n[QNN — A beginner’s overview and breakdown of codeDay 10 — Quantum30 Challenge 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The universe is unimaginably vast, billions of galaxies…](https:\/\/medium.com\/@kyeq1\/the-great-perceptual-filter-the-terrifying-reason-the-universe-feels-empty-58460b3fe9b8?source=post_page---read_next_recirc--b1a722b41027----1---------------------d7f7b3cd_9e72_40c5_98cc_b22a888b8e1f--------------)\n\n3d ago\n\n[A clap icon 139A response icon 10](https:\/\/medium.com\/@kyeq1\/the-great-perceptual-filter-the-terrifying-reason-the-universe-feels-empty-58460b3fe9b8?source=post_page---read_next_recirc--b1a722b41027----1---------------------d7f7b3cd_9e72_40c5_98cc_b22a888b8e1f--------------)\n\n![VQE & QAOA in Python: A Step‑by‑Step PyMC Variational Guide](https:\/\/miro.medium.com\/v2\/resize:fit:679\/format:webp\/1*eQQd6G_GwwJItlZ2hB_8pw.png)\n\n[![QuarkAndCode](https:\/\/miro.medium.com\/v2\/resize:fill:20:20\/1*N098LoAzsqGv17g66NlrDA.jpeg)](https:\/\/medium.com\/@QuarkAndCode?source=post_page---read_next_recirc--b1a722b41027----2---------------------d7f7b3cd_9e72_40c5_98cc_b22a888b8e1f--------------)\n\n[QuarkAndCode](https:\/\/medium.com\/@QuarkAndCode?source=post_page---read_next_recirc--b1a722b41027----2---------------------d7f7b3cd_9e72_40c5_98cc_b22a888b8e1f--------------)\n\n[VQE & QAOA in Python: A Step‑by‑Step PyMC Variational GuideLearn to build VQE and QAOA in Python using PyMC’s variational API — step by step workflows, ADVI\/ELBO tracking, callbacks, and a Max Cut…](https:\/\/medium.com\/@QuarkAndCode\/vqe-qaoa-in-python-a-step-by-step-pymc-variational-guide-7628c3007ac0?source=post_page---read_next_recirc--b1a722b41027----2---------------------d7f7b3cd_9e72_40c5_98cc_b22a888b8e1f--------------)\n\nSep 29, 2025\n\n![From Vacuum Tubes to Nanosheets: The Complete History of the Transistor — How We Got Here and What…](https:\/\/miro.medium.com\/v2\/resize:fit:679\/format:webp\/1*k78jU6CqIr-D0LlESr6f3A.png)\n\n[![Radha Kulkarni](https:\/\/miro.medium.com\/v2\/resize:fill:20:20\/1*Wc9l3r5uc7KPbkDwOLS7bA.jpeg)](https:\/\/medium.com\/@iamRadhaKulkarni?source=post_page---read_next_recirc--b1a722b41027----3---------------------d7f7b3cd_9e72_40c5_98cc_b22a888b8e1f--------------)\n\n[Radha Kulkarni](https:\/\/medium.com\/@iamRadhaKulkarni?source=post_page---read_next_recirc--b1a722b41027----3---------------------d7f7b3cd_9e72_40c5_98cc_b22a888b8e1f--------------)\n\n[From Vacuum Tubes to Nanosheets: The Complete History of the Transistor — How We Got Here and What…There are inventions that quietly rearrange the world. 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This article provides more of a mathematical interpretation of the term.\n\n**Superposition.** Whenever you search for this word in the context of Quantum Mechanics, the general and most common answer you get is\n\n> ‘Superposition is the ability of a (quantum) particle to exist in multiple states at the same time until its measured’\n\nThis is the definition that I got when I Googled the term. Though for a beginner, this is good and enough, this definition can be misleading at times. Let’s refine our understanding of this concept and clarify any misconceptions that might arise from preconceived notions. In yesterday’s post, we defined a wave function as a **mathematical** tool to represent a particle. So obviously, there is some abstract mathematics involved.\n\n## The Basis of Superposition: Linear Algebra and Vector Spaces\nTo comprehend superposition fully, we must first explore its mathematical foundations. In linear algebra, we encounter vector spaces and basis.\n\nTo keep it simple, if I have the color spectrum and the three primary colors — red, blue, and yellow, then the spectrum is the vector space while the primary colors are the basis. Here, we also have to understand that all these primary colors are completely distinct and independent, which in mathematical terms is known as ‘linearly independent’.\n\nA linear combination is just the addition of basis vectors with a scalar. So for the color green, we get a linear combination\n\nPress enter or click to view image in full size\n\n![](https:\/\/miro.medium.com\/v2\/resize:fit:700\/1*Lmeicn9Eff0ZtbdmlKRmFg.png)\n\nTo get a clearer understanding of these concepts you can refer 3Blue1Brown videos on the fundamentals of linear algebra.\n\n## Wave Function and Its Role in Superposition\nIn the context of quantum mechanics, we use the wave function to represent quantum particles. The wave function is a linear combination of basis states, much like mixing primary colors to create different shades. Each basis state corresponds to a specific quantum state, and the coefficients in the linear combination represent the probability amplitudes associated with each state.\n\n## Understanding Quantum Superposition\nSuperposition in quantum mechanics is not a simultaneous existence of a particle in multiple positions. Instead, it denotes that the quantum particle exists in a combination of possible states, each with an associated probability amplitude. Until measured or observed, the particle’s exact state remains uncertain.\n\nGet Anjanakrishnan’s stories in your inbox\n\nJoin Medium for free to get updates from this writer.\n\nMathematically, for a quantum system described by a wave function \\|ψ⟩, it can be in a superposition of basis vectors, which is called basics states in quantum physics, represented as:\n\n![Here, all the Φ’s represent the basics states and a’s represent the corresponding](https:\/\/miro.medium.com\/v2\/resize:fit:578\/1*tA3Y_cKMJjsxhwUZ6F9s5Q.png)\n\nThe Φ’s represent the basis states and a’s represent a complex number and the corresponding basis state’s probability amplitude\n\nBut doesn’t it look like simultaneously being in multiple states? Let’s take an example where I will consider position coordinates, for simplicity.\n\nImagine a particle described by a wave function \\|ψ⟩ = α\\|0⟩ + β\\|1⟩, where \\|0⟩ and \\|1⟩ represent two possible states. It may initially seem as if the particle exists simultaneously in both states, much like a body at the position 5x + 3y might appear to be at both 5x and 3y coordinates simultaneously. However, this is not the case.\n\nIn reality, the position 5x + 3y merely represents a point between the linearly independent x and y axes. Similarly, the wave function \\|ψ⟩ = α\\|0⟩ + β\\|1⟩ signifies that the quantum particle exists in a coherent combination of the states \\|0⟩ and \\|1⟩ until a measurement is made.\n\nJust as the body’s position is determined by proportions (5 and 3) along the x and y axes, the quantum particle’s state is determined by the complex probability amplitudes α and β associated with each basis state. These amplitudes represent the probabilities of finding the particle in states \\|0⟩ and \\|1⟩ upon measurement.\n\nThe crucial distinction between classical and quantum systems lies in the measurement process. In classical cases, the function representing a body’s position remains unchanged. However, in quantum mechanics, upon measurement, the wave function collapses to one of the basis states, with probabilities given by the squared magnitudes of the probability amplitudes. This collapse is a fundamental property of quantum mechanics and leads to specific outcomes when measurements are performed.\n\nIn summary, the analogy with position coordinates clarifies that superposition does not imply simultaneous existence in multiple states. Instead, it denotes a combination of possible states described by the wave function, with a definitive state emerging only upon measurement. coordinates for simplicity.\n\nPhew!!! That was a lot of math.\n\n## Conclusion\nQuantum superposition, a truly intriguing phenomenon, serves as the bedrock for the swiftly evolving Quantum Industry. It forms the backbone of Quantum Computing, which harnesses this enigmatic property to achieve remarkable advancements in various fields.\n\nIf you want to know a bit about the weird behavior exhibited by particles due to superposition, check out the video by Up and Atom\n\nAnd if you have more time, you can watch the 1-hour long version of the above video\n\n## References","meta_canonical":null}

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Meta Description	Superposition - Beyond the Misconceptions Day 5- Quantum30 challenge As we approach the end of the first week of QuantumComputingIndia’s #Quantum30 challenge, it’s essential to explore the …
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Boilerpipe Text	4 min read Aug 5, 2023 Day 5- Quantum30 challenge As we approach the end of the first week of ’s #Quantum30 challenge, it’s essential to explore the concept of ‘Superposition’ in quantum physics. This article provides more of a mathematical interpretation of the term. Superposition. Whenever you search for this word in the context of Quantum Mechanics, the general and most common answer you get is ‘Superposition is the ability of a (quantum) particle to exist in multiple states at the same time until its measured’ This is the definition that I got when I Googled the term. Though for a beginner, this is good and enough, this definition can be misleading at times. Let’s refine our understanding of this concept and clarify any misconceptions that might arise from preconceived notions. In yesterday’s post, we defined a wave function as a mathematical tool to represent a particle. So obviously, there is some abstract mathematics involved. The Basis of Superposition: Linear Algebra and Vector Spaces To comprehend superposition fully, we must first explore its mathematical foundations. In linear algebra, we encounter vector spaces and basis. To keep it simple, if I have the color spectrum and the three primary colors — red, blue, and yellow, then the spectrum is the vector space while the primary colors are the basis. Here, we also have to understand that all these primary colors are completely distinct and independent, which in mathematical terms is known as ‘linearly independent’. A linear combination is just the addition of basis vectors with a scalar. So for the color green, we get a linear combination Press enter or click to view image in full size To get a clearer understanding of these concepts you can refer 3Blue1Brown videos on the fundamentals of linear algebra. Wave Function and Its Role in Superposition In the context of quantum mechanics, we use the wave function to represent quantum particles. The wave function is a linear combination of basis states, much like mixing primary colors to create different shades. Each basis state corresponds to a specific quantum state, and the coefficients in the linear combination represent the probability amplitudes associated with each state. Understanding Quantum Superposition Superposition in quantum mechanics is not a simultaneous existence of a particle in multiple positions. Instead, it denotes that the quantum particle exists in a combination of possible states, each with an associated probability amplitude. Until measured or observed, the particle’s exact state remains uncertain. Get Anjanakrishnan’s stories in your inbox Join Medium for free to get updates from this writer. Mathematically, for a quantum system described by a wave function \|ψ⟩, it can be in a superposition of basis vectors, which is called basics states in quantum physics, represented as: The Φ’s represent the basis states and a’s represent a complex number and the corresponding basis state’s probability amplitude But doesn’t it look like simultaneously being in multiple states? Let’s take an example where I will consider position coordinates, for simplicity. Imagine a particle described by a wave function \|ψ⟩ = α\|0⟩ + β\|1⟩, where \|0⟩ and \|1⟩ represent two possible states. It may initially seem as if the particle exists simultaneously in both states, much like a body at the position 5x + 3y might appear to be at both 5x and 3y coordinates simultaneously. However, this is not the case. In reality, the position 5x + 3y merely represents a point between the linearly independent x and y axes. Similarly, the wave function \|ψ⟩ = α\|0⟩ + β\|1⟩ signifies that the quantum particle exists in a coherent combination of the states \|0⟩ and \|1⟩ until a measurement is made. Just as the body’s position is determined by proportions (5 and 3) along the x and y axes, the quantum particle’s state is determined by the complex probability amplitudes α and β associated with each basis state. These amplitudes represent the probabilities of finding the particle in states \|0⟩ and \|1⟩ upon measurement. The crucial distinction between classical and quantum systems lies in the measurement process. In classical cases, the function representing a body’s position remains unchanged. However, in quantum mechanics, upon measurement, the wave function collapses to one of the basis states, with probabilities given by the squared magnitudes of the probability amplitudes. This collapse is a fundamental property of quantum mechanics and leads to specific outcomes when measurements are performed. In summary, the analogy with position coordinates clarifies that superposition does not imply simultaneous existence in multiple states. Instead, it denotes a combination of possible states described by the wave function, with a definitive state emerging only upon measurement. coordinates for simplicity. Phew!!! That was a lot of math. Conclusion Quantum superposition, a truly intriguing phenomenon, serves as the bedrock for the swiftly evolving Quantum Industry. It forms the backbone of Quantum Computing, which harnesses this enigmatic property to achieve remarkable advancements in various fields. If you want to know a bit about the weird behavior exhibited by particles due to superposition, check out the video by Up and Atom And if you have more time, you can watch the 1-hour long version of the above video References
Markdown	[Sitemap](https://medium.com/sitemap/sitemap.xml) [Open in app](https://play.google.com/store/apps/details?id=com.medium.reader&referrer=utm_source%3DmobileNavBar&source=post_page---top_nav_layout_nav-----------------------------------------) Sign up [Sign in](https://medium.com/m/signin?operation=login&redirect=https%3A%2F%2Fmedium.com%2F%40anjanakrishnan3100%2Fsuperposition-beyond-the-misconceptions-b1a722b41027&source=post_page---top_nav_layout_nav-----------------------global_nav------------------) [Medium Logo](https://medium.com/?source=post_page---top_nav_layout_nav-----------------------------------------) [Write](https://medium.com/m/signin?operation=register&redirect=https%3A%2F%2Fmedium.com%2Fnew-story&source=---top_nav_layout_nav-----------------------new_post_topnav------------------) [Search](https://medium.com/search?source=post_page---top_nav_layout_nav-----------------------------------------) Sign up [Sign in](https://medium.com/m/signin?operation=login&redirect=https%3A%2F%2Fmedium.com%2F%40anjanakrishnan3100%2Fsuperposition-beyond-the-misconceptions-b1a722b41027&source=post_page---top_nav_layout_nav-----------------------global_nav------------------) ![](https://miro.medium.com/v2/resize:fill:32:32/1dmbNkD5D-u45r44go_cf0g.png) # Superposition - Beyond the Misconceptions [![Anjanakrishnan](https://miro.medium.com/v2/da:true/resize:fill:32:32/0u9mqhRhRykwAenMf)](https://medium.com/@anjanakrishnan3100?source=post_page---byline--b1a722b41027---------------------------------------) [Anjanakrishnan](https://medium.com/@anjanakrishnan3100?source=post_page---byline--b1a722b41027---------------------------------------) Follow 4 min read · Aug 5, 2023 21 1 [Listen](https://medium.com/m/signin?actionUrl=https%3A%2F%2Fmedium.com%2Fplans%3Fdimension%3Dpost_audio_button%26postId%3Db1a722b41027&operation=register&redirect=https%3A%2F%2Fmedium.com%2F%40anjanakrishnan3100%2Fsuperposition-beyond-the-misconceptions-b1a722b41027&source=---header_actions--b1a722b41027---------------------post_audio_button------------------) Share Day 5- Quantum30 challenge As we approach the end of the first week of [QuantumComputingIndia](https://medium.com/u/1b400b39fb87?source=post_page---user_mention--b1a722b41027---------------------------------------) ’s \#Quantum30 challenge, it’s essential to explore the concept of ‘Superposition’ in quantum physics. This article provides more of a mathematical interpretation of the term. Superposition. Whenever you search for this word in the context of Quantum Mechanics, the general and most common answer you get is > ‘Superposition is the ability of a (quantum) particle to exist in multiple states at the same time until its measured’ This is the definition that I got when I Googled the term. Though for a beginner, this is good and enough, this definition can be misleading at times. Let’s refine our understanding of this concept and clarify any misconceptions that might arise from preconceived notions. In yesterday’s post, we defined a wave function as a mathematical tool to represent a particle. So obviously, there is some abstract mathematics involved. ## The Basis of Superposition: Linear Algebra and Vector Spaces To comprehend superposition fully, we must first explore its mathematical foundations. In linear algebra, we encounter vector spaces and basis. To keep it simple, if I have the color spectrum and the three primary colors — red, blue, and yellow, then the spectrum is the vector space while the primary colors are the basis. Here, we also have to understand that all these primary colors are completely distinct and independent, which in mathematical terms is known as ‘linearly independent’. A linear combination is just the addition of basis vectors with a scalar. So for the color green, we get a linear combination Press enter or click to view image in full size ![](https://miro.medium.com/v2/resize:fit:700/1Lmeicn9Eff0ZtbdmlKRmFg.png) To get a clearer understanding of these concepts you can refer 3Blue1Brown videos on the fundamentals of linear algebra. ## Wave Function and Its Role in Superposition In the context of quantum mechanics, we use the wave function to represent quantum particles. The wave function is a linear combination of basis states, much like mixing primary colors to create different shades. Each basis state corresponds to a specific quantum state, and the coefficients in the linear combination represent the probability amplitudes associated with each state. ## Understanding Quantum Superposition Superposition in quantum mechanics is not a simultaneous existence of a particle in multiple positions. Instead, it denotes that the quantum particle exists in a combination of possible states, each with an associated probability amplitude. Until measured or observed, the particle’s exact state remains uncertain. ## Get Anjanakrishnan’s stories in your inbox Join Medium for free to get updates from this writer. Subscribe Subscribe Mathematically, for a quantum system described by a wave function \\|ψ⟩, it can be in a superposition of basis vectors, which is called basics states in quantum physics, represented as: ![Here, all the Φ’s represent the basics states and a’s represent the corresponding](https://miro.medium.com/v2/resize:fit:578/1tA3Y_cKMJjsxhwUZ6F9s5Q.png) The Φ’s represent the basis states and a’s represent a complex number and the corresponding basis state’s probability amplitude But doesn’t it look like simultaneously being in multiple states? Let’s take an example where I will consider position coordinates, for simplicity. Imagine a particle described by a wave function \\|ψ⟩ = α\\|0⟩ + β\\|1⟩, where \\|0⟩ and \\|1⟩ represent two possible states. It may initially seem as if the particle exists simultaneously in both states, much like a body at the position 5x + 3y might appear to be at both 5x and 3y coordinates simultaneously. However, this is not the case. In reality, the position 5x + 3y merely represents a point between the linearly independent x and y axes. Similarly, the wave function \\|ψ⟩ = α\\|0⟩ + β\\|1⟩ signifies that the quantum particle exists in a coherent combination of the states \\|0⟩ and \\|1⟩ until a measurement is made. Just as the body’s position is determined by proportions (5 and 3) along the x and y axes, the quantum particle’s state is determined by the complex probability amplitudes α and β associated with each basis state. These amplitudes represent the probabilities of finding the particle in states \\|0⟩ and \\|1⟩ upon measurement. The crucial distinction between classical and quantum systems lies in the measurement process. In classical cases, the function representing a body’s position remains unchanged. However, in quantum mechanics, upon measurement, the wave function collapses to one of the basis states, with probabilities given by the squared magnitudes of the probability amplitudes. This collapse is a fundamental property of quantum mechanics and leads to specific outcomes when measurements are performed. In summary, the analogy with position coordinates clarifies that superposition does not imply simultaneous existence in multiple states. Instead, it denotes a combination of possible states described by the wave function, with a definitive state emerging only upon measurement. coordinates for simplicity. Phew!!! That was a lot of math. ## Conclusion Quantum superposition, a truly intriguing phenomenon, serves as the bedrock for the swiftly evolving Quantum Industry. It forms the backbone of Quantum Computing, which harnesses this enigmatic property to achieve remarkable advancements in various fields. If you want to know a bit about the weird behavior exhibited by particles due to superposition, check out the video by Up and Atom And if you have more time, you can watch the 1-hour long version of the above video ## References [Quantum Physics](https://medium.com/tag/quantum-physics?source=post_page-----b1a722b41027---------------------------------------) [Quantum Superposition](https://medium.com/tag/quantum-superposition?source=post_page-----b1a722b41027---------------------------------------) [Quantum Mechanics](https://medium.com/tag/quantum-mechanics?source=post_page-----b1a722b41027---------------------------------------) [Linear Algebra](https://medium.com/tag/linear-algebra?source=post_page-----b1a722b41027---------------------------------------) [Quantum Computing](https://medium.com/tag/quantum-computing?source=post_page-----b1a722b41027---------------------------------------) 21 21 1 [![Anjanakrishnan](https://miro.medium.com/v2/resize:fill:48:48/0u9mqhRhRykwAenMf)](https://medium.com/@anjanakrishnan3100?source=post_page---post_author_info--b1a722b41027---------------------------------------) [![Anjanakrishnan](https://miro.medium.com/v2/resize:fill:64:64/0u9mqhRhRykwAenMf)](https://medium.com/@anjanakrishnan3100?source=post_page---post_author_info--b1a722b41027---------------------------------------) Follow [Written by Anjanakrishnan](https://medium.com/@anjanakrishnan3100?source=post_page---post_author_info--b1a722b41027---------------------------------------) [160 followers](https://medium.com/@anjanakrishnan3100/followers?source=post_page---post_author_info--b1a722b41027---------------------------------------) ·[28 following](https://medium.com/@anjanakrishnan3100/following?source=post_page---post_author_info--b1a722b41027---------------------------------------) A curious learner. Follow ## Responses (1) ![](https://miro.medium.com/v2/resize:fill:32:32/1dmbNkD5D-u45r44go_cf0g.png) Write a response [What are your thoughts?](https://medium.com/m/signin?operation=register&redirect=https%3A%2F%2Fmedium.com%2F%40anjanakrishnan3100%2Fsuperposition-beyond-the-misconceptions-b1a722b41027&source=---post_responses--b1a722b41027---------------------respond_sidebar------------------) Cancel Respond [![Kshitij Gurumoorthy](https://miro.medium.com/v2/resize:fill:32:32/1_IY38QkJ4aqg_VlD-ZmZ1A.jpeg)](https://medium.com/@kshitijguru256?source=post_page---post_responses--b1a722b41027----0-----------------------------------) [Kshitij Gurumoorthy](https://medium.com/@kshitijguru256?source=post_page---post_responses--b1a722b41027----0-----------------------------------) [Aug 5, 2023 (edited)](https://medium.com/@kshitijguru256/greatly-written-ab62923f7989?source=post_page---post_responses--b1a722b41027----0-----------------------------------) ``` Greatly written. Took time to understand, had to do some Google searches to finally come to the conclusion that this quantum superposition is directly related to Young's double-slit experiment (or at least conceptually). Correct me if I'm wrong :D1… more ``` 1 reply Reply ## More from Anjanakrishnan ![Quantum Annealing for absolute beginners](https://miro.medium.com/v2/resize:fit:679/format:webp/0T_UUcH2HHZhVEl3E.png) [![Anjanakrishnan](https://miro.medium.com/v2/resize:fill:20:20/0u9mqhRhRykwAenMf)](https://medium.com/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----0---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) [Anjanakrishnan](https://medium.com/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----0---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) [Quantum Annealing for absolute beginnersDay 14 — Quantum30 Challenge](https://medium.com/@anjanakrishnan3100/quantum-annealing-for-absolute-beginners-d38c51ac2b3f?source=post_page---author_recirc--b1a722b41027----0---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) Aug 14, 2023 [A clap icon 9](https://medium.com/@anjanakrishnan3100/quantum-annealing-for-absolute-beginners-d38c51ac2b3f?source=post_page---author_recirc--b1a722b41027----0---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) ![Quantum Cryptography for absolute beginners](https://miro.medium.com/v2/resize:fit:679/format:webp/05j12taJOYyYSDrtk.png) [![Anjanakrishnan](https://miro.medium.com/v2/resize:fill:20:20/0u9mqhRhRykwAenMf)](https://medium.com/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----1---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) [Anjanakrishnan](https://medium.com/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----1---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) [Quantum Cryptography for absolute beginnersDay 16 — Quantum30 Challenge](https://medium.com/@anjanakrishnan3100/quantum-cryptography-for-absolute-beginners-5e74b09401d?source=post_page---author_recirc--b1a722b41027----1---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) Aug 16, 2023 [A clap icon 23](https://medium.com/@anjanakrishnan3100/quantum-cryptography-for-absolute-beginners-5e74b09401d?source=post_page---author_recirc--b1a722b41027----1---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) ![DiVincenzo's Criteria for absolute beginners](https://miro.medium.com/v2/resize:fit:679/format:webp/0j2jR00umx3hAiny6.png) [![Anjanakrishnan](https://miro.medium.com/v2/resize:fill:20:20/0u9mqhRhRykwAenMf)](https://medium.com/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----2---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) [Anjanakrishnan](https://medium.com/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----2---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) [DiVincenzo's Criteria for absolute beginnersDay 13 — Quantum30 Challenge](https://medium.com/@anjanakrishnan3100/divincenzos-criteria-for-absolute-beginners-f7f40a45bdb7?source=post_page---author_recirc--b1a722b41027----2---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) Aug 13, 2023 [A clap icon 6](https://medium.com/@anjanakrishnan3100/divincenzos-criteria-for-absolute-beginners-f7f40a45bdb7?source=post_page---author_recirc--b1a722b41027----2---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) ![QNN — A beginner’s overview and breakdown of code](https://miro.medium.com/v2/resize:fit:679/format:webp/1ddYL8602tdtWB3fQngfT3Q.png) [![Anjanakrishnan](https://miro.medium.com/v2/resize:fill:20:20/0u9mqhRhRykwAenMf)](https://medium.com/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----3---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) [Anjanakrishnan](https://medium.com/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027----3---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) [QNN — A beginner’s overview and breakdown of codeDay 10 — Quantum30 Challenge 2.0](https://medium.com/@anjanakrishnan3100/qnn-a-beginners-overview-and-breakdown-of-code-d4f62a0947f2?source=post_page---author_recirc--b1a722b41027----3---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) Sep 10, 2023 [A clap icon 12A response icon 2](https://medium.com/@anjanakrishnan3100/qnn-a-beginners-overview-and-breakdown-of-code-d4f62a0947f2?source=post_page---author_recirc--b1a722b41027----3---------------------3669fe15_5190_446c_80c2_b3ac4eb5798a--------------) [See all from Anjanakrishnan](https://medium.com/@anjanakrishnan3100?source=post_page---author_recirc--b1a722b41027---------------------------------------) ## 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Readable Markdown	[![Anjanakrishnan](https://miro.medium.com/v2/da:true/resize:fill:32:32/0u9mqhRhRykwAenMf)](https://medium.com/@anjanakrishnan3100?source=post_page---byline--b1a722b41027---------------------------------------) 4 min read Aug 5, 2023 Day 5- Quantum30 challenge As we approach the end of the first week of ’s \#Quantum30 challenge, it’s essential to explore the concept of ‘Superposition’ in quantum physics. This article provides more of a mathematical interpretation of the term. Superposition.* Whenever you search for this word in the context of Quantum Mechanics, the general and most common answer you get is > ‘Superposition is the ability of a (quantum) particle to exist in multiple states at the same time until its measured’ This is the definition that I got when I Googled the term. Though for a beginner, this is good and enough, this definition can be misleading at times. Let’s refine our understanding of this concept and clarify any misconceptions that might arise from preconceived notions. In yesterday’s post, we defined a wave function as a mathematical tool to represent a particle. So obviously, there is some abstract mathematics involved. ## The Basis of Superposition: Linear Algebra and Vector Spaces To comprehend superposition fully, we must first explore its mathematical foundations. In linear algebra, we encounter vector spaces and basis. To keep it simple, if I have the color spectrum and the three primary colors — red, blue, and yellow, then the spectrum is the vector space while the primary colors are the basis. Here, we also have to understand that all these primary colors are completely distinct and independent, which in mathematical terms is known as ‘linearly independent’. A linear combination is just the addition of basis vectors with a scalar. So for the color green, we get a linear combination Press enter or click to view image in full size ![](https://miro.medium.com/v2/resize:fit:700/1Lmeicn9Eff0ZtbdmlKRmFg.png) To get a clearer understanding of these concepts you can refer 3Blue1Brown videos on the fundamentals of linear algebra. ## Wave Function and Its Role in Superposition In the context of quantum mechanics, we use the wave function to represent quantum particles. The wave function is a linear combination of basis states, much like mixing primary colors to create different shades. Each basis state corresponds to a specific quantum state, and the coefficients in the linear combination represent the probability amplitudes associated with each state. ## Understanding Quantum Superposition Superposition in quantum mechanics is not a simultaneous existence of a particle in multiple positions. Instead, it denotes that the quantum particle exists in a combination of possible states, each with an associated probability amplitude. Until measured or observed, the particle’s exact state remains uncertain. Get Anjanakrishnan’s stories in your inbox Join Medium for free to get updates from this writer. Mathematically, for a quantum system described by a wave function \\|ψ⟩, it can be in a superposition of basis vectors, which is called basics states in quantum physics, represented as: ![Here, all the Φ’s represent the basics states and a’s represent the corresponding](https://miro.medium.com/v2/resize:fit:578/1tA3Y_cKMJjsxhwUZ6F9s5Q.png) The Φ’s represent the basis states and a’s represent a complex number and the corresponding basis state’s probability amplitude But doesn’t it look like simultaneously being in multiple states? Let’s take an example where I will consider position coordinates, for simplicity. Imagine a particle described by a wave function \\|ψ⟩ = α\\|0⟩ + β\\|1⟩, where \\|0⟩ and \\|1⟩ represent two possible states. It may initially seem as if the particle exists simultaneously in both states, much like a body at the position 5x + 3y might appear to be at both 5x and 3y coordinates simultaneously. However, this is not the case. In reality, the position 5x + 3y merely represents a point between the linearly independent x and y axes. Similarly, the wave function \\|ψ⟩ = α\\|0⟩ + β\\|1⟩ signifies that the quantum particle exists in a coherent combination of the states \\|0⟩ and \\|1⟩ until a measurement is made. Just as the body’s position is determined by proportions (5 and 3) along the x and y axes, the quantum particle’s state is determined by the complex probability amplitudes α and β associated with each basis state. These amplitudes represent the probabilities of finding the particle in states \\|0⟩ and \\|1⟩ upon measurement. The crucial distinction between classical and quantum systems lies in the measurement process. In classical cases, the function representing a body’s position remains unchanged. However, in quantum mechanics, upon measurement, the wave function collapses to one of the basis states, with probabilities given by the squared magnitudes of the probability amplitudes. This collapse is a fundamental property of quantum mechanics and leads to specific outcomes when measurements are performed. In summary, the analogy with position coordinates clarifies that superposition does not imply simultaneous existence in multiple states. Instead, it denotes a combination of possible states described by the wave function, with a definitive state emerging only upon measurement. coordinates for simplicity. Phew!!! That was a lot of math. ## Conclusion Quantum superposition, a truly intriguing phenomenon, serves as the bedrock for the swiftly evolving Quantum Industry. It forms the backbone of Quantum Computing, which harnesses this enigmatic property to achieve remarkable advancements in various fields. If you want to know a bit about the weird behavior exhibited by particles due to superposition, check out the video by Up and Atom And if you have more time, you can watch the 1-hour long version of the above video ## References
Shard	77 (laksa)
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