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Biodiversity

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Biodiversity
Since the time man became different from other animals inhabiting the Earth, he has been making a lot of progress using all that he can. For ages, he treated nature as a vast storehouse of resources without paying any heed to the fact that his unscrupulous use of natural resources might pose a danger to all other species coexisting with him. He considered himself the only creature on this planet which was entitled to all the riches. Ignorant of the evil consequences of his ever- increasing and never-quenchable thirst for pleasure, he looked down upon every other species and treated himself as a master. He destroyed habitats of innumerable species to make room for avenues that provided him convenience and pleasure. The loss of habitats caused the large-scale extinction of many organisms. This harm to the lives of organisms affected human health adversely and today, the whole world has started taking immense interest in biodiversity. Taking into consideration the importance of biodiversity, the United Nations designated the year 2010 as the International Year of Biodiversity. The term “Biological Diversity” was coined by the wildlife scientist and conservationist, Raymond F. Dasmann, in 1968. Through a book, he advocated conservation. The term gained currency within a short span of time and by the 1980s, it came into common usage in science and environmental policy. The term’s contracted form “biodiversity” is said to have been most likely coined by W.G. Rosen in 1985 while planning the 1986 National Forum on Biological Diversity organised by the National Research Council (NRC). It first appeared in a publication in 1988 when entomologist E.O. Wilson used it as the tide of the proceedings of that forum. The 1992 United Nations Earth Summit defined biological diversity as “the variability among living organisms, from all sources, including inter alia, terrestrial, marine, and other aquatic ecosystems, and ecological complexes of which they are the part : this includes diversity within species, between species, and of ecosystems.
As far as biodiversity is concerned, it is not evenly distributed. Flora and fauna diversity depends on climate, altitude, soil and the presence of other species. In 2006, many species were formally classified as rare, endangered or threatened.
Scientists have expressed the view that millions of more species are at risk which has not been formally recognised. Even though terrestrial biodiversity declines from the equator to the poles, this cannot be verified in the case of aquatic ecosystems, especially in marine ecosystems. Generally, terrestrial biodiversity is up to 25 times greater than ocean biodiversity. A biodiversity hotspot is a region with a high level of endemic species. Hotspot was a term
coined by Dr Norman Myers. There are many hotspots in the world most of which are located in the tropics and are mainly forests.
Brazil’s Atlantic Forestisconsideredone major hotspot which is home to 20,000 plant species, 1,350 vertebrates and millions of insects, about half of which are not found anywhere else in the world. The island of Madagascar, particularly the unique Madagascar dry deciduous forests and lowland rain-forests, possesses a high ratio of endemism. Indonesia’s 17,000 islands cover 7,35,355 square miles. They contain lOpercentof the world’s flowering plants, 12 percent of mammals and 17 percent of reptiles, amphibians and birds. Biodiversity is the result of 3.5 billion years of evolution. Though scientists have not been able to ascertain the exact period of origin of species, but they think it to have occurred a few million years after the formation of the Earth. Nevertheless, according to scientists, archaea, bacteria, protozoans and similar single-celled organisms had started inhabiting this Earth approximately 600 million years ago. The history of biodiversity during the Phanerozoic (the last 540 million years) starts with rapid growth during the Cambrian explosion. This period is thought to be the time during which nearly every phylum of multicellular organisms first appeared. Over the next 400 million years or so, global diversity was marked by periodic, massive losses called mass extinction. A significant loss occurred when rainforests collapsed in the carboniferous. The worst was the Permo- triassic extinction that took place around 251 million years ago. It took vertebrates 30 million years to recover from this event. As per fossil records, the last few million years witnessed the greatest biodiversity in history.
Estimates of the present global macroscopic species diversity vary from 2 million to 100 million, best of which is estimated somewhere near 13-14 million, the vast majority comprising arthropods.
The fact is, however, this that biodiversity is under threat across the globe. India also does not present any
different picture and its considerable biodiversity is under threat. Biodiversity here has been mainly measured by
the numbers of plants and vertebrates and their presence is greatest in the Western Ghats and northeast.
Both the areas are also included in the world’s list of hotspots of biodiversity i.e. small geographic areas with high
species diversity. Of the two areas, the Western Ghats have more endemic species which are found nowhere else,
Threats to species are mainly due to decline in the areas of their habitats, fragmentation of habitats and decline in
habitat quality. Hunting has also been found to be a cause of extinction, especially in the case of some mammals.
Fragmentation also raises the extinction risk, because isolated subpopulations can become extinct one by one due
to not being repopulated. Stochastic declines in small subpopulations make it more likely that they will become
extinct and this is further aggravated by the reduction of genetic variability in subpopulations. Species with
already restricted ranges are particularly vulnerable to these threats. For the terrestrial species, the declines in
habitat quality and quantity arise from the conversion of forests and grasslands into agricultural land, of natural
forests to monoculture plantations and from grazing and woodcutting pressures. In some areas, invasion by
exotic species of plants also results in habitat degradation. For example, Peruvian thorny tree Prosopis julijlora in
the dry parts of northern India have replaced the native species, Acacia milotica(Babool) and South American
flowering bush lantana Camara has spread in the sub-Himalayan belt. For aquatic and semiaquatic
species, the declines in habitat quality are due to diversion of ground and surface water, resulting in drying up of
streams and other water bodies, from siltation, and pollution from pesticides and other chemicals. Freshwater
fishes are also threatened by the introduction of exotic species which are either predator or competitors.
We should do our best to preserve the biodiversity in the country because it is valuable on account of many factors. It has great economic value. Economic value comprises pharmaceutical uses also. Ecosystem value is another important aspect of biodiversity. Loss of biodiversity may cause large unpredictable changes in an ecosystem, thereby adversely affecting agriculture and human health. Loss of biodiversity also indirectly affects tourism. Some areas in India, like Kerala or Tamil Nadu, attract people due to their richness with regard to biodiversity also. Last but not least, there is existence value of biodiversity. Conservation of biodiversity is a major area of concern. Joint Forest Management and Eco-development schemes were initiated in the 1980s and 1990s. Local communities exercise influence over the exploitation of the natural assets and they have the power to degrade them or prevent others from degrading them if they are motivated to do so. The best way of preserving the biodiversity is, undoubtedly, to assign the full rights to revenue flows from non­extractive uses such as tourism to the local communities, together with a democratic and transparent institution that allows them to resolve internal common pool problems. In addition, rights to extractive uses, at least with some restriction, would not degrade the resource. Local communities, if made to participate thus in preservation, feel some sense of confidence and this will act as an incentive both to maintain the resource and to exclude the outside appropriators. In several cases, the local communities may be motivated and taken into confidence, if they are simply allowed to use their respective areas for grazing, firewood collection, timber, and collection of other forest produce in and around existing “Protected Areas” (Wildlife Sanctuaries and National Parks).
Many debates over the Tribal Rights Bill have suggested that neither conservationists nor tribal rights activists have seriously considered a solution in regard to the transfer of tourist revenues to local communities. Many experts have, however, suggested that there should have been much more meaningful local involvement in conservation management. Incentive payments, rather than coercive regulation, would probably be the much better option for conservation efforts. Some experts have also opined that a misconception related to extractive human use is incompatible with biodiversity conservation. In some cases, as in the famous bird refuge at Keoladeo Ghana, biodiversity depends on certain human uses such as grazing. The ban on grazing had an adverse impact because it resulted in water bird habitat being choked by unwanted vegetation. The pattern of dispossession and alienation of forest communities and failed state regulation is very much evident in northeastern States in India. They are demographically different from the rest of the country because Scheduled Tribes constitute a majority of the population. As far as statistics are concerned, there are no systematic comparisons of the performance of the northeastern States in forest conservation with the rest of the country. Statistics show that hunting has reduced wildlife populations in these areas considerably. There should be a serious attempt to apply the provisions ‘bf the Wildlife Protection Act restricting hunting in these areas.
While a discussion is on with regard to conservation of natural resources, mention must be made of the Government of India’s initiatives. For example, the monitorable targets for the Twelfth Plan include greening 5 million ha under Green India Mission including 1.5 million ha of degraded lands, afforestation and eco- restoration of 0.9 million ha of ecologically sensitive areas; Technology-based monitoring of forest cover, biodiversity and growing stock including change- monitoring on periodical basis through dedicated satellite by 2017 and establishment of open web-basedNational Forestry and Environmental Information system for research and public accessibility by 2015; Engagement of Village Green Guards/Community Foresters for every Joint Forest Management (JFM) village by 2016; Establishing forestry seed bank in forest circles and Model Nursery in every district with information on public portal by 2014. Besides, 20 percent of veterinary professionals in the country will be trained in treating wildlife; Integrated Ecotourism District Plans covering 10 percent of all potential Protected Areas (PAs) by 2017; Promoting participation of private sector, civil societies, NGOs and philanthropists in animal welfare. The Government will also do its best to restore 0.1 million ha of wetlands/inland lakes/water bodies by 2017. Mapping and preparation of biodiversity management plans for deserts (both cold and arid), coastal areas, important coral zones, wetlands, mangroves and so on are to be completed by 2017 according to the Twelfth Five- Year Plan document.
Taking conservation issue seriously is a good step indeed. According to recent media reports, some States have adopted science-based conservation methods to increase the dwindling number of tigers which have adopted transparent constructive ‘public-private partnership’ model and have forged ties with research organisations. Tamil Nadu is one of the States which have a keen focus on conservation, and Karnataka has presented a very good example of such a public-private partnership. The population estimate for 2010 was 1,706 tigers compared with 1,411 in 2006. The counting exercise should be carried out annually, not every four years. The foundation for the aforementioned exercise is being contemplated by the Wildlife Institute of India and the National Tiger Conservation Authority along with the leading conservationists. They are going to decide the methodology for future monitoring and assessment of tiger population. We should look forward to the same with regard to other species also. Biodiversity is very essential for the existence of this planet itself and it should be taken seriously by all not only in India but also across the globe.

Must Read: 

Important Amendments of the Indian Constitution

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Amendment of the Indian Constitution

24th Amendment of the Indian Constitution Act, 1971: It affirms the power of the Parliament to amend any part of the Constitution including Fundamental Rights.

31st Amendment of the Indian Constitution Act, 1973:  Increases the elective strength of the Lok Sabha from 525 to 545

36th Amendment of the Indian Constitution Act, 1975: Sikkim became the 22nd State of the Indian Union.

37th Amendment of the Indian Constitution Act, 1975: Was passed by the parliament on April 26, 1975, to provide for a Legislative Assembly and 1 Council of Ministers to Arunachal Pradesh, the country’s north-eastern most nation Territory.

Pr Constitution (38th Amendment) Act, 1975: The Act makes the declaration of emergency non-judiciable.

Constitution (39th Amendment) Act, 1975: The Act places beyond challenge in courts the election to Parliament of a person holding the office of Prime Minister or Speaker and the election of President and Vice-President.

40th Amendment of the Indian Constitution Act, 1976: This Amendment has three-fold objectives :

  •  It places beyond challenge in courts some major Central laws;
  •  It gives similar protection to several State enactments;
  •  It provides that the limits of the territorial waters and the maritime zones of India .

The Constitution (42nd Amendment) Act, 1976: (also known as mini-constitution)

43rd Amendment of the Indian Constitution Act, 1978:  This Act repealed some of the provisions of the Constitution (42nd Amendment) Act passed during the Emergency.

45th Amendment of the Indian Constitution Act, 1980: seeks to extend reservation of seats for Scheduled Castes and Scheduled Tribes and the representation of the Anglo- Indians in the Lok Sabha and the State Assemblies for 10 years.

The Constitution (46th Amendment) Act, 1982: plug loopholes and realize sales tax dues

49th Amendment of the Indian Constitution Act, 1984: the provisions of the Sixth Schedule to the Constitution to be made applicable to the tribal areas of the State of Tripura.

The Constitution (52nd Amendment) Act, 1985: popularly known as Anti Defection Law.

53rd Amendment of the Indian Constitution Act, 1986: It confers Statehood on Mizoram and ensures against unnecessary interference by the Central Government by the laws relative to spheres of social relationship and community conduct applicable to Mizoram.

The Constitution (54th Amendment) Act, 1986: It enhances the salaries of Judges of High Courts and Supreme Court of India.

The Constitution (55th Amendment) Act, 1987: It grants Statehood to Arunachal Pradesh which consequently became the 24th State of the Indian Union.

56th Amendment of the Indian Constitution Act, 1987: It confers Statehood on Goa and forms a new Union Territory of Daman and Diu. Goa thus became the 25th State of the Indian Republic.

The Constitution (57th Amendment) Act, 1987: It made a special provision for the setting up of the new State of Goa.

58th Amendment of the Indian Constitution Act, 1988: It provides for special arrangements with regard to reservation of seats for Scheduled Tribes in the State of Arunachal Pradesh, Nagaland, Mizoram, and Meghalaya.

The Constitution (59th Amendment) Act, 1988: It empowered the Central Government to impose Emergency in Punjab when deemed necessary.

The Constitution (61st Amendment) Act, 1989: It lowered the voting age from 21 to 18.

62nd Amendment of the Indian Constitution Act, 1989: It provided for the extension by another 10 years of reservation of seats in the Parliament and State Assemblies for the Scheduled Castes and Tribes and reservation for Anglo-Indian Community by nomination.

The Constitution (63rd Amendment) Act, 1989: It repealed Amendment 59 which empowered the government to impose emergency in Punjab.

The Constitution (64th Amendment) Act, 1990: It extended the President’s rule in Punjab by six months.

66th Amendment of the Indian Constitution Act, 1990: To bring land reforms within the purview of 9th Schedule of the Constitution.

The Constitution (68th Amendment) Act, 1991: It extended the President’s rule in Punjab up to a total period of 5 years.

1987-1991 : – Punjab placed under president’s rule

The Constitution (69th Amendment) Act, 1991: Delhi made National Capital Region. The Act also made provision for Legislative assembly and a council of ministers for Delhi.

70th Amendment of the Indian Constitution Act, 1992: The amendment provides for the inclusion of members of the legislature of Pondicherry and Delhi.

71st Amendment of the Indian Constitution Act, 1992: to include Konkani, Manipuri and Nepali Languages in the 8th Schedule of the Constitution.

The Constitution (72nd Amendment) Act, 1992:  to determine the number of reserved seats for STs in the State Assembly of Tripura.

73rd Amendment of the Indian Constitution Act, 1993: relating to Panchayats inserted in the constitution to provide Gram Sabha, the constitution of panchayats at the village and other levels, direct elections to all seats, fixing the tenures, reservation for SC, ST and 33% seats for women etc.

74th Amendment of the Indian Constitution Act, 1993: relating to Municipalities, i.e., Nagar Panchayats, Municipal Councils and Municipal Corporations.

The Constitution (77th Amendment) Act, 1995: (constitutional validity in the debate) Article 16(4A) provides reservation in promotion for the SC and the ST.

The Constitution (One Hundred Seventeenth Amendment): It provides that all the Scheduled Castes and Scheduled Tribes notified in the Constitutional shall be deemed to be backward.

The Constitution (79th Amendment) Act, 1999: Extended the reservations for SC/ST in services as also nomination of 2 Anglo-Indians to Lok Sabha up to 2010.

80th Amendment of the Indian Constitution Act, 2000: Related to the revenue sharing between the Centre and the States

The Constitution (81st Amendment) Act, 2000: Related to carrying forward backlog vacancies of Scheduled Castes and Scheduled Tribes.

82nd Amendment of the Indian Constitution Act, 2000: Related to relaxation in qualifying marks and reservation of posts in super specialty courses in Medical and Engineering disciplines, etc. for Scheduled Castes/Tribes etc.

83rd Amendment of the Indian Constitution Act, 2000: Related to the reservation of seats under Panchayati Raj in Arunachal Pradesh.

The Constitution (84th Amendment) Act, 2000: (NDA govt. – smaller states) Related to creating of new States of the Jharkhand, Chhatisgarh, and Uttaranchal.

85th Amendment of the Indian Constitution Act, 2001: Amended Article 16(4A) to provide for consequential seniority in promotion by virtue of the rule of reservation for the Government servants belonging to the Scheduled Castes and the Scheduled Tribes.

The Constitution (86th Amendment) Act, 2002: State shall provide free and compulsory education to all children of the age of six to fourteen years.

87th Amendment of the Indian Constitution Act, 2003: shall be substituted.

The Constitution (88th Amendment) Act, 2003: (service tax) This Article provides for the insertion of a new article 268A which states that taxes on services shall be levied by the Government of India and such tax shall be collected and appropriated by the government of India and the States in the manner provided in clause

The Constitution (89th Amendment) Act, 2003:(Bifurcation of Nat. Commission for SC and ST) This Article provides for the amendment of Article 338 and insertion of a new article 338A which provides that there shall be a National Commission for ST.

The Constitution (90 Amendments) Act, 2003: This Amendment provided that for elections to the Legislative Assembly of the State of Assam, the representation of the Scheduled Tribes and non-Scheduled Tribes in the constituencies included in the Bodoland Territorial Areas District, so notified, and existing prior to the constitution of the Bodoland Territorial Areas District, shall be maintained.

91st Amendment of the Indian Constitution Act, 2003: (strengthens anti-defection law) This Article provides that the total number of Ministers, including the Prime Minister, in the Council of Ministers shall not exceed fifteen percent of the total number members of the House of the people.

The Constitution (92nd Amendment) Act, 2003: This Article provides for the inclusion of four new languages, viz. Bodo, Dogri, Maithili and Santhali in the Eighth Schedule of the Constitution.

93rd Amendment of the Indian Constitution Act, 2005: In this Amendment, a provision has been inserted that the State can make laws for the advancement of the SC, ST or the OBCs of citizens in matters of admission to educational institutions.

The Constitution (94th Amendment) Act, 2006: This article provides that in the proviso, for the word “Bihar”, the words “Chhattisgarh, Jharkhand” shall be substituted.

The Constitution (95th Amendment) Act, 2009: This article provides that the words “sixty years”, the words “seventy years” shall be substituted.

96th Amendment of the Indian Constitution Act, 2011: This article provides that the word, “Oriya”, the word “Odia” shall be substituted.

The Constitution (97th Amendment) Act, 2011: This article provides that Fundamental Rights and Directive Principles of State Policy

The Constitution (98th Amendment) Act, 2012: to empower the Governor of Karnataka to take steps to develop the Hyderabad-Karnataka Region.  As per the Statements of Objects and Reasons of the Bill, this Region includes the districts of Gulbarga, Bidar, Raichur, Koppal, Yadgir, and Bellary.

Must Read:

Constitution Of India

Parts of the Constitution

Fundamental Duties Incorporated in Constitution of India

Constitutional Development in India From Regulating Act 1773 to Govt. of India Act 1935

Politics in India

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politics-in-india
politics-in-india

Politics in India takes place within the framework of a constitution. India is a federal parliamentary democratic republic in which the President of India is head of state and the Prime Minister of India is the head of government. The constitution defines the organisation, powers and limitations of both central and state governments.

There is provision for a bicameral legislature consisting of an Upper House, i.e. Rajya Sabha, which represent the states of the Indian federation and a lower house i.e. Lok Sabha that represents the people of India as a whole. Indian constitution provides for an independent Judiciary headed by the Supreme Court to adhere and protect the constitution and to settle disputes between the centre and the states or between the states, it can also nullify any central or state laws if they are against the constitution.

In India, elections are held according to The Representation of People Act, 1951. This Act was enacted before first General Election by the provisional parliament under Article 327 of Indian Constitution. The Act includes provisions for election of both the houses of parliament and state legislatures. It also has provisions for offenses and corrupt practices related to elections. Procedure for resolution of disputes or doubts in election result is also mentioned in the Representation of People Act.

Read Also: Financial inclusion

The Constitution says in Act 324(2) that the Commission will be composed of a Chief Election Commissioner aided by other Election Commissioners appointed by the President of India. In this light, and further by provisions of the Representation of People Act, 1951, The Election Commission of India was established to take care of elections in India including Presidential, Parliamentary, and State elections.

The governments, union or state, are formed through elections held every five years (unless otherwise specified), by having the majority of members in their respective lower houses (Lok Sabha in the centre and Vidhan Sabha in states). India had its first general election in 1951, which was dominated by Indian National Congress, and went on to dominate the successive elections, up till 1977, when the first non-Congress government was formed for the first time in independent India. The 1990s saw the end of Single Party domination and rise of Coalition Governments. The elections for 16th Lok Sabha were held in April and May 2014.

One feature of the political parties in India is that the parties are generally woven around their leaders, the leaders actively playing a dominant role, the role of leadership can be transferred and tends to take dynastic route.

India has a multi-party system, where there are a number of national as well as regional parties. A regional party may gain a majority and rule a particular state. If a party is represented in more than 4 states, it would be labelled a national party. Out of the 66 years of India’s independence, India has been ruled by the Indian National Congress (INC) for 53 of those years.

Must Read: Indian Citizenship

National Parties

A registered party large political parties which were earlier recognised as a National Party before 2014 elections. They are:

  • Indian National Congress
  • Communist Party of India
  • Bharatiya Janata Party
  • Bahujan Samaj Party 
  • Samajwadi Party

However in recent Lok Sabha Elections (2014) most of the parties from the aforesaid list have lost their National Party title and only two parties Bhartiya Janta Party (BJP) and Indian National Congress (INC) are now National Parties of India. The status of National Party has not been revoked from CPI because of its early foundation.

These status are given and revoked by the Election Commission in light of the provision of the Representation of People Act.

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Cross-Entropy Benchmarking (XEB): Verifying Quantum Supremacy and Circuit Fidelity

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cross entropy benchmarking xeb

Table of Contents

  1. Introduction
  2. Motivation for Cross-Entropy Benchmarking (XEB)
  3. Principles of Cross-Entropy Benchmarking
  4. Classical vs Quantum Sampling
  5. XEB Fidelity Metric
  6. Mathematical Definition
  7. Practical Implementation Steps
  8. Random Quantum Circuit Generation
  9. Circuit Depth and Qubit Count
  10. Measuring Output Probabilities
  11. Estimating Ideal Probabilities Classically
  12. Cross-Entropy Difference and Fidelity
  13. Advantages Over Other Benchmarks
  14. Sources of Error and Noise
  15. Application to Quantum Supremacy Experiments
  16. Google Sycamore and XEB
  17. Limitations of Cross-Entropy Benchmarking
  18. Relation to Quantum Volume and RB
  19. Systematic Bias and Error Mitigation
  20. Conclusion

1. Introduction

Cross-entropy benchmarking (XEB) is a powerful technique used to assess the fidelity of quantum circuits, particularly in the context of random circuit sampling. It gained prominence through quantum supremacy experiments and offers a way to compare quantum and classical outputs.

2. Motivation for Cross-Entropy Benchmarking (XEB)

As quantum systems increase in size, traditional benchmarks like tomography become impractical. XEB provides a scalable way to estimate how closely a quantum circuit’s output matches theoretical expectations.

3. Principles of Cross-Entropy Benchmarking

The idea is to:

  • Run a random quantum circuit on real hardware
  • Measure output bitstrings
  • Compare their probabilities with the ideal theoretical distribution

4. Classical vs Quantum Sampling

For a random quantum circuit of sufficient depth, classical simulation becomes intractable. XEB exploits this to detect if a quantum computer is outperforming classical algorithms.

5. XEB Fidelity Metric

Fidelity \( F_{ ext{XEB}} \) is computed by comparing measured bitstring probabilities with ideal values:

  • Higher \( F_{ ext{XEB}} \) indicates better quantum circuit performance
  • Fidelity drops in the presence of noise or decoherence

6. Mathematical Definition

Let \( {x_i} \) be the set of sampled bitstrings and \( P(x_i) \) their ideal probabilities:
\[
F_{ ext{XEB}} = 2^n \langle P(x_i)
angle – 1
\]
where \( n \) is the number of qubits and \( \langle P(x_i)
angle \) is the average over sampled bitstrings.

7. Practical Implementation Steps

  1. Generate random circuit of given depth and size
  2. Run it on quantum hardware
  3. Measure a large number of output bitstrings
  4. Calculate ideal probabilities for those bitstrings (on a classical simulator)
  5. Compute \( F_{ ext{XEB}} \)

8. Random Quantum Circuit Generation

Circuits use:

  • Randomized single- and two-qubit gates
  • Repeated layers (cycles)
  • Architecture-specific connectivity constraints

9. Circuit Depth and Qubit Count

Deeper circuits and more qubits increase sampling complexity. XEB becomes more powerful as classical simulation becomes infeasible for verifying results.

10. Measuring Output Probabilities

Each bitstring occurs with probability \( P(x) \). Frequencies are tallied over many trials (~10⁵ or more) to estimate the distribution.

11. Estimating Ideal Probabilities Classically

Ideal probabilities are computed via exact simulation:

  • Feasible for \( \leq 40 \) qubits
  • Approximation or truncation required beyond that

12. Cross-Entropy Difference and Fidelity

  • Ideal uniform distribution yields \( F_{ ext{XEB}} pprox 0 \)
  • Perfect quantum output gives \( F_{ ext{XEB}} = 1 \)
  • Noisy hardware results in intermediate values

13. Advantages Over Other Benchmarks

  • Scalable to large systems
  • Tolerant to SPAM errors
  • Captures global system fidelity, not just per-gate errors

14. Sources of Error and Noise

  • Gate infidelity
  • Crosstalk
  • Measurement errors
  • SPAM noise (partially suppressed)

15. Application to Quantum Supremacy Experiments

Google’s 2019 Sycamore experiment used XEB to:

  • Demonstrate 53-qubit sampling fidelity
  • Show 200s quantum runtime vs 10⁵ years classically
  • Declare quantum supremacy for random circuit sampling

16. Google Sycamore and XEB

The team achieved \( F_{ ext{XEB}} pprox 0.0024 \), sufficient for claiming quantum advantage. Cross-entropy validated the quantum-classical gap.

17. Limitations of Cross-Entropy Benchmarking

  • Sensitive to simulator accuracy
  • Assumes availability of ideal probabilities
  • Not applicable to structured circuits (only random circuits)

18. Relation to Quantum Volume and RB

  • RB (Randomized Benchmarking): gate-level fidelity
  • QV (Quantum Volume): system-level capability
  • XEB: circuit-level fidelity on unstructured workloads

19. Systematic Bias and Error Mitigation

  • Averaging over multiple circuits
  • Circuit compilation with noise mitigation
  • Crosstalk-aware layout and scheduling

20. Conclusion

Cross-entropy benchmarking provides a robust and scalable method for evaluating quantum circuits, especially in the context of quantum supremacy. As devices grow, XEB will remain central to certifying and comparing quantum processors.

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Important Geographical Lines

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A geographical lines of longitude is the half of an imaginary great circle on the Earth’s surface, terminated by the North Pole and the South Pole, connecting points of equal longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude.

Important Geographical Lines

  • A Curzon line is the polish-Russian frontier setup in 1945.
  • Dead line is the line or boundary of a military prison, which prisoners are not allowed to cross.
  • Green Line is a demarcation line between the Greek and Turkish Cypriot communities.
  • Hindenburg line separates Germany from Poland.
  • Pak-Iran border line was demarcated on 24th Sep: 1872.
  • Line of control is b/w Azad Kashmir & Occupied Kashmir.
  • Mc Mohan line is the boundary line between India and China. It was demarcated in 1914.
  • Radcliff line is the boundary between Pakistan and India. It was demarcated in 1947 by Sir Cyril Radcliff.
  • 17th parallel line is the boundary line between North Vietnam and the South Vietnam.
  • 24th parallel Line lies in Rann of Kutch. It is frontier between Pakistan and India.
  • 38th Parallel line is the boundary between North and South Korea.
  • 49th Parallel Line is the boundary line between Canada and the USA.
  • Plimsoll Lime is a horizontal line on a merchant ship to which a ship the upper limit to which a ship may be legally loaded.
  • Dead line is a boundary line around a military prison which prisoners are forbidden to cross.
  • Durand line is 1300 mile long frontier b/w Pakistan & Afghanistan demarcated in 1893 Fileil -95. it has over 200 passes.
  • Green line is a painted line in Nicosia (Cyprus) that serves as a demarcation line b/w Greek & Turkish Cypriot communities.
  • Maginot line is French line of fortification built in WWII along the German border from Switzerland to Belgium. It divides France from Germany.
  • Maginot line divides France from Germany.
  • Mannerheim line was defensive fortification line on the Karelian Isthmus built by Finland against the Soviet Union.
  • Oder-neisse Line was boundary b/w Germany & Poland during WWII.

Also, Read:

Important Geographical Discoveries

Geographical Indication (GI) Status