Quantum circuit

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Quantum_circuit 

 

Circuit that performs teleportation of a qubit. This circuit consists of both quantum gates and measurements. Measurement is a quantum phenomena that does not occur in classical circuits.

In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly other actions. The minimum set of actions that a circuit needs to be able to perform on the qubits to enable quantum computation is known as DiVincenzo's criteria.

Circuits are written such that the horizontal axis is time, starting at the left hand side and ending at the right. Horizontal lines are qubits, doubled lines represent classical bits. The items that are connected by these lines are operations performed on the qubits, such as measurements or gates. These lines define the sequence of events, and are usually not physical cables.

The graphical depiction of quantum circuit elements is described using a variant of the Penrose graphical notation. Richard Feynman used an early version of the quantum circuit notation in 1986.

Reversible classical logic gates

Most elementary logic gates of a classical computer are not reversible. Thus, for instance, for an AND gate one cannot always recover the two input bits from the output bit; for example, if the output bit is 0, we cannot tell from this whether the input bits are 01 or 10 or 00.

However, reversible gates in classical computers are easily constructed for bit strings of any length; moreover, these are actually of practical interest, since irreversible gates must always increase physical entropy. A reversible gate is a reversible function on n-bit data that returns n-bit data, where an n-bit data is a string of bits x₁,x₂, ...,x_n of length n. The set of n-bit data is the space {0,1}ⁿ, which consists of 2ⁿ strings of 0's and 1's.

More precisely: an n-bit reversible gate is a bijective mapping f from the set {0,1}ⁿ of n-bit data onto itself. An example of such a reversible gate f is a mapping that applies a fixed permutation to its inputs. For reasons of practical engineering, one typically studies gates only for small values of n, e.g. n=1, n=2 or n=3. These gates can be easily described by tables.

Quantum logic gates

The quantum logic gates are reversible unitary transformations on at least one qubit. Multiple qubits taken together are referred to as quantum registers. To define quantum gates, we first need to specify the quantum replacement of an n-bit datum. The quantized version of classical n-bit space {0,1}ⁿ is the Hilbert space

${\displaystyle H_{\operatorname {QB} (n)}=\ell ^{2}(\{0,1\}^{n}).}$

This is by definition the space of complex-valued functions on {0,1}ⁿ and is naturally an inner product space. ${\displaystyle \ell ^{2}}$ refers to the 2-norm. This space can also be regarded as consisting of linear combinations, or superpositions, of classical bit strings. Note that H_QB(n) is a vector space over the complex numbers of dimension 2ⁿ. The elements of this vector space are the possible state-vectors of n-qubit quantum registers.

Using Dirac ket notation, if x₁,x₂, ...,x_n is a classical bit string, then

${\displaystyle |x_{1},x_{2},\cdots ,x_{n}\rangle \quad }$

is a special n-qubit register corresponding to the function which maps this classical bit string to 1 and maps all other bit strings to 0; these 2ⁿ special n-qubit registers are called computational basis states. All n-qubit registers are complex linear combinations of these computational basis states.

Quantum logic gates, in contrast to classical logic gates, are always reversible. One requires a special kind of reversible function, namely a unitary mapping, that is, a linear transformation of a complex inner product space that preserves the Hermitian inner product. An n-qubit (reversible) quantum gate is a unitary mapping U from the space H_QB(n) of n-qubit registers onto itself.

Typically, we are only interested in gates for small values of n.

A reversible n-bit classical logic gate gives rise to a reversible n-bit quantum gate as follows: to each reversible n-bit logic gate f corresponds a quantum gate W_f defined as follows:

${\displaystyle W_{f}(|x_{1},x_{2},\cdots ,x_{n}\rangle )=|f(x_{1},x_{2},\cdots ,x_{n})\rangle .}$

Note that W_f permutes the computational basis states.

Of particular importance is the controlled NOT gate (also called CNOT gate) W_CNOT defined on a quantized 2 qubit. Other examples of quantum logic gates derived from classical ones are the Toffoli gate and the Fredkin gate.

However, the Hilbert-space structure of the qubits permits many quantum gates that are not induced by classical ones. For example, a relative phase shift is a 1 qubit gate given by multiplication by the phase shift operator:

${\displaystyle P(\varphi )={\begin{bmatrix}1&0\\0&e^{i\varphi }\end{bmatrix}},}$

so

${\displaystyle P(\varphi )|0\rangle =|0\rangle \quad P(\varphi )|1\rangle =e^{i\varphi }|1\rangle .}$

Reversible logic circuits

Main article: reversible computing

Again, we consider first reversible classical computation. Conceptually, there is no difference between a reversible n-bit circuit and a reversible n-bit logic gate: either one is just an invertible function on the space of n bit data. However, as mentioned in the previous section, for engineering reasons we would like to have a small number of simple reversible gates, that can be put together to assemble any reversible circuit.

To explain this assembly process, suppose we have a reversible n-bit gate f and a reversible m-bit gate g. Putting them together means producing a new circuit by connecting some set of k outputs of f to some set of k inputs of g as in the figure below. In that figure, n=5, k=3 and m=7. The resulting circuit is also reversible and operates on n+m−k bits.

We will refer to this scheme as a classical assemblage (This concept corresponds to a technical definition in Kitaev's pioneering paper cited below). In composing these reversible machines, it is important to ensure that the intermediate machines are also reversible. This condition assures that intermediate "garbage" is not created (the net physical effect would be to increase entropy, which is one of the motivations for going through this exercise).

Note that each horizontal line on the above picture represents either 0 or 1, not these probabilities. Since quantum computations are reversible, at each 'step' the number of lines must be the same number of input lines. Also, each input combination must be mapped to a single combination at each 'step'. This means that each intermediate combination in a quantum circuit is a bijective function of the input.

Now it is possible to show that the Toffoli gate is a universal gate. This means that given any reversible classical n-bit circuit h, we can construct a classical assemblage of Toffoli gates in the above manner to produce an (n+m)-bit circuit f such that

${\displaystyle f(x_{1},\ldots ,x_{n},\underbrace {0,\dots ,0} )=(y_{1},\ldots ,y_{n},\underbrace {0,\ldots ,0} )}$

where there are m underbraced zeroed inputs and

${\displaystyle (y_{1},\ldots ,y_{n})=h(x_{1},\ldots ,x_{n})}$.

Notice that the end result always has a string of m zeros as the ancilla bits. No "rubbish" is ever produced, and so this computation is indeed one that, in a physical sense, generates no entropy. This issue is carefully discussed in Kitaev's article.

More generally, any function f (bijective or not) can be simulated by a circuit of Toffoli gates. Obviously, if the mapping fails to be injective, at some point in the simulation (for example as the last step) some "garbage" has to be produced.

For quantum circuits a similar composition of qubit gates can be defined. That is, associated to any classical assemblage as above, we can produce a reversible quantum circuit when in place of f we have an n-qubit gate U and in place of g we have an m-qubit gate W. See illustration below:

The fact that connecting gates this way gives rise to a unitary mapping on n+m−k qubit space is easy to check. In a real quantum computer the physical connection between the gates is a major engineering challenge, since it is one of the places where decoherence may occur.

There are also universality theorems for certain sets of well-known gates; such a universality theorem exists, for instance, for the pair consisting of the single qubit phase gate U_θ mentioned above (for a suitable value of θ), together with the 2-qubit CNOT gate W_CNOT. However, the universality theorem for the quantum case is somewhat weaker than the one for the classical case; it asserts only that any reversible n-qubit circuit can be approximated arbitrarily well by circuits assembled from these two elementary gates. Note that there are uncountably many possible single qubit phase gates, one for every possible angle θ, so they cannot all be represented by a finite circuit constructed from {U_θ, W_CNOT}.

Quantum computations

So far we have not shown how quantum circuits are used to perform computations. Since many important numerical problems reduce to computing a unitary transformation U on a finite-dimensional space (the celebrated discrete Fourier transform being a prime example), one might expect that some quantum circuit could be designed to carry out the transformation U. In principle, one needs only to prepare an n qubit state ψ as an appropriate superposition of computational basis states for the input and measure the output Uψ. Unfortunately, there are two problems with this:

• One cannot measure the phase of ψ at any computational basis state so there is no way of reading out the complete answer. This is in the nature of measurement in quantum mechanics.
• There is no way to efficiently prepare the input state ψ.

This does not prevent quantum circuits for the discrete Fourier transform from being used as intermediate steps in other quantum circuits, but the use is more subtle. In fact quantum computations are probabilistic.

We now provide a mathematical model for how quantum circuits can simulate probabilistic but classical computations. Consider an r-qubit circuit U with register space H_QB(r). U is thus a unitary map

${\displaystyle H_{\operatorname {QB} (r)}\rightarrow H_{\operatorname {QB} (r)}.}$

In order to associate this circuit to a classical mapping on bitstrings, we specify

• An input register X = {0,1}^m of m (classical) bits.
• An output register Y = {0,1}ⁿ of n (classical) bits.

The contents x = x₁, ..., x_m of the classical input register are used to initialize the qubit register in some way. Ideally, this would be done with the computational basis state

${\displaystyle |{\vec {x}},0\rangle =|x_{1},x_{2},\cdots ,x_{m},\underbrace {0,\dots ,0} \rangle ,}$

where there are r-m underbraced zeroed inputs. Nevertheless, this perfect initialization is completely unrealistic. Let us assume therefore that the initialization is a mixed state given by some density operator S which is near the idealized input in some appropriate metric, e.g.

${\displaystyle \operatorname {Tr} \left({\big |}|{\vec {x}},0\rangle \langle {\vec {x}},0|-S{\big |}\right)\leq \delta .}$

Similarly, the output register space is related to the qubit register, by a Y valued observable A. Note that observables in quantum mechanics are usually defined in terms of projection valued measures on R; if the variable happens to be discrete, the projection valued measure reduces to a family {E_λ} indexed on some parameter λ ranging over a countable set. Similarly, a Y valued observable, can be associated with a family of pairwise orthogonal projections {E_y} indexed by elements of Y. such that

${\displaystyle I=\sum _{y\in Y}\operatorname {E} _{y}.}$

Given a mixed state S, there corresponds a probability measure on Y given by

${\displaystyle \operatorname {Pr} \{y\}=\operatorname {Tr} (S\operatorname {E} _{y}).}$

The function F:X → Y is computed by a circuit U:H_QB(r) → H_QB(r) to within ε if and only if for all bitstrings x of length m

${\displaystyle \left\langle {\vec {x}},0{\big |}U^{*}\operatorname {E} _{F(x)}U{\big |}{\vec {x}},0\right\rangle =\left\langle \operatorname {E} _{F(x)}U(|{\vec {x}},0\rangle ){\big |}U(|{\vec {x}},0\rangle )\right\rangle \geq 1-\epsilon .}$

Now

${\displaystyle \left|\operatorname {Tr} (SU^{*}\operatorname {E} _{F(x)}U)-\left\langle {\vec {x}},0{\big |}U^{*}\operatorname {E} _{F(x)}U{\big |}{\vec {x}},0\right\rangle \right|\leq \operatorname {Tr} ({\big |}|{\vec {x}},0\rangle \langle {\vec {x}},0|-S{\big |})\|U^{*}\operatorname {E} _{F(x)}U\|\leq \delta }$

so that

${\displaystyle \operatorname {Tr} (SU^{*}\operatorname {E} _{F(x)}U)\geq 1-\epsilon -\delta .}$

Theorem. If ε + δ < 1/2, then the probability distribution

${\displaystyle \operatorname {Pr} \{y\}=\operatorname {Tr} (SU^{*}\operatorname {E} _{y}U)}$

on Y can be used to determine F(x) with an arbitrarily small probability of error by majority sampling, for a sufficiently large sample size. Specifically, take k independent samples from the probability distribution Pr on Y and choose a value on which more than half of the samples agree. The probability that the value F(x) is sampled more than k/2 times is at least

${\displaystyle 1-e^{-2\gamma ^{2}k},}$

where γ = 1/2 - ε - δ.

This follows by applying the Chernoff bound.

Fetal abduction

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Fetal_abduction 

Fetal abduction refers to the rare crime of child abduction by kidnapping of an at term pregnant woman and extraction of her fetus through a crude cesarean section. Dr. Michael H. Stone and Dr. Gary Brucato have alternatively referred to this crime as "fetus-snatching" or "fetus abduction." Homicide expert Vernon J. Geberth has used the term "fetal kidnapping." In the small number of reported cases, a few pregnant victims and about half of their fetuses survived the assault and non-medically performed cesarean.

Fetal abduction does not refer to medically induced labor or obstetrical extraction. The definition of the subject does not include compulsory cesarean sections for medical reasons nor child removal from parents for court-approved child protection. However, the "Children of the Disappeared" (desaparecidos) in the Argentine Dirty War are an example of criminal fetal abduction in state institutions as detailed by testimonies on cesarean delivery on desaparecidas and child adoption in a military hospital. Historical atrocities of cesarean extraction for fetal murder (not for child adoption) fall outside the subject definition.

Abductor profile

Fetal abduction is mostly perpetrated by women, usually after organized planning. The abductor may befriend the pregnant victim. In some cases, the abductor impersonates a pregnant and later a puerperal mother, using weight gain and a prosthesis to fake a pregnancy and cutting of the reproductive organs to replicate injuries gained during birth. Some abductors then take the neonate to a hospital. The National Center for Missing and Exploited Children’s spokesperson, Cathy Nahirny, stated in 2007, “Many times the abductor fakes a pregnancy and when it is time to deliver the baby, must abduct someone else's child”. Criminal motives include delusions of fulfilling a partner relationship, child-bearing and childbirth.

Statistics

The National Center for Missing and Exploited Children recorded 18 cases of fetal abductions in the United States between 1983 and 2015, which represented 6% of the recorded 302 cases of infant abduction.

List of reported cases and attempts

Of the current list of 25 reported cases (not including attempts), 4 of the mothers and 13 of their fetuses survived. (This list distinguishes an attempted fetal abduction as without either murder of the mother or extraction of the fetus. An attempt can include severe injury to the mother and fetus.)

Fetal abduction cases

1974

• In Philadelphia in November 1974, a 36-year-old woman named Winifred Ransom hacked and shot to death 26-year-old Margaret Sweeney. Sweeney was 8 months pregnant at the time. After first knocking Sweeney unconscious, Ransom cut the fetus out of Sweeney with a butcher knife. Sweeney regained consciousness during the operation, at which point Ransom struck her with a hatchet at least 20 times and then shot her 3 times. Ransom buried Sweeney beneath the floorboards of her kitchen. Ransom's husband eventually alerted authorities roughly 3 days later. Police found the body November 16. The baby girl survived and was cared for by her grandfather. Ransom was acquitted on the grounds of insanity. She was released from Byberry State Hospital mental institution after 20 months.

1987

• In Albuquerque, New Mexico, Cindy Ray was eight months pregnant when she was kidnapped at Kirtland Air Force Base outside a prenatal clinic. Darci Pierce was nineteen years old when she strangled the pregnant woman to death. She used her car keys to open Ray's womb, snatching the unharmed fetus, Millie. Millie survived, and Pierce was sentenced to 30 years to life for her crime.

1995

• In Addison, Illinois, Deborah Evans was murdered in her apartment. Jacqueline Williams, her boyfriend Fedell Caffey and her cousin Lavern Ward went into Evans' home and shot her in the head. She had three children and was pregnant with a fourth. Two of Evans' children were murdered along with their mother. Evans' murderers then proceeded to cut through her womb with scissors and remove the fetus. One of the children, a baby boy, survived, as did the fetus. The three murderers were caught and sentenced to life in prison.

1996

• In Tuscaloosa, Alabama, seventeen-year-old Carethia Curry was murdered by her friend, 29-year-old Felicia Scott. Curry was abducted by her friend on a night out. She was found three months later, stuffed in a garbage can at the bottom of a fifty-foot ravine with several gunshot wounds to the head, her torso sliced open. The baby girl Curry was carrying survived, and Scott was jailed for life.

1998

• In Fresno, California, Margarita Flores was eight months pregnant when she received a phone call from Josephina Saldana, who offered her gifts of baby furniture and a free one-year supply of diapers. Flores went to a warehouse to collect them and was murdered. Saldana was caught at a hospital the day afterwards carrying a dead fetus that she claimed to have just given birth to. Saldana committed suicide three days after her conviction for kidnapping and murdering Flores and her unborn child and three weeks before her sentencing to life imprisonment.

2000

• In Ravenna, Ohio, Theresa Andrews was twenty-three years old and pregnant when she ran into Michelle Bica. Bica was thirty-nine-years-old and was pretending to be pregnant at the time, and the two exchanged addresses. Then Bica started stalking Andrews. On September 27, 2000, Bica invited the woman to her home, then killed her, extracted the fetus she was carrying, and buried the woman in her garage. The baby survived, and Bica claimed he was her son. When Bica was being investigated by the FBI, she became fearful of punishment for her crime and shot herself.

https://www.jw.org/en/library/magazines/g20010722/Coping-With-an-Unspeakable-Tragedy/

2003

• In Okemah, Oklahoma, Carolyn Simpson was twenty-one years old and six months pregnant when she was shot and killed. She worked at a casino, where her murderer, Effie Goodson, age thirty-seven, was a regular customer. Goodson offered to give Simpson a ride home, and Simpson was later found in a ditch two miles away from her abductor. The baby, removed from the mother's womb three months premature, did not survive. When Goodson brought the fetus to the hospital, the child was pronounced dead, and it was discovered that she was not the mother. Goodson was found unable to stand for a trial, and three years later was sentenced to life in prison.

2004

• In Girardot (Cundinamarca), Colombia in April 2004, a case was reported in which both the mother and child survived. (Aseneth Piedrahita drugged Sol Angela Cartagena Bernal and extracted her fetus. Reportedly the perpetrator had medical knowledge.)
• In Skidmore, Missouri, Bobbie Jo Stinnett died of strangulation at the age of twenty-three at the hands of thirty-seven-year-old Lisa M. Montgomery. The two had been in contact previously; they were both rat terrier breeders in a dog show circuit. Montgomery had even e-mailed the victim, telling her that she wished to purchase one of her dogs. Montgomery faked a pregnancy, and on December 16, she drove from her Kansas home to Skidmore, Missouri. After strangling Stinnett to death, Montgomery cut open her abdomen and took her one-month-premature daughter. An hour later, the victim's mother found her body, and less than twenty-four hours later Victoria Jo Stinnett, the victim's stolen fetus, was found healthy in Melvern, Kansas. Lisa Montgomery was incarcerated, and a jury subsequently sentenced Montgomery, 43, to death. Montgomery was executed by lethal injection on January 13, 2021, at the United States Penitentiary in Terre Haute, Indiana.

2006

• In East St. Louis, Illinois on September 15, 2006, the pregnant Jimella Tunstall was murdered by her childhood friend Tiffany Hall. She was knocked unconscious and her unborn baby was cut from her abdomen with a pair of scissors. Neither survived the attack. Tunstall's body was left in a vacant lot. Hall also drowned Tunstall's three children, ages one, two, and seven, and left their bodies in the washer and dryer machines in the family's apartment. Hall was sentenced to life in prison in June 2008.

2008

• In Kennewick, Washington, Araceli Camacho Gomez, age twenty-seven, was stabbed to death by twenty-three-year-old Phiengchai Sisouvanh Synhavong. Gomez's hands and feet were bound with yarn throughout the attack, and her fetus was cut from her womb with a box cutter. The child survived the vicious attack. Synhavong called the police for help and attempted to pass the fetus off as her own. It quickly became apparent to authorities that she was lying and guilty of the crime. Synhavong was sentenced in 2010 to life in prison without parole.
• In Wilkinsburg, Pennsylvania, pregnant eighteen-year-old Kia Johnson was murdered during a fetal abduction by Andrea Curry-Demus, who had previously spent eight years in prison for stabbing another expectant mother to obtain her unborn baby. Curry-Demus had also seized a child from a hospital. Johnson's body was later found in Curry-Demus' apartment. The baby survived.

2009

• In Worcester, Massachusetts, Julie A. Corey, 35, murdered Darlene Haynes, 23, and extracted her fetus. The baby, Sheila Marie survived. Corey was convicted by jury and sentenced to life imprisonment in February 2014.
• In Portland, Oregon, Korena Elaine Roberts, 29, murdered pregnant Heather Megan Snively, 21, before cutting the fetus out of Snively's uterus. Roberts had been faking a pregnancy to her boyfriend and family, claiming she was expecting twins. She posted advertisements for baby items on Craigslist, and after multiple attempts to meet with other pregnant women fell through, she was able to lure Snively to her Beaverton-area home where she lived with her boyfriend and her two children on June 5, 2009. She then murdered Snively in the bathroom and cut the fetus, a baby boy, out of Snively's uterus. After covering Snively's body in carpet and hiding it in a crawlspace beneath the house, Roberts called her boyfriend, Yan Shubin, claiming she needed help delivering her baby. He came home to find Roberts in the bathtub with the water running, crying uncontrollably and holding the baby boy, who was not breathing. Paramedics took Roberts and the baby to the hospital, where doctors determined that Roberts had not given birth. Hospital staff called police, who arrested Roberts and located Snively's body in Roberts' home that night. The baby boy could not be revived and was pronounced dead at the hospital. An autopsy showed that Snively suffered between 15 and 30 blows, mostly to the back of her head, as well as multiple cuts to her right breast and abdomen, and bite marks on her right arm. The medical examiner was able to determine that while the head injuries likely knocked Snively unconscious, it was the abdominal incisions and blood loss that killed her. Roberts pleaded guilty to one count of aggravated murder and agreed to life in prison without the possibility of parole.

2011

• In Bowling Green, Kentucky, Kathy Coy cut out Jamie Stice's fetus and left Stice to bleed to death on a rural road. Coy initially claimed she'd given birth to the baby five weeks premature, but doctors determined that the baby wasn't hers. Police found that Coy was friends on Facebook with Stice and another pregnant woman. The other woman was unharmed, but police grew suspicious when they couldn't find Stice. After intense questioning, Coy led police to Stice's body. Coy pleaded guilty but mentally ill to avoid the death penalty. In March 2012, she was sentenced to life imprisonment.
• In Milwaukee, Wisconsin, Annette Morales-Rodriguez kidnapped Martiza Ramirez-Cruz, beat her to death and cut her fetus out of the womb. The fetus was just days away from being due. According to a criminal complaint, Morales-Rodriguez called police hours later to report that she'd just given birth in her shower and the baby wasn't breathing. The fetus was pronounced dead, and an autopsy determined the baby did not belong to Morales-Rodriguez.
• In Oakdale, Louisiana, Pamela Causey-Fregia killed pregnant Victoria Marie Perez with blunt force trauma. Causey tried to convince her husband, who was leaving her, that she was pregnant, despite her family believing she had a hysterectomy. She burned the body and buried it on her property. Causey's young children witnessed the murder and alerted police in 2015. In March 2018 Causey-Fregia pled guilty to murder and was sentenced to life imprisonment.

2013

• In Mogale City, South Africa in January 2013, Loretta Cooke extracted the fetus of Valencia Behrens. The mother was found dead, the fetus survived.
• In Johannesburg, South Africa on July 31, 2013, Zandile Makulana extracted Pretty Tsanga's fetus. Neither the mother nor her fetus survived.

2015

• In Longmont, Colorado, 34-year-old Dynel Lane posted a Craigslist ad advertising free maternity clothes. When the seven months pregnant 26-year-old Michelle Wilkins responded to the ad, Lane broke a lava lamp over her head and stabbed her in the neck with glass from the broken lamp, before removing the fetus from her body. According to police reports, Lane's husband got home and she claimed to have had a miscarriage. Her husband found the baby in the bath tub, rolled her over and saw her gasping for air; he then took both Lane and the baby to the hospital. The baby was actually dead or died within minutes. Wilkins survived the attack and while in Lane's basement she was able to lock the door, call 911, and get medical assistance. On April 29, 2016 Lane was sentenced to 100 years imprisonment. According to Colorado law, no homicide charge was brought as the mother survived and the neonate was found to have been not viable. The September 14, 2015 episode of the Dr. Phil interview of Michelle details Michelle's story as of then.
• In Bronx, New York City, Ashleigh Wade, 22, was accused of killing Angelikque Sutton, 22, and taking her baby who survived.

2017

• In Fargo, North Dakota, William Hoehn (32 years old) and Brooke Crews (38) were charged on August 28, 2017 with conspiring to kidnap and murder pregnant Savanna Greywind (22) and to kidnap her baby. Greywind's body was found in the river 8 days after she disappeared on August 19. The newborn, named Haisley Jo, survived. Crews pled guilty and said Greywind was still alive when she performed the cesarean on her.

2019

• A nine-month pregnant 19-year-old Chicago woman, Marlen Ochoa-Lopez (surname alternately given as Ochoa-Uriostegui in some reporting), was lured to a house with the promise of free baby clothes on April 23, and then strangled. Police believe that "the baby was forcibly removed following that murder" and a 46-year-old woman living at the residence subsequently called emergency services and stated that she had just given birth to the infant. The baby boy was stated to be in critical condition then. The deceased mother's body was found on the property on May 15. The boy, named Yovanny Jadiel Lopez, died several weeks later from brain damage. Clarisa Figueroa and her daughter, Desiree Figueroa were charged with first degree murder among other counts, Clarisa's husband Piotr Bobak was charged with associated crimes.

2020

• On August 28, Flavia Godinho Mafra was lured to a fake baby shower in Santa Catarina, Brazil. She was later found dead due to cuts from her abdomen due to her baby being removed, and from being struck with a brick. A 26 year old suspect was arrested in connection with the murder.
• 21 year old Reagan Simmons-Hancock, who was 8 months pregnant, was killed on October 9 in New Boston, Texas. Her baby was cut from her body. Taylor Parker, who claimed to only know Reagan by her first name, had been the photographer at Hancock’s wedding the year before and had spent time with Reagan the week of the murder going out for a “girl’s day” and visited Reagan and her husband’s home the night before telling them she was to be induced the following day. The day the murders occurred. Taylor was later arrested in Oklahoma in connection with the case.

Fetal abduction attempts

2009

• In Washington, DC in December 2009, Teka Adams, 29 years old, homeless and nine months pregnant, was abducted by acquaintance Veronica Deramous, aged 40. Deramous enlisted the help of her seventeen-year-old son to tie up Adams and hold her captive for four days. During those four days, Deramous unsuccessfully attempted to extract the fetus. Adams was able to escape, barely clinging to life and severely injured. A neighbor called 911, and both Adams and her fetus survived. The cesarean was completed at a hospital and the baby was named Miracle. In November 2010 Veronica Deramous was sentenced to 25 years imprisonment on a plea bargain for first-degree assault.

Buddhism in Southeast Asia

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Buddhism_in_Southeast_Asia 

 

The 9th century Borobudur Buddhist stupa in Central Java

Buddhism in Southeast Asia includes a variety of traditions of Buddhism including two main traditions: Mahāyāna Buddhism and Theravāda Buddhism. Historically, Mahāyāna Buddhism had a prominent position in this region, but in modern times most countries follow the Theravāda tradition. Southeast Asian countries with a Theravāda Buddhist majority are Thailand, Cambodia, Laos and Myanmar, all mainland countries.

Vietnam continues to have a Mahāyāna majority due to Chinese influence. Indonesia was Mahāyāna Buddhist since the time of the Sailendra and Srivijaya empires, but Mahāyāna Buddhism in Indonesia is now largely practiced by the Chinese diaspora, as in Singapore and Malaysia. Mahāyāna Buddhism is the predominant religion of Chinese communities in Singapore, Malaysia, Brunei, and Indonesia.

History

Main articles: History of Buddhism in Southeast Asia, History of Indian influence on Southeast Asia, and Indianization of Southeast Asia

Further information: Indianised kingdom, Indosphere, Srivijaya, Khmer Empire, and Buddhism in Vietnam

Early traditions and origins

Prince Siddhartha shaves his hair and becomes an ascetic. Borobudur bas-relief, 9th century.

Buddhism reached Southeast Asia both directly over sea from India and indirectly from Central Asia and China in a process that spanned most of the first millennium CE.

In the third century B.C., there was disagreement among Ceylonese monks about the differences in practices between some councils of Bhikkhu monks and Vajjian Monks. The Bhikkhu monks affirmed Theravada traditions and rejected some of the practices of the Vajjian monks. It is thought that this sparked the split between Theravada and Mahayana Buddhism.

Theravada Buddhism was formed and developed by Ceylon Bhikkhus during a period spanning from the third century B.C. to fifth century A.D. Ceylonese influence, however, did not reach Southeast Asia until the eleventh century A.D. Theravada Buddhism developed in Southern India and then traveled through Sri Lanka, Burma, and into Thailand, Cambodia, Laos and Beyond.

In the twelfth century, Mahayana Buddhism developed in Northern India and traveled through Tibet, China and into Vietnam, Indonesia and beyond.

Buddhism is thought to have entered Southeast Asia from trade with India, China and Sri Lanka during the 1st, 2nd and 3rd centuries. One of the earliest accounts of Buddhism in Southeast Asia was of a Theravada Buddhist mission sent by the Indian emperor Ashoka to modern-day Burma in 250 BCE. The mission was received by the Mon kingdom and many people were converted to Buddhism. Via this early encounter with Buddhism, as well as others due to the continuous regional trade between Southeast Asia, China and South Asia, Buddhism spread throughout Southeast Asia. After the initial arrival in modern-day Burma, Buddhism spread throughout mainland Southeast Asia and into the islands of modern-day Malaysia and Indonesia. There are two primary forms of Buddhism found in Southeast Asia, Theravada and Mahayana. Theravada Buddhism spread from India to Sri Lanka then into the region as outlined above, and primarily took hold in the modern states of Burma, Cambodia, Laos, Thailand and southern Vietnam. Mahayana Buddhism is thought to have spread from both China and India during the first and second century into Southeast Asia. Mahayana took root primarily in maritime Southeast Asia, although there was also a strong influence in Vietnam, in part due to their connection with China.

Srivijaya, Java and the Khmer Empire

Srivijayan Art

 

A 9th century Srivijayan art bronze Avalokiteshvara of Bidor in Perak, Malaysia.

 

A bronze Maitreya statue from Komering, South Sumatra, Indonesia, 9th century Srivijayan art.

 

Avalokiteshvara of Chaiya, the bronze torso of Padmapani, 8th century Srivijayan art, Chaiya, Southern Thailand, demonstrate the Central Java art influence.

During the 5th to 13th centuries, The Southeast Asian empires were influenced directly from India, so that these empires essentially followed the Mahāyāna tradition. The Srivijaya Empire to the south and the Khmer Empire to the north competed for influence, and their art expressed the rich Mahāyāna pantheon of bodhisattvas.

Srivijaya, a maritime empire centred at Palembang on the island of Sumatra in Indonesia, adopted Mahāyāna and Vajrayāna Buddhism under a line of rulers named the Sailendras. Yijing described Palembang as a great centre of Buddhist learning where the emperor supported over a thousand monks at his court. Yijing also testified to the importance of Buddhism as early as the year 671 and advised future Chinese pilgrims to spend a year or two in Palembang. Srivijaya declined due to conflicts with the Chola rulers of India, before being destabilised by the Islamic expansion from the 13th century.

Between 8th to 11th century, Medang Mataram kingdom flourished in Central Java ruled by Sailendra dynasty, which also the ruling family of Srivijaya. The reign of King Panangkaran (r. 760—780) saw the rise of Buddhist Mahayana influence in central Java, as the Sailendran kings became the ardent patron of Buddhism. Numerous Buddhist temples and monuments were erected in the region. Notable example includes Kalasan, Manjusrigrha, Plaosan, and the grand stone mandala Borobudur, completed during the reign of Samaratungga (r. 819–838) in early 9th century. The period marked the apogee of Buddhist civilization in Indonesia.

Cambodian statue of Avalokiteśvara Bodhisattva. Sandstone, 7th century CE

From the 9th to the 13th centuries, the Mahāyāna Buddhist and Hindu Khmer Empire dominated much of the Southeast Asian peninsula. Under the Khmer, more than 900 temples were built in Cambodia and in neighbouring Thailand. Angkor was at the centre of this development, with a temple complex and urban organisation able to support around one million urban dwellers.

Early spread of Theravada Buddhism

There are many factors that contributed to the early spread of Theravada Buddhism throughout Southeast Asia. The main three ways in which the religion was transported into the region is through systems of trade, marriage, and missionary work. Buddhism has always been a missionary religion and Theravada Buddhism was able to spread due to the work and travel of missionaries. The Mon people are an ethnic group from Burma (Myanmar) that contributed to the success of Theravada Buddhism within Indochina. Buddhism was likely introduced to the Mon people during the rule of Ashoka Maurya, the third emperor of the Mauryan Dynasty (268-232 BCE) in India. Ashoka ruled his kingdom in accordance with Buddhist law and throughout his reign he dispatched court ambassadors and missionaries to bring the teachings of the Buddha to the east and Macedonia, as well to parts of Southeast Asia. India had trading routes that ran through Cambodia, allowing for the spread of these ideologies to easily occur. The Mons are one of the earliest ethnic groups from Southeast Asia and as the region shifted and grew, new inhabitants to Burma adopted the Mon people's culture, script, and religion.

The middle of the 11th century saw a decline of Buddhism in Southeast Asia. From the 11th to 13th century the Khmer Empire dominated the Southeast Asian peninsula. Hinduism was the primary religion of the Khmer Empire, with a smaller portion of people also adhering to Mahayana Buddhism. During the Khmer Rule, Theravada Buddhism was only found in parts of Malaysia, northwest Thailand, and lower Burma. Theravada Buddhism experienced a revival under the rule of Anawrahta Minsaw (1014–1077 AD). Anawrahta was the ruler of the Pagan Empire in Burma and is considered to be the founder of the modern Burmese nation. Anawrahta embraced and revived the Mon people's form of Theravada Buddhism through his building of schools and monasteries that taught and supported Theravada ideologies. The success of Theravada Buddhism in Burma under the rule of Anawrahta allowed for the later revival and growth of Buddhism in neighboring Southeast Asian countries, such as Thailand, Laos, and Cambodia. The influences of the Mon people as well as the Pagan Empire are still felt today throughout the region. Currently, the Southeast Asian countries with the highest amounts of practicing Theravada Buddhists are Myanmar, Thailand, Laos, and Cambodia.

Political power and resistance

Vietnamese Buddhist monk Quảng Đức self-immolation in 1963, protesting the persecution of Buddhists by the South Vietnamese government.

 

See also: Buddhist crisis and Buddhist Uprising

Buddhism has long been characterized by some scholars as an other-worldly religion, that is not rooted in economic and political activity. That is in part due to the influence of German sociologist, Max Weber, who was a prominent scholar of religion that has had a significant impact on the way Southeast Asian Buddhism is studied. Many contemporary scholars of Buddhism in Southeast Buddhism are starting to move away from the Weberian school of thought and identifying the role Buddhism has played in economic, political and every-day life in the region. Buddhism has also played a role in the consolidation of power and political resistance to throughout history, dating back to as early as the 10th and 11th century. Buddhist resistance has been a part of many significant historical moments, from the resistance to colonization and colonial powers, the creation of nation-states and the consolidation of political power within kingdoms and states.

Some of the earliest accounts of religious conflict that trace back to the 11th century took place in modern-day Burma. There was tension between Buddhist kings looking to create a more uniform religion and different sects of Buddhist worship. In particular, there was resistance from the cult of Nat worship, a religious practice that predates Buddhism in Burma. Buddhist kings of the time attempted to unify the different sects of Buddhism by the elimination of heretical movements. This was done so in order to maintain their power over their people and in an effort to purify the faith.

During the Nguyen dynasty of Vietnam in the 19th and 20th century, there was a strain between Confucian rulers and practitioners of Buddhism monks during the early unification of the empire. The rulers had a fear of potential rebellions emerging from monastic sites in the countryside and heavily criticized the spiritual practices of Buddhist sects, including a belief in invulnerability based on merit. After an attempt to de-legitimize Buddhist faith in the eyes of Vietnamese people through this criticism of their practices, they declared a war on Buddhism to squash any resistance to the consolidation of their empire

During the late 19th century and early 20th century, there were Buddhist resistance movements in the kingdom of Siam. These resistance movements were led by holy men or phu mi bun who had great power due to a high accumulation of merit. Some of these men claimed to have powers of invulnerability to enemy bullets and shared their powers through bathing others in holy water. An early phu mi bun rebellion was led by a former Buddhist monk, Phaya Phap, who resisted increased taxes in the province of Chiang Mai and proclaimed he would be the new, ideal Buddhist king of the region. These movements were not associated with mainstream Buddhism of the time, but many of the leaders had been ordained monks and utilized some Buddhist symbolism and philosophies.

Buddhist resistance also played a role in anti-colonialism movements. During the British colonization of Burma in the 19th century, there was intense Buddhist militarization and resistance against the colonial occupiers in an effort to restore the ideal Buddhist monarchy. There have also been more recent Buddhist resistance movements in Southeast Asia. After the communist takeover of Laos in 1975, some Buddhist monks feared that Buddhism was threatened by the Pathet Lao government. Many monks fled from Laos to Thailand and helped fund resistance movements from across the border. Monks who stayed in Laos supported resistance fighters with food and medical supplies. Another act of Buddhist resistance took place in Saigon in 1963 when a Mahayana Buddhist monk, Thích Quảng Đức, self-immolated in the middle of a busy intersection. This self-immolation was an act of protest of the regime of South Vietnamese President Ngo Dinh Diem, a member of the Catholic minority who ruthlessly persecuted and suppressed the Buddhist community.

Theravada traditions

The shaving ceremony of Theravada Buddhist monk to prepares ordain into Sangha Buddhist priesthood.

Theravada Buddhism in Southeast Asia is rooted in Ceylonese Buddhism that traveled from Sri Lanka to Burma and later to lower Thailand.

The Buddha, the Dhamma, and the Sangha are the three fundamental aspects of Theravāda Buddhist thought. The Buddha is the teacher of gods and men. The Dhamma consists of the teachings of the Buddha. It is the Noble Path made through the words and deeds of the Buddha that is to be followed. The path leads the follower from the Realm of Desire, to the Realm of Form, the Formless Realm with the ultimate destination being Nibbāna. The Sangha (gathering) refers to the two types of followers of the Buddha: laity and monastic. The monastic members strictly adhere to the Buddhist monastic discipline, known as the Vinaya. Theravadin Bhikkhu lead a very disciplined life modeled after the Buddha, going from Pabbajjā or novice ordination (sāmaṇera) to Upasampada or higher ordination (Bhikkhu).

Mahāyāna traditions

Vietnamese Buddhist nun.

Mahāyāna Buddhism in SE Asia is rooted in Buddhist traditions that traveled from Northern India through Tibet and China and eventually made their way to Vietnam, Indonesia and other parts of southeast Asia.

Mahāyāna Buddhism consists of a large variety of different sūtras. A defining feature of Mahāyāna Buddhism is its inclusiveness of a wide range of doctrines. The Mahāyāna tradition includes the doctrine of the three bodies of the Buddha (trikāya). The first is the body of transformation (nirmānakāya), the second is the body of bliss/enjoyment (sambhogakāya), and the third is the body of law/essence (dharmakāya). Each body makes sense of a different function of the Buddha. Another common theme in the Mahāyāna tradition of Buddhism, is the path of the bodhisattva. Stories are told about prior lives of the Buddha as a bodhisttva. These stories teach the qualities that are desirable to a good Mahāyāna Buddhist. Bodhisttvas are selfless as they care not only for their own salvation, liberation, and happiness, but also for the salvation, liberation, and happiness of others. A bodhisttva will make it almost all of the way to Nirvana, but go back in order to help others go farther.

Buddhism by country

Buddhist temple of Wat Arun in Bangkok, Thailand. Currently Buddhism is the major faith in Thailand and neighboring Myanmar, Cambodia and Laos

Currently, there are approximately 190–205 million Buddhists in Southeast Asia, making it the second largest religion in the region, after Islam. Approximately 35 to 38% of the global Buddhist population resides in Southeast Asia. The following is a list of Southeast Asian countries from most to least adherents of Buddhism as a percent of the population.

• Thailand has the largest number of Buddhists with approximately 95% of its population of 67 million adhering to Buddhism, placing it at around 63.75 million.
• Myanmar has around 48 million Buddhists, with 89% of its 54 million citizens practicing Theravada Buddhism. Around 1% of the population, mainly the Chinese, practice Mahayana Buddhism alongside Taoism, but are strongly influenced by Theravada Buddhism.
• Vietnam may have a large number of Buddhists, but the Communist government under-reports the religious adherence of its citizens. It is estimated to have around 44 million Buddhists, around half its population. The majority of Vietnamese people practice Mahayana Buddhism due to the large amount of Chinese influence.
• Cambodia has 97.9% of its total population adheres to Theravada Buddhism, placing its Buddhist population at around 14 million which mark as one of the world's highest Buddhist nations by percentage. By the end of 2017, there are 4,872 Buddhist temples (Wat) accommodating 69,199 Buddhist monks that play the important role to maintain the existence of Buddhism and preserve Buddhist culture in Cambodia.
• Malaysia has about 20% of its citizens, mainly ethnic Chinese, with significant numbers of ethnic Thais, Khmers, Sinhalese and migrant workers, practising Buddhism. The Chinese mainly practice Mahayana Buddhism, but due to the efforts of Sinhalese monks as well as historical links with Thailand, Theravada also enjoys a significant following.
• Communist Laos has around 5 million Buddhists, who form roughly 70% of its population.
• Indonesia has around 4.75 million Buddhists (2% of its population), mainly amongst its Chinese population. Most Indonesian Buddhists adhere to Theravada Buddhism, mainly of the Thai tradition.
• Singapore have around 2 million Buddhists, forming around 33% of their populations respectively. Singapore has the most vibrant Buddhist scene with all three major traditions having large followings. Mahayana Buddhism has the largest presence amongst the Chinese, while many immigrants from countries such as Myanmar, Thailand and Sri Lanka practice Theravada Buddhism.
• Philippines have around under 1% of the total population.
• Brunei, which has the smallest population in Southeast Asia, has around 13% of its citizens and a significant migrant worker population adhering to Buddhism, at around 65,000.

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  Thai Buddhist monks on pilgrimage

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  Novice monks in Myanmar

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  Buddhist monks pilgrim in Indonesia