CN107332628B - Computer coding method based on quantum entanglement and least square method - Google Patents
Computer coding method based on quantum entanglement and least square method Download PDFInfo
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Abstract
The invention provides a computer coding information transmission method based on quantum entanglement and least square method, comprising: the sending end and the receiving end jointly obey a group of constraint conditions, each binary information bit is expressed into a quantum entanglement form, adjacent binary information bits are in a quantum entanglement state, the sending end encodes binary information to be transmitted according to the quantum entanglement, the sending end transmits the binary information in a one-to-one and one-to-many form according to needs, and the receiving end measures and decodes the binary information according to the constraint conditions to realize correct judgment of the information bits. The invention realizes the coding of binary information of the computer by the quantum entanglement principle, and overcomes the influence of the vulnerability of quantum entanglement on quantum coding, quantum calculation and the like in the actual measurement. The invention determines the position relation of the binary information by the least square method, optimizes the judgment of the quantum entanglement condition by the probability statistical method, and can meet the basic requirements of the binary information transmission in quantum calculation and quantum coding.
Description
Technical Field
The invention relates to the technical field of quantum computation and computer information coding, in particular to a computer coding method based on quantum entanglement and a least square method.
Background
Quantum (Quantum) is an important concept of modern physics, and is a basic unit capable of showing the characteristics of a certain substance or physical quantity, which was originally proposed by the german physicist m.planck in 1900.
Quantum Entanglement (Quantum Entanglement) is a Quantum mechanical phenomenon, defined theoretically, that is described as a particular class of Quantum states having a composite system of two or more members, which cannot be decomposed into Tensor products (tensors products) of the respective Quantum states of the member systems. In general, quantum entanglement is the phenomenon that particles in a system consisting of two or more particles may be spatially separated but interact with each other.
The continuous development of the fields of quantum mechanics theory, quantum computation and the like provides powerful guarantee for the development of modern information technology. In 1951, D.Bohm reforms EPR thought in Quantum theory, and two spin components are used to replace the original coordinates and momentum, thereby laying the foundation for further research, especially experimental inspection. In 1952, d.bohm published two articles in succession on "reviews of physics", which presented implicit variable explanations of quantum mechanics. In 2000, the national institute of standards achieved a four-ion entangled state on an ion trap system. In 2005, the national institute of standards and austria brueck group declared that six and eight ion entangled states were achieved, respectively. In 2016, 12 months, the Panjianwei team of the Chinese science and technology university prepares an entangled photon source with optimal comprehensive performance by two different methods, so that the ten-photon entanglement is successfully realized for the first time, and the world record prepared by photon entanglement states is refreshed. In 2017, 6, 15, a famous magazine science reports a message that quantum entanglement of thousands of kilometers is realized for the first time by a quantum satellite of China 'ink horn' in the form of a cover paper, and compared with the previous record of the highest quantum transmission distance of 144 kilometers, the crossing means that quantum communication is a key step forward on a practical road.
Quantum entanglement is the scientific basis for the research of quantum invisible transmission, quantum key distribution, quantum computation and the like. However, the effects of many practical factors, such as: due to the limitation of experimental conditions and the influence of unavoidable environmental noise, the prepared entangled state is not all the maximum entangled state. Quantum communication and quantum computation using such entangled states will result in information distortion. Therefore, improving the actual quantum entangled state to approach the pure entangled state is an important research problem in the research of quantum information.
Applications of quantum entanglement include: quantum communication is applied to quantum state invisible transmission. Quantum entanglement can realize quantum secret communication, and the most safe information security transmission in theory at present is achieved. Quantum computing is applied to quantum computers, but the following major problems need to be solved: quantum algorithms, quantum codes, physical systems implementing quantum computing, and the like.
With the breakthrough achievements obtained in the field of quantum research in recent years, research on quantum computers has been further advanced. Feynman encounters the problem that the amount of calculated data becomes abnormally large in the research of simulating the quantum phenomenon; thus, the idea of using the quantum system configuration computer to simulate quantum phenomena is generated, and the operation time is reduced much.
In the eighties of the 20 th century, the research of quantum computers mainly stays in the theoretical research stage. Until the nineties of the 20 th century, P.Shor of Bell laboratories proved that quantum computers could complete logarithm arithmetic and quantum prime factorization algorithms, and the algorithms pose a serious threat to widely used RSA encryption algorithms, accelerating the development process of quantum computers.
In 2009, the world's first programmable general-purpose quantum computer was formally produced in the united states. Quantum computers were not studied for the purpose of replacing existing computers. The key problem is that it is really too difficult to experimentally achieve manipulation of microscopic quantum states. Computer code is the basis for computer implemented control and computation, and various information is represented internally in the computer in binary form. At present, there are certain limitations to the wide implementation and use of quantum computers, and there are many limitations to the research of quantum computing, including the research of quantum algorithms and quantum coding. However, with the continued development of quantum theory and technology, the potential market is enormous.
Disclosure of Invention
Technical problem to be solved
Due to the limitation of practical factors, the measurement of quantum information has the problems of distortion and the like, and in order to better realize the measurement of the quantum information, the invention aims to provide a computer coding method based on quantum entanglement and a least square method, complete the exchange of information in the information transmission realized by a computer, use the quantum entanglement to realize the coding of binary information 0 and 1, and be capable of completing the measurement and the correctness judgment of the information in one-to-one and one-to-many communication.
(II) technical scheme
In order to solve the technical problem, the invention provides a computer-coded information transmission method based on quantum entanglement and least square method, comprising:
part1, converting the transmitted information into a computer coding form based on quantum entanglement;
part2, the transmitting end transmits the information which is converted into the computer coding form based on quantum entanglement;
and Part3, after receiving the information transmitted by the transmitting end, the receiving end performs measurement and decoding according to the constraint conditions, and then judges the correctness of each bit of information.
The constraint condition is the basis for realizing communication based on computer coding of quantum entanglement and least square method, and is a rule to be followed by both the sending end and the receiving end. The constraints employed for computer coding based on quantum entanglement and least squares are described below.
Constraint Condition (1): the quantum entanglement state is described in a mathematical form
|φ>= ε|0>+ μ|1>
Wherein, |0>And |1>Representing two possible states of a qubit, the probability of measuring qubit 0 being | ε2Measuring the probability of qubit 1 as | μ tint2And ideally satisfies | ε -2+ |μ|2= 1。
Constraint Condition (2): in the actual measurement, the definition is made by the influence of the actual conditions
| |ε|2+ |μ|2– 1|<= df
Where df is the error of a given measurement. When the actual measurement error is less than or equal to df, defining that the measured numerical value is close to correct, and meeting the condition of quantum entanglement state; otherwise, the measured value is defined to be inaccurate and not meet the condition of quantum entanglement state.
Constraint Condition (3): a distance D is defined. In binary coding (p1, p2, …, pi, …, pn)2In (3), the binary digit at the first bit is denoted as p1, and sequentially denoted as pi (i =1,2, …) from the lower bit to the upper bit, and the last bit is denoted as pn. Defining the value of the distance D of p1 as 1, the value of the distance D of p2Is 2; by analogy, the value of the distance D of pi is i, and the value of the distance D of the last pn is n.
Ideally, the distance D has a positive integer value. However, in actual measurement, the measured value of the distance D is a real number.
Constraint Condition (4): the sign function Sgn (value) is defined as
When the value is less than 0, the return value of the sign function sgn (value) is 0.
When the value is greater than 0, the sign function sgn (value) returns a value of 1.
Constraint Condition (5): each bit of the computer code based on quantum entanglement and its adjacent bit can produce quantum entanglement, and the adjacent information bit is in entangled state:
|φ>= dp|0>+ dq|1>
wherein the probability of measuring qubit 0 is | dp2The probability of measuring qubit 1 is | dq2And ideally satisfies | dp2+ |dq|2= 1。
Constraint Condition (6): the hypothesis testing mathematics of computer coding based on quantum entanglement and least squares is described below
Accept H0: | ts-td | < C
Rejection H0: ts-td | > C
Where ts is the probability of measuring a value under ideal conditions, td is the probability of measuring a value under actual conditions, and C is the probability of an error threshold.
Constraint Condition (7): in the least squares method, it is assumed that the observed values of the measurement are (x1, y1), (x2, y2), …, (xn, yn).
The best fit function of the least squares method is defined as
y = k*x
Where y and x are both real numbers and k is set to be constant. There are any two real points d1 and d2, and N1 and N2 are integers:
(A) assuming that N1< = d1< d2 is satisfied, in the least square method, it is determined that d1 and N1 satisfy the best fit condition. Setting the value of d1 to N1;
(B) assuming that d1< d2< = N2 is satisfied, in the least square method, it is determined that d2 and N2 satisfy the best fit condition. The value of d2 was set to N2.
In Part1, the step of converting the information into a quantum entanglement-based computer-encoded form includes:
the transmitting end determines the value of the distance D before transmitting information. In binary coding (p1, p2, …, pi, …, pn), the binary bit at the first bit is denoted p1, the value of distance D defining p1 is 1, the value of distance D defining p2 is 2, and so on, the value of distance D defining pi is i.
Each binary information bit is represented in quantum entangled state
|φ>= α|0>+ β|1>
α and β are measured probabilities for |0> and |1> qubits.
The transmitting end needs to convert each bit in the code into the following form before transmitting information
Sgn(val)
When the binary bit is 0, val = -D (α)2, β2);
When the binary digit is 1, val = D (α)2, β2)。
Adjacent binary information bits (pi, pj)2In a quantum entangled state, a quantum entangled state form
|φ>= dp|0>+ dq|1>
dp and dq are the measured probabilities for |0> and |1> qubits.
Each bit of information transmitted has a uniform form
Sgn (sign bit D (α)2, β2))，(dp2, dq2)
In Part2, a sender transmits information that has been converted into a quantum entanglement-based computer-encoded form, including:
the sending end adopts a one-to-one or one-to-many form to transmit according to the requirement:
wherein, the one-to-one sending process is that the sending end A sends information to the receiving end B;
the one-to-many transmission process is for the sender S to transmit information to the receivers Cs (c1, c2, …, ci, …, cn), where each ci is a peer-to-peer receiver.
The transmission process is performed in parallel, with each bit of information being transmitted independently of the other.
In Part3, after the receiving end obtains the information transmitted from the transmitting end, the receiving end receives and measures the information according to the constraint condition, decodes the information, and then judges the correctness of each bit of information.
The receiving end follows Sgn (sign bit D (α)2, β2))，(dp2, dq2) Receives and measures information.
The receiving end measures the values of α and β, and in the actual measurement, the calculation is carried out according to | | α2+ |β|2– 1|<The constraint condition of = df verifies whether the binary information bit satisfies the condition of the entangled state, so as to determine whether the measured value of the binary information bit is accurate.
When the binary information bits do not satisfy the condition of the entangled state, the computer-coded hypothesis test based on quantum entanglement and least squares verifies α:
accept H0 | ts- α -td- α | < C- α
Reject H0 | ts _ α -td _ α | > = C _ α
Where ts _ α is the probability of α being measured under ideal conditions, td _ α is the probability of α being measured under actual conditions, and C _ α is the probability of α being the error threshold.
Hypothesis testing verification β:
accept H0 | ts- β -td- β | < C- β
Reject H0 | ts _ β -td _ β | > = C _ β
Where ts _ β is the probability of β being measured under ideal conditions, td _ β is the probability of β being measured under actual conditions, and C _ β is the probability of β being the error threshold.
When the binary information bit does not satisfy the condition of the entangled state, if it is assumed that the verification tests α and β, wherein the probability that one of α and β is correct, i.e., the H0 is accepted, and the probability that the other measurement exceeds the error threshold is incorrect, i.e., the H0 is rejected, indicate that the corresponding probability of the qubit of the binary bit is affected by practical factors and is in a weak entangled state.
When the binary information bit does not satisfy the condition of the entangled state, if it is assumed that either of the verification verifications α and β is incorrect, H0 is rejected, indicating that the qubit of the binary bit has been freed from the entangled state by the effect of practical factors.
And the receiving end measures the distance D according to the constraint condition of the least square method.
The receiving end decodes the binary information bit according to Sgn (sign bit D).
When the value of the measurement acquisition value is less than 0, the return value of the sign function sgn (value) is 0, and the binary information bit value is 0.
When the value of the measurement acquisition value is greater than 0, the return value of the sign function sgn (value) is 1, and the value of the binary information bit is 1.
The receiving end measures the numerical values of dp and dq, and the calculation is carried out according to | dp |2+ |dq|2– 1|<The constraint of = df verifies whether the adjacent information bits satisfy the condition of the entangled state.
In adjacent binary information bits (pi, pj)2When the binary information bit pi does not satisfy the condition of the entangled state, the hypothesis test of computer coding based on quantum entanglement and least squares verifies dp:
accept H0: | ts _ dp-td _ dp | < C _ dp
Rejection H0: ts _ dp-td _ dp | > C _ dp
Hypothesis testing verifies dq:
accept H0: | ts _ dq-td _ dq | < C _ dq
Rejection H0: is ts _ dq-td _ dq | > C _ dq
Wherein ts _ dp and ts _ dq are probabilities of ideally measuring dp and dq, td _ dp and td _ dq are probabilities of actually measuring dp and dq, and C _ dp and C _ dq are probabilities of error critical values of dp and dq.
When the binary information bit pi does not satisfy the condition of the entangled state, if the hypothesis test verifies dp and dq, wherein one of dp and dq is correct, i.e. accepting H0, and the probability that the other measurement result exceeds the error threshold is incorrect, i.e. rejecting H0, it indicates that the corresponding probability of the qubit of the binary information bit pi is affected by the actual factor to have an error, and the binary information bit pi is in a weakly entangled state.
When the binary information bit pi does not satisfy the condition of the entangled state, if the test is assumed to verify that either dp or dq is incorrect, i.e., H0 is rejected, it is stated that the qubit of the binary information bit pi has been released from the entangled state by the effect of the actual factors.
The measurement method for the binary information bit pj is the same as that for its neighboring binary information bit pi.
After the receiving end finishes the measurement, the information is decoded and the binary code is returned (p1, p2, …, pi, …, pn)2。
(III) advantageous effects
The invention has the advantages that the information exchange can be effectively carried out through the information transmission of the computer coding method based on the quantum entanglement and the least square method, the accuracy requirement in the information transmission process based on the quantum calculation is met, the measurement error caused by the fragility of the quantum and the limitation of the actual condition can be effectively overcome, and the quantum entanglement state in the actual measurement is displayed.
Drawings
Fig. 1 is a flowchart of a computer encoding method based on quantum entanglement and least squares.
Detailed Description
Embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
Einstein proposed a "paradoxical" physical assumption in 1935. In his hypothesis, two particles fly away in opposite directions, eventually reaching the far ends of a constellation. Assuming that the two particles are always in an "entangled" state, i.e., they are "psychologically sensitive" in the sense of quantum mechanics, one particle can immediately sense everything that happens to its twin brother, then when one particle is measured, the other particle is immediately affected by this measurement behavior as if the twin pair were able to transceive mysteriously and instantaneously through space.
For the assumption of a.einstein, experiments on light quanta were performed: a photon signal is transmitted through an optical fiber, a pair of photons at one end is activated by laser, and a photon at the other end reacts immediately. There is no exchange of energy, yet the particles still share information in some way, and there is no spatio-temporal theory that can explain how this non-localization results.
When studying quantum systems, each quantum system has an associated wave function. Each quantum can only be described by its various probabilities, not by any exact numerical representation. The probability is determined entirely by the wave function. The probability of a particle appearing at a given location is related to the wave function of the particle at that location. Although in classical physics, the position and velocity of a moving object can theoretically be measured, determined and predicted one hundred percent. In the micro-particle world, the motion of objects cannot be predicted, and any prediction is a prediction in a statistical sense essentially. Thus, quantum theory is probabilistic in nature.
The invention provides a computer coding information transmission method based on quantum entanglement and least square method, which can be divided into: the sending end encodes binary information to be transmitted according to quantum entanglement, the sending end transmits the binary information in a one-to-one or one-to-many mode according to needs, and the receiving end performs measurement and decoding according to constraint conditions to achieve correct judgment of information bits.
The specific implementation steps of the transmitting end are as follows.
The sending end determines the value of the distance D before transmitting information, and each binary information bit is expressed as a quantum entanglement state: i phi>= α|0>+β|1>Sgn (sign bit D (α) is encoded by the values 0 and 1 of the binary bit2, β2))。
Adjacent binary information bits are represented in quantum entangled state form: i phi > = dp |0> + dq |1 >.
The sending end completes computer coding, and each bit of binary information has the following format
Sgn (sign bit D (α)2, β2))，(dp2, dq2)
The transmission process is performed in parallel, with each bit of information being transmitted independently of the other.
The specific implementation steps of the receiving end are as follows.
After the receiving end obtains the information transmitted by the transmitting end, the receiving end receives and measures the information according to the constraint condition, decodes the information and then judges the correctness of each bit of information.
The receiving end follows Sgn (sign bit D (α)2, β2))，(dp2, dq2) Receives and measures information.
The receiving end measures the values of α and β and intactly according to | | α2+ |β|2– 1|<The constraint of = df verifies whether the binary information bit satisfies the condition of entanglement to determine whether the measured value of the binary information bit is correct. And when the binary information bit does not meet the condition of the entangled state, carrying out hypothesis test to judge whether the binary information bit is in the weak entangled state or the entangled state is released.
And the receiving end measures the distance D according to the constraint condition of the least square method.
The receiving end decodes the binary information bit according to the sign bit D, and determines that the binary information bit value is 0 or 1.
The receiving end measures the numerical values of dp and dq, and the noncircular distribution is realized according to | dp |2+ |dq|2– 1|<The constraint of = df verifies whether the adjacent information bits satisfy the condition of the entangled state. And when the binary information bit does not meet the condition of the entangled state, carrying out hypothesis test to judge whether the adjacent information bit is in the weak entangled state or the entangled state is released.
Decoding is successful, and transmission information is obtained.
Example 1: and the transmission of binary information 0110 from the sending end A to the receiving end B is realized.
From known, send end toThe information sent by the receiving end is (0110)2Setting distance D at transmitting end, coding in binary system
(p1, p2, p3, p4)2
The binary digit at the 1 st bit is p1, which is denoted as p2 and p3 from low to high, and the last bit is p4, i.e., n = 4. The value of the distance D for p1 is set to 1, the value of the distance D for p2 is set to 2, and so on.
The value of the distance D is recorded as D1=1，D2=2，D3=3 and D4= 4。
The least square method of the constraint Condition (7) is set to y = k × x, k =1, that is, y = x. The least squares method determines the position of the binary information in its encoding.
Before transmitting information, the sender needs to convert each bit in the code into the following form:
sgn (sign bit D (α)2, β2))，(dp2, dq2)
When the binary information bit is 0, val defining sgn (val) is a negative number; when the binary information bit is 1, val defining sgn (val) is a positive number. Each bit of binary information is represented in quantum entangled state form: i phi>= α|0>+β|1>The probabilities α and β of quantum entanglement are α2=0.1 and β2=0.9。
Adjacent binary information bits are represented in quantum entangled state form: i phi>= dp|0>+ dq|1>. Setting dp2= 0.2，dq2= 0.8。
From known information (0110)2It can be seen that the sender a encodes each bit of information as Sgn (sign bit D (α)2, β2))，(dp2, dq2) It is concretely as follows:
p1={-1(0.1, 0.9), (0.2, 0.8)}
p2={ 2(0.1, 0.9), (0.2, 0.8)}
p3={ 3(0.1, 0.9), (0.2, 0.8)}
p4={-4(0.1, 0.9), (0.2, 0.8)}
when the transmission conditions are ideal, that is, the measured values are all within the correct error range, the constraint conditions of the above coding and observing are measured as follows:
the sign function sgn (val) is defined as: when the value val is less than 0, returning to 0; when the value val is greater than 0, 1 is returned.
The receiving end receives p1= { -1(0.1, 0.9), (0.2, 0.8) }.
The measurement yields a distance D =1, which is the first digit according to the least squares method y = x, Sgn (val) being negative, represented by | | | α | |2+ |β|2– 1|<= df =0.1, yielding |0.1+ 0.9-1 | =0<df =0.1, α and β satisfy the entanglement condition by | | dp | non-woven hair2+ |dq|2– 1|<Is = df, so, |0.2+ 0.8-1 | =0<df, the entanglement condition is satisfied with the adjacent bits.
Then the bit value is 0 after p1 is decoded.
The receiving end receives p2= { 2(0.1, 0.9), (0.2, 0.8) }.
The measurement yields a distance D =2, which is the second bit according to the least squares method y = x, sgn (val) is a positive number, α and β satisfy the entanglement condition, and the entanglement condition is satisfied with the adjacent bits.
Then the bit value is 1 after p2 is decoded.
And so on.
The receiving end receives p3= { 3(0.1, 0.9), (0.2, 0.8) }.
The measurement yields a distance D =3, which is the third bit according to the least squares method y = x, sgn (val) is a positive number, α and β satisfy the entanglement condition, and the entanglement condition is satisfied with the adjacent bit.
Then the bit value is 1 after p3 is decoded.
The receiving end receives p4= { -4(0.1, 0.9), (0.2, 0.8) }.
The measurement yields a distance D =4, which is the fourth bit according to the least squares method y = x, sgn (val) is negative, α and β satisfy the entanglement condition, and the entanglement condition is satisfied with the adjacent bits.
Then the bit value is 0 after p4 is decoded.
And decoding the received information into 0110 to finish the correct transmission of the information.
Example 2: the transmission of binary information 0110 from the transmitting end S to the receiving ends Cs _1 and Cs _2 is realized.
As known, the information sent by the sending end to the receiving end is (0110)2。
The least square method of the constraint Condition (7) is set to y = k × x, k =1, that is, y = x.
From known information (0110)2The sender S encodes each bit of information into { Sgn (sign bit D (α))2, β2))，(dp2,dq2) It is concretely as follows:
p1={-1(0.1, 0.9), (0.2, 0.8)}
p2={ 2(0.1, 0.9), (0.2, 0.8)}
p3={ 3(0.1, 0.9), (0.2, 0.8)}
p4={-4(0.1, 0.9), (0.2, 0.8)}
assume that the receiving end Cs _1 receives the information of
p1={-1.2(0.1, 0.9), (0.2, 0.8)}
p2={ 2.25(0.1, 0.9), (0.2, 0.8)}
p3={ 3(0.1, 0.9), (0.2, 0.8)}
p4={-4(0.1, 0.9), (0.2, 0.8)}
Value D of distance D from receiving end Cs _11=1.2 and D2=2.25, i.e. the distance offset value in this case is large, in practice D1=1 and D2=2。
Satisfies N1 according to (A) of constraint Condition (7)<= d1<d2, then in the fitting, d1 and N1 are determined to satisfy the best fit condition. The value of d1 was set to N1. From p1, N1=1<d1=1.2<D2=2.25, obtaining D according to least squares1=1。
N1=2 is satisfied by (a) of p2 in accordance with constraint Condition (7)<D2=2.25, obtain D2=2。
Assume that the receiving end Cs _2 receives the information of
p1={-1.3(0.1, 0.9), (0.2, 0.8)}
p2={2.2(0.1, 0.9), (0.2, 0.8)}
p3={ 2.25(0.1, 0.9), (0.2, 0.8)}
p4={-4(0.1, 0.9), (0.2, 0.8)}
Assuming that N1< = d1< d2 is satisfied according to (a) of the constraint Condition (7), it is determined that d1 and N1 satisfy the best fit Condition in the least square method. The value of d1 was set to N1.
From p2, N1=2<= d1=2.2<d2= 2.25. Thus, setting D2=2。
Assuming that d1< d2< = N2 is satisfied according to (B) of the constraint Condition (7), it is determined that d2 and N2 satisfy the best fit Condition in the least square method. The value of d2 was set to N2.
From p3, d1=2.2<d2=2.25<= N2= 3. Thus, the following are set: d3=3。
According to (a) and (B) of the constraint Condition (7), information is decoded at the receiving end Cs _1 and the receiving end Cs _ 2: 0110.
example 3: and judging the quantum entanglement state according to hypothesis testing.
Assuming that the sending end sends information 0110 to the receiving end, the information measured by the receiving end is as follows:
p1={-1.1(0.1, 0.9), (0.9, 0.1)}
pi ={ 2.2(0.1, 0.9), (0.9, 0.1)}
pj ={ 2.25(0.1, 0.9), (0.5, 0.11)}
p4={ -4(0.1, 0.9), (0.9, 0.1)}
set D2Is a distance of pi, D3Is the distance of pj.
In the least squares method, pi and pj are adjacent bits, which can be derived from the distance values of pi and pj.
According to the constraint Condition (5), each bit of the computer code based on quantum entanglement and its adjacent bits will generate quantum entanglement, and the adjacent binary information bits are in entangled state: i phi > = dp |0> + dq |1 >.
Constraint Condition (2) is defined in actual measurement under the influence of actual conditions
||ε|2+ |μ|2– 1|<= df=0.1。
Measuring contiguous bits of information (dp) of pi2, dq2) And quantum entanglement relationship is satisfied.
The neighbor entanglement condition for pj is:
|0.5+0.11–1|=0.39>df =0.1。
in measuring pj and adjacent information bits, (dp)2, dq2) The quantum entanglement relationship is not satisfied, and therefore, the measured value of pj is judged to be affected and changed.
According to the constraint Condition (6), when the binary information bits pj do not satisfy the Condition of the entangled state, the hypothesis test of computer coding based on the quantum entanglement and least square method verifies dp, setting C _ dq = C _ dp =0.1, and Sqrt () is an open square function.
Accept H0: | ts _ dp-td _ dp | < C _ dp
Rejection H0: ts _ dp-td _ dp | > C _ dp
From the known pj, | ts _ dp = Sqrt (0.9) -td _ dp = Sqrt (0.5) | = 0.24> C _ dp = 0.1.
Therefore, H0 is rejected.
Hypothesis testing validation dq
Accept H0: | ts _ dq-td _ dq | < C _ dq
Rejection H0: is ts _ dq-td _ dq | > C _ dq
From the known pj, | ts _ dq = Sqrt (0.1) -td _ dq = Sqrt (0.11) | = 0.015< C _ dq = 0.1.
Thus, the binary information bit pj is illustrated as being weakly entangled with adjacent bits.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (1)
1. A computer encoding method based on quantum entanglement and least squares, comprising:
part1, converting the transmitted information into a computer coding form based on quantum entanglement;
part2, the sending end transmits the information which is converted into the computer coding form based on quantum entanglement;
part3, after receiving the information transmitted by the transmitting end, the receiving end measures and decodes according to the constraint condition, and then judges the correctness of each bit of information;
the constraint condition is the basis for realizing communication based on the computer coding of the quantum entanglement and least square method, and is a rule to be followed by both the sending end and the receiving end;
the constraint conditions adopted by the computer coding based on the quantum entanglement and least square method are described as follows;
constraint Condition (1): the quantum entanglement state is described in a mathematical form
|φ>= ε|0>+ μ|1>
Wherein, |0>And |1>Representing two possible states of a qubit, the probability of measuring qubit 0 being | ε2Measuring the probability of qubit 1 as | μ tint2And ideally satisfies | ε -2+ |μ|2= 1；
Constraint Condition (2): in the actual measurement, the definition is made by the influence of the actual conditions
| |ε|2+ |μ|2– 1|<= df
Where df is the given measurement error; when the actual measurement error is less than or equal to df, defining that the measured numerical value is close to correct, and meeting the condition of quantum entanglement state; otherwise, defining that the measured value is inaccurate and does not meet the condition of quantum entanglement state;
constraint Condition (3): defining a distance D; in binary coding (p1, p2, …, pi, …, pn)2In the above description, the binary digit at the first bit is denoted as p1, the binary digits from the lower bit to the upper bit are denoted as pi (i =1,2, …), and the last bit is denoted as pn; defining the value of the distance D of p1 as 1 and the value of the distance D of p2 as 2; by analogy, the numerical value of the distance D of pi is i, and the numerical value of the distance D of the last pn is n;
in an ideal case, the value of the distance D is a positive integer; however, in actual measurement, the measured value of the distance D is a real number;
constraint Condition (4): the sign function Sgn (value) is defined as
When the value is less than 0, the return value of the sign function sgn (value) is 0;
when the value is greater than 0, the return value of the sign function sgn (value) is 1;
constraint Condition (5): quantum entanglement is generated to each bit and adjacent bit of computer code based on quantum entanglement, and adjacent information bits are in entangled state
|φ>= dp|0>+ dq|1>
Wherein the probability of measuring qubit 0 is | dp2The probability of measuring qubit 1 is | dq2And ideally satisfies | dp2+ |dq|2= 1；
Constraint Condition (6): the hypothesis testing mathematics of computer coding based on quantum entanglement and least squares is described below
Accept H0: | ts-td | < C
Rejection H0: ts-td | > C
Wherein ts is the probability of measuring a value under an ideal condition, td is the probability of measuring a value under an actual condition, the measured value refers to the probability of measuring qubit 0 and the probability of measuring qubit 1 in a quantum entangled state, and C is the probability of an error critical value;
constraint Condition (7): in the least squares method, it is assumed that the observed values of the measurement are (x1, y1), (x2, y2), …, (xn, yn);
the best fit function of the least squares method is defined as
y = k*x
Wherein y and x are real numbers, and k is set as a constant; there are any two real points d1 and d2, N1 and N2 are integers;
(A) assuming that N1< = d1< d2 is satisfied, then in a least squares method, it is determined that d1 and N1 satisfy a best fit condition; setting the value of d1 to N1;
(B) assuming that d1< d2< = N2 is satisfied, in a least square method, it is determined that d2 and N2 satisfy a best fit condition; setting the value of d2 to N2;
in Part1, the step of converting the information into a quantum entanglement-based computer-encoded form includes:
the sending end determines the value of the distance D before transmitting information, in binary coding (p1, p2, …, pi, …, pn), the binary bit at the first bit is marked as p1, the value of the distance D defining p1 is 1, the value of the distance D defining p2 is 2, and so on, the value of the distance D defining pi is i;
each binary information bit is represented in quantum entangled state
|φ>= α|0>+ β|1>
α and β are measured probabilities for |0> and |1> qubits;
the transmitting end needs to convert each bit in the code into the following form before transmitting information
Sgn(val)
When the binary bit is 0, val = -D (α)2, β2)；
When the binary digit is 1, val = D (α)2, β2)；
Adjacent binary information bits (pi, pj)2In a quantum entangled state, a quantum entangled state form
|φ>= dp|0>+ dq|1>
dp and dq are the measured probabilities for the corresponding |0> and |1> qubits;
each bit of information transmitted has a uniform form
Sgn (sign bit D (α)2, β2))，(dp2, dq2)
In Part2, a sender transmits information that has been converted into a quantum entanglement-based computer-encoded form, including:
the sending end transmits in a one-to-one and one-to-many mode according to the requirement;
wherein, the one-to-one sending process is that the sending end A sends information to the receiving end B;
the one-to-many sending process is that the sender S sends information to the receivers Cs (c1, c2, …, ci, …, cn), where each ci is a peer-to-peer receiver;
the transmission process is executed in parallel, and the transmission of each information bit is independent;
in Part3, after the receiving end obtains the information transmitted by the transmitting end, the receiving end receives and measures the information according to the constraint condition, decodes the information, and then judges the correctness of each bit of information;
the receiving end follows Sgn (sign bit D (α)2, β2))，(dp2, dq2) Receive and measure information in the format of (1);
the receiving end measures the values of α and β, and in the actual measurement, the calculation is carried out according to | | α2+ |β|2– 1|<The constraint condition of = df verifies whether the binary information bit meets the condition of an entangled state or not so as to judge whether the measured value of the binary information bit is accurate or not;
when the binary information bits do not satisfy the condition of the entangled state, the computer-coded hypothesis test based on quantum entanglement and least squares verifies α:
accept H0 | ts- α -td- α | < C- α
Reject H0 | ts _ α -td _ α | > = C _ α
Wherein ts _ α is the probability of α being measured under ideal conditions, td _ α is the probability of α being measured under actual conditions, and C _ α is the probability of α being the error threshold;
hypothesis testing verification β:
accept H0 | ts- β -td- β | < C- β
Reject H0 | ts _ β -td _ β | > = C _ β
Wherein ts _ β is the probability of β being measured under ideal conditions, td _ β is the probability of β being measured under actual conditions, and C _ β is the probability of β being the error threshold;
when the binary information bit does not satisfy the condition of the entangled state, if the hypothesis tests α and β verify that one of α and β is correct, i.e., accept H0, and the probability that the other measurement result exceeds the error threshold is incorrect, i.e., reject H0, the corresponding probability of the qubit of the binary bit is affected by practical factors, and the corresponding probability is in a weak entangled state;
when the binary information bit does not satisfy the condition of the entangled state, if any one of the proof-of-check α and β is assumed to be incorrect, H0 is rejected, which indicates that the qubit of the binary bit has been released from the entangled state due to practical factors;
the receiving end measures the distance D according to the constraint condition of the least square method;
the receiving end decodes the binary information bit according to the Sgn (sign bit D);
when the value obtained by measurement is less than 0, the return value of the sign function sgn (value) is 0, and the binary information bit value is 0;
when the value obtained by measurement is greater than 0, the return value of the sign function sgn (value) is 1, and the binary information bit value is 1;
the receiving end measures the numerical values of dp and dq, and the calculation is carried out according to | dp |2+ |dq|2– 1|<A constraint condition of = df verifies whether adjacent information bits satisfy a condition of an entangled state;
in adjacent binary information bits (pi, pj)2When the binary information bit pi does not satisfy the condition of the entangled state, the hypothesis test of computer coding based on quantum entanglement and least squares verifies dp:
accept H0: | ts _ dp-td _ dp | < C _ dp
Rejection H0: ts _ dp-td _ dp | > C _ dp
Hypothesis testing verifies dq:
accept H0: | ts _ dq-td _ dq | < C _ dq
Rejection H0: is ts _ dq-td _ dq | > C _ dq
Wherein ts _ dp and ts _ dq are probabilities of measuring dp and dq under an ideal condition, td _ dp and td _ dq are probabilities of measuring dp and dq under an actual condition, and C _ dp and C _ dq are probabilities of error critical values of dp and dq;
when the binary information bit pi does not meet the condition of the entangled state, if the hypothesis test verifies dp and dq, wherein one of dp and dq is correct, namely accepting H0, and the probability that the other measurement result exceeds the error threshold value is incorrect, namely rejecting H0, the corresponding probability of the quantum bit of the binary information bit pi is influenced by actual factors, so that an error occurs, and the binary information bit pi is in a weak entangled state;
when the binary information bit pi does not meet the condition of the entangled state, if the test is supposed to verify that any one of dp and dq is incorrect, H0 is rejected, which indicates that the quantum bit of the binary information bit pi is influenced by actual factors to release the entangled state;
the measurement method of the binary information bit pj is the same as that of the adjacent binary information bit pi;
after the receiving end finishes the measurement, the information is decoded and the binary code is returned (p1, p2, …, pi, …, pn)2。
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