CN108388948A - A kind of type conversion designs method from quantum image to quantum real signal - Google Patents
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Abstract
The present invention provides a kind of type conversion designs method from quantum image to quantum real signal, belongs to Quantum signal processing field.The present invention utilizes the controlled door of quantum and single quantum bit door, according to IEEE754 international standards, build from quantum gray level image to the quantum types conversion of 2 dimension real signals and from quantum coloured image to quantum the types conversion of 2 dimension triple channel real signals quantum wire, to provide necessary basis for subsequent Quantum signal processing (such as by quantum wavelet application to quantum image).The present invention embody quantum information processing signal processing high efficiency：The quantum wire complexity that the type of quantum gray level image to the dimension real signal of quantum 2 is converted and the type of quantum coloured image to the dimension triple channel real signal of quantum 2 is converted is all into O (1).
Description
Technical field
The present invention relates to Quantum signal processing fields, are specifically the classes being related to from quantum image to quantum real signal
The design method of type conversion.
Background technology
Quantum signal processing is quantum calculation and the product that signal processing technology is combined, the concurrency of quantum calculation and folded
Additivity is that Quantum signal processing is basic better than classical signals processing.Image is a kind of integer signal, therefore quantum image procossing
It is the subdomains of Quantum signal processing.
In quantum calculation, information unit is indicated with quantum bit, and there are two basic quantum states for it | 0>With | 1>, fundamental quantity
Sub- state is referred to as ground state.One quantum bit can be the linear combination of two ground state, be commonly referred to as superposition state, be represented by | ψ
>=a | 0>+b|1>, wherein a and b are two plural numbers.
Tensor product is to be combined small vector space, constitutes a kind of method of bigger vector space, uses symbolTable
Show.For two ground state | u>With | v>, their tensor productCommon dummy suffix notation | uv>, | u>|v>Or | u, v>Table
Show, such as ground state | 0>With | 1>, their tensor product is represented by
For the n times tensor product of matrix UIt can write a Chinese character in simplified form intoFor quantum state | u>N times tensor productAlso it can write a Chinese character in simplified form into
Quantum wire can be made of the quantum bit door of a sequence, in the expression figure of quantum wire, every line all tables
Show the line of quantum wire, the execution sequence of quantum wire is from left to right.Quantum bit door can be conveniently with matrix form
It indicates, single quantum bit door can be indicated with one 2 × 2 unitary matrice U, i.e. U+U=I, wherein U+ are the conjugate transposition squares of U
Battle array, I is unit matrix.X (NOT gate),It is the n times tensor product of I.The titles of some basic quantum bit gates, symbol and corresponding
Matrix expression see Fig. 1.Most important muliti-qubit door is U controlled, by control quantum bit and target quantum bit, when
It when control bit is 1, is indicated with stain, when control bit is 0, is shown by white dots.Work as U=X, at this time controlled U be referred to as it is controlled
NOT gate.As U=Swap (Swap is also referred to as swap gate), it is referred to as Fredkin (controlled exchange doors) for controlled U at this time.
The title and symbolic indication of the common muliti-qubit door of the above are shown in Fig. 2.
According to 754 international standards of IEEE, the regulation of 32 bit single-precision floating point real numbers is as shown in table 1.In table 1, symbol
Position 0 indicates positive number, and 1 indicates that negative, ± ∞ indicate positive minus infinity, and NaN expressions are not a numbers.
132 single-precision floating point real numbers of table
| Sign bit | Exponent (8 bit) | Mantissa's (23 bit) | Floating number |
| 0 or 1 | 0 | 0 | ±0 |
| 0 or 1 | 0 | Non-zero binary number m | ±0.m×2-126 |
| 0 or 1 | k(1≤k≤254) | Binary number m | ±1.m×2k-127 |
| 0 or 1 | 255 | 0 | ±∞ |
| 0 or 1 | 255 | Non-zero number | NaN |
A gray scale can be indicated with 8 quantum bits：
|f(x,y)>=| c8c7c6c5c4c3c2c1> (1)
Wherein ci∈ { 0,1 }, i=1, K, 8.
Further, n+8 quantum bits can indicate a width gray level image：
Wherein | f (x, y)>Indicate image coordinate (x, y) gray value, | x>Indicate the x coordinate of signal, | y>Indicate letter
Number x coordinate, the size of image is 2n-k×2k, k, n are positive integer.
N+10 quantum bits can indicate a width coloured image：
WhereinThe gray level image of red channel, green channel and blue channel is stored respectively, i.e.,
Here, | fr(x,y)>,|fg(x,y)>,|fb(x,y)>Indicate three channels of image coordinate (x, y) gray value,
|x>Indicate the x coordinate of signal, | y>Indicate the x coordinate of signal, the size of image is 2n-k×2k, k, n are positive integer.
A single precision floating datum is stored with the quantum state of 32 quantum bits, i.e.,
Wherein | S (x, y)>=| Sxy>Stored symbols position,Exponent is stored,Mantissa is stored,
The storage that quantum 2 ties up real signal is expressed as
Wherein | l (x, y)>Indicate signal position (x, y) real number value, | x>Indicate the x coordinate of signal, | y>Indicate letter
Number x coordinate, the size of signal is 2n-k×2k, k, n are positive integer.
The storage that quantum 2 ties up triple channel real signal is expressed as
WhereinOne 2 dimension real signal is stored respectively, i.e.,
Here, | l1(x,y)>,|l2(x,y)>,|l3(x,y)>Indicate three channels of signal position (x, y) real number value,
|x>Indicate the x coordinate of signal, | y>Indicate the x coordinate of signal, the size of signal is 2n-k×2k, k, n are positive integer.
Invention content
The present invention provides the design method converted from quantum image to the type of quantum real signal, including quantum gray level image
The design method and quantum coloured image converted to the type of the dimension real signal of quantum 2 tie up the type of triple channel real signal to quantum 2
The design method of conversion solves the type transfer problem from quantum image to quantum real signal, so as to using at quantum signal
Reason technology (such as quantum wavelet transform) removes processing quantum image.
The present invention solves the above problems by the following technical programs：
The present invention utilizes the controlled door of quantum and single quantum bit door, and according to 754 international standards of IEEE, structure is grey from quantum
Spending image, the types of 2 dimension triple channel real signals turn to the type conversion of the dimension real signal of quantum 2 and from quantum coloured image to quantum
The quantum wire changed.
A kind of type conversion designs method from quantum image to quantum real signal, the method using the controlled door of quantum and
Single quantum bit door builds the type conversion of the 2 dimension real signals from quantum gray level image to quantum according to 754 international standards of IEEE
With the quantum wire of the type conversion of 2 dimension triple channel real signals from quantum coloured image to quantum.
Invention specific design scheme and step be：
1, quantum gray level image ties up the design method of the type conversion of real signal to quantum 2
The displacement P that shuffles is realized
P|c8c7c6c5c4c3c2c1>=| c7c6c5c4c3c2c1c8> (9)
The quantum realization circuit for replacing P shuffle as shown in figure 3, its schematic diagram is as shown in Figure 4.Quantum wire in Fig. 3 is by 7
Swap gate is constituted.
Pi expressions continuously perform the i displacement P that shuffles, i.e.,
Pi=PK P (10)
PiQuantum realize circuit as shown in figure 5, its schematic diagram is as shown in Figure 6.Quantum wire in Fig. 5 is shuffled by i to be set
The quantum wire for changing P is constituted.
Gradation conversion is as shown in table 2 at the rule of single precision floating datum.
2 gradation conversion of table at single precision floating datum rule
According to regular in table 2, quantum wire such as Fig. 7 institutes that design is converted from quantum image to the type of quantum real signal
Show, schematic diagram is as shown in Figure 8.In the figure 7, using 8 swap gates to initial stateOn, it obtains
Wherein | ψG>Indicate a width gray level image, as shown in formula (2), | f (x, y)>Indicate image in coordinate (x, y)
Gray value, | x>Indicate the x coordinate of signal, | y>Indicate the x coordinate of signal, the size of image is 2n-k×2k, k, n are just whole
Number.
Dashed box 1 in Fig. 7 is applied to quantum state | ξ1>On, it obtains
WhereinIndicate signal the real number value of position (x, y) exponent, such as
Shown in formula (5).
Then the dashed box 2 in Fig. 7 is applied to quantum state | ξ2>On, it obtains
Wherein | l (x, y)>Indicate signal position (x, y) real number value, as shown in formula (5), | x>Indicate the x of signal
Coordinate, | y>Indicate the x coordinate of signal, the size of signal is 2n-k×2k, k, n are positive integer, | ψ2>2 dimension real signal of storage, such as
Shown in formula (6).Quantum wire in analysis chart 8 finds that the complexity of circuit is a constant unrelated with signal magnitude, because
The complexity of this circuit is (1) O.
2, quantum coloured image ties up the design method of the type conversion of triple channel real signal to quantum 2
The quantum wire of the type conversion of 2 dimension triple channel real signals is as shown in Figure 9 from quantum coloured image to quantum.Scheming
In 9, using 8 swap gates to initial stateOn, it obtains
Wherein | ψC>Indicate a width coloured image, as shown in formula (3), | fr(x,y)>,|fg(x,y)>,|fb(x,y)>Table
Diagram is as three channels are in the gray value of coordinate (x, y), as shown in formula (4), | x>Indicate the x coordinate of signal, | y>Indicate letter
Number x coordinate, the size of image is 2n-k×2k, k, n are positive integer.
Then three controlled GQ circuits in Fig. 9 are acted on into quantum state | ξ4>On, it finally obtains storage quantum 2 and ties up threeway
The quantum state of road real signal | ψ3>.Wherein GQ is the quantum wire that quantum 2 ties up real signal, as shown in fig. 7, quantum state | ψ3>Such as public affairs
Shown in formula (7).Quantum wire in analysis chart 9 finds that the complexity of circuit is a constant unrelated with signal magnitude, therefore
The complexity of circuit is (1) O.
Advantages of the present invention is with effect：
The present invention solves the type transfer problem from quantum image to quantum real signal, devises quantum gray level image and arrives
Quantum 2 ties up the type conversion of real signal and quantum coloured image ties up the quantum wire that the type of triple channel real signal is converted to quantum 2
Road, to provide necessary basis for subsequent Quantum signal processing (such as by quantum wavelet application to quantum image).This
Invent the high efficiency for embodying quantum information processing in signal processing：The type that quantum gray level image ties up real signal to quantum 2 turns
It changes and quantum coloured image ties up the quantum wire complexity converted of type of triple channel real signal all into O (1) to quantum 2.
Description of the drawings
Fig. 1 is the expression figure of fundamental quantity cervical orifice of uterus of the present invention；
Fig. 2 is the title and symbol table diagram of muliti-qubit door of the present invention；
Fig. 3 is that the quantum of the invention for shuffling displacement P realizes line map；
Fig. 4 is the schematic diagram that the quantum of the invention for shuffling displacement P realizes line map；
Fig. 5 is P of the present inventioniQuantum realize line map；
Fig. 6 is P of the present inventioniQuantum realize line map schematic diagram；
Fig. 7 is that the quantum for the type conversion that quantum gray level image of the present invention ties up real signal to quantum 2 realizes line map；
Fig. 8 is that the quantum for the type conversion that quantum gray level image of the present invention ties up real signal to quantum 2 realizes the letter of line map
Figure；
Fig. 9 is that the quantum for the type conversion that quantum coloured image of the present invention ties up triple channel real signal to quantum 2 realizes circuit
Figure.
Figure 10 is that the quantum for the type conversion example that a quantum gray level image of the invention ties up real signal to quantum 2 realizes line
Lu Tu.
Figure 11 is that the quantum for the type conversion example that a quantum gray level image of the invention ties up real signal to quantum 2 realizes line
The schematic diagram of road figure.
Figure 12 is the quantum for the type conversion example that a quantum coloured image of the invention ties up triple channel real signal to quantum 2
Realize line map.
Specific implementation mode
The invention will be further described with reference to embodiments.
A kind of type conversion designs method from quantum image to quantum real signal, the method using the controlled door of quantum and
Single quantum bit door builds the type conversion of the 2 dimension real signals from quantum gray level image to quantum according to 754 international standards of IEEE
With the quantum wire of the type conversion of 2 dimension triple channel real signals from quantum coloured image to quantum.
The type conversion realization process of 2 dimension real signals is from quantum gray level image to quantum：
A gray scale can be indicated with 8 quantum bits：
|f(x,y)>=| c8c7c6c5c4c3c2c1> (15)
Wherein ci∈ { 0,1 }, i=1 ..., 8；
N+8 quantum bits can indicate a width gray level image：
Wherein | f (x, y)>Indicate image coordinate (x, y) gray value, | x>Indicate the x coordinate of signal, | y>Indicate letter
Number x coordinate, the size of image is 2n-k×2k, k, n are positive integer.
A single precision floating datum is stored with the quantum state of 32 quantum bits, i.e.,
Wherein | S (x, y)>=| Sxy>Stored symbols position,Exponent is stored,Mantissa is stored,
The storage that quantum 2 ties up real signal is expressed as
Wherein | l (x, y)>Indicate signal position (x, y) real number value, | x>Indicate the x coordinate of signal, | y>Indicate letter
Number x coordinate, the size of signal is 2n-k×2k, k, n are positive integer.
The displacement P that shuffles is realized
P|c8c7c6c5c4c3c2c1>=| c7c6c5c4c3c2c1c8> (19)
It is shuffled using 7 swap gate realizations and replaces P, P is realized with the quantum wire of the i displacement P that shufflei, i.e.,
Pi=PK P (20)
Using 8 swap gates to initial stateOn, it obtains
Wherein | ψG>A width gray level image is indicated, as shown in formula (16).
Multiple quantum controlled not-gates are applied to quantum state | ξ1>On, it obtains
WhereinIndicate signal the real number value of position (x, y) exponent, such as
Shown in formula (17).
Then controlled not-gate and it is controlled Pi arrive quantum state | ξ2>On, it obtains
Wherein | l (x, y)>Indicate signal position (x, y) real number value, as shown in formula (17), | x>Indicate the x of signal
Coordinate, | y>Indicate the x coordinate of signal, the size of signal is 2n-k×2k, k, n are positive integer, | ψ2>2 dimension real signal of storage, such as
Shown in formula (18).
One 22× 2 gray level image
It can be stored in following quantum state：
Design conversion quantum wire is as shown in Figure 10, and schematic diagram is as shown in figure 11.Quantum state in Figure 10 | ψG>Such as
Shown in formula (28), coordinate is indicated with 3 quantum bits.Quantum wire in Figure 10 is by quantum greyscale image transitions at following
Quantum 2 ties up real signal：
The quantum wire of the type conversion of 2 dimension triple channel real signals realizes that process is from quantum coloured image to quantum：
N+10 quantum bits can indicate a width coloured image：
WhereinThe gray level image of red channel, green channel and blue channel is stored respectively, i.e.,
Here, | fr(x,y)>,|fg(x,y)>,|fb(x,y)>Indicate three channels of image coordinate (x, y) gray value,
|x>Indicate the x coordinate of signal, | y>Indicate the x coordinate of signal, the size of image is 2n-k×2k, k, n are positive integer.
The storage that quantum 2 ties up triple channel real signal is expressed as
WhereinOne 2 dimension real signal is stored respectively, i.e.,
Wherein, | l1(x,y)>,|l2(x,y)>,|l3(x,y)>Indicate three channels of signal position (x, y) real number value,
|x>Indicate the x coordinate of signal, | y>Indicate the x coordinate of signal, the size of signal is 2n-k×2k, k, n are positive integer.
Using 8 swap gates to initial stateOn, it obtains
Wherein | ψC>Indicate a width coloured image, as shown in formula (30), | fr(x,y)>,|fg(x,y)>,|fb(x,y)>
Indicate three channels of image coordinate (x, y) gray value, as shown in formula (31), | x>Indicate the x coordinate of signal, | y>It indicates
The size of the x coordinate of signal, image is 2n-k×2k, k, n are positive integer.
Then type conversion quantum wire that three controlled quantum gray level images to quantum 2 are tieed up to real signal acts on quantum
State | ξ4>On, finally obtain the quantum state that storage quantum 2 ties up triple channel real signal | ψ3>；Quantum state | ψ3>As shown in formula (32).
The gray level image in three channels of red, green, blue of one coloured image is：
V1=V2=V3=V (35)
Wherein V1,V2,V3Indicate that the size in three channels is 2 respectively2× 2 gray scale, shown in V such as formula (24).
Then this colour can be stored in following quantum state：
Wherein | ψG>As shown in formula (25).
It is as shown in figure 12 that design converts quantum wire.Quantum state in Figure 12 | ψC>As shown in formula (36), coordinate
It is indicated with 3 quantum bits.Quantum coloured image is converted into following quantum 2 and ties up triple channel letter in fact by the quantum wire in Figure 12
Number：
Wherein | ψ2>As shown in formula (26).
The preferred embodiment of the invention is illustrated above, but the present invention is not limited to embodiment,
Those skilled in the art can also make various equivalent modifications under the premise of without prejudice to the invention spirit
Or replace, these equivalent modifications or replacement are all contained in scope of the present application.
Claims (3)
1. a kind of type conversion designs method from quantum image to quantum real signal, which is characterized in that the method utilization
The controlled door of son and single quantum bit door, according to 754 international standards of IEEE, structure 2 dimension real signal from quantum gray level image to quantum
Type conversion and from quantum coloured image to quantum 2 dimension triple channel real signals types conversion quantum wire.
2. a kind of type conversion designs method from quantum image to quantum real signal according to claim 1, feature exist
In the type conversion realization process of the 2 dimension real signals from quantum gray level image to quantum is：
A gray scale can be indicated with 8 quantum bits：
|f(x,y)>=| c8c7c6c5c4c3c2c1> (1)
Wherein ci∈ { 0,1 }, i=1 ..., 8；
N+8 quantum bits can indicate a width gray level image：
Wherein | f (x, y)>Indicate image coordinate (x, y) gray value, | x>Indicate the x coordinate of signal, | y>Indicate the x of signal
The size of coordinate, image is 2n-k×2k, k, n are positive integer；
A single precision floating datum is stored with the quantum state of 32 quantum bits, i.e.,
Wherein | S (x, y)>=| Sxy>Stored symbols position,Exponent is stored,Mantissa is stored,
The storage that quantum 2 ties up real signal is expressed as
Wherein | l (x, y)>Indicate signal position (x, y) real number value, | x>Indicate the x coordinate of signal, | y>Indicate the x of signal
The size of coordinate, signal is 2n-k×2k, k, n are positive integer；
The displacement P that shuffles is realized
P|c8c7c6c5c4c3c2c1>=| c7c6c5c4c3c2c1c8> (5)
It is shuffled using 7 swap gate realizations and replaces P, P is realized with the quantum wire of the i displacement P that shufflei, i.e.,
Pi=PK P (6)
Using 8 swap gates to initial stateOn, it obtains
Wherein | ψG>A width gray level image is indicated, as shown in formula (2)；
Multiple quantum controlled not-gates are applied to quantum state | ξ1>On, it obtains
WhereinIndicate signal in the exponent of the real number value of position (x, y), such as formula
(3) shown in；
Then controlled not-gate and controlled PiDoor arrives quantum state | ξ2>On, it obtains
Wherein | l (x, y)>Indicate signal position (x, y) real number value, as shown in formula (3), | x>Indicate the x coordinate of signal,
|y>Indicate the x coordinate of signal, the size of signal is 2n-k×2k, k, n are positive integer, | ψ2>2 dimension real signal of storage, such as formula
(4) shown in.
3. the type amount of translation of design according to claim 12 dimension triple channel real signals from quantum coloured image to quantum
Sub-line road, is characterized in that, the quantum wire of the type conversion of the 2 dimension triple channel real signals from quantum coloured image to quantum is real
Now process is：
N+10 quantum bits can indicate a width coloured image：
WhereinThe gray level image of red channel, green channel and blue channel is stored respectively, i.e.,
Here, | fr(x,y)>,|fg(x,y)>,|fb(x,y)>Indicate three channels of image coordinate (x, y) gray value, | x>
Indicate the x coordinate of signal, | y>Indicate the x coordinate of signal, the size of image is 2n-k×2k, k, n are positive integer；
The storage that quantum 2 ties up triple channel real signal is expressed as
WhereinOne 2 dimension real signal is stored respectively, i.e.,
Wherein, | l1(x,y)>,|l2(x,y)>,|l3(x,y)>Indicate three channels of signal position (x, y) real number value, | x>
Indicate the x coordinate of signal, | y>Indicate the x coordinate of signal, the size of signal is 2n-k×2k, k, n are positive integer；
Using 8 swap gates to initial stateOn, it obtains
Wherein | ψC>Indicate a width coloured image, as shown in formula (10), | fr(x,y)>,|fg(x,y)>,|fb(x,y)>Indicate figure
As three channels are in the gray value of coordinate (x, y), as shown in formula (11), | x>Indicate the x coordinate of signal, | y>Indicate signal
The size of x coordinate, image is 2n-k×2k, k, n are positive integer；
Then type conversion quantum wire that three controlled quantum gray level images to quantum 2 are tieed up to real signal acts on quantum state | ξ4
>On, finally obtain the quantum state that storage quantum 2 ties up triple channel real signal | ψ3>；Quantum state | ψ3>As shown in formula (12).
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| CN101710171A (en) * | 2009-10-23 | 2010-05-19 | 南京大学 | Universal AC measurement method for external quantum efficiency of solar battery |
| US20110317177A1 (en) * | 2010-06-24 | 2011-12-29 | Canon Kabushiki Kaisha | Image processing apparatus, image processing method, and recording apparatus |
| CN106208667A (en) * | 2016-07-20 | 2016-12-07 | 广东双核电气有限公司 | Novel quantum generator power supply converting system |
| CN107153632A (en) * | 2017-05-10 | 2017-09-12 | 广西师范大学 | A kind of method that quantum Haar wavelet transformations realize quantum wire design |
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|---|---|---|---|---|
| CN101710171A (en) * | 2009-10-23 | 2010-05-19 | 南京大学 | Universal AC measurement method for external quantum efficiency of solar battery |
| US20110317177A1 (en) * | 2010-06-24 | 2011-12-29 | Canon Kabushiki Kaisha | Image processing apparatus, image processing method, and recording apparatus |
| CN106208667A (en) * | 2016-07-20 | 2016-12-07 | 广东双核电气有限公司 | Novel quantum generator power supply converting system |
| CN107153632A (en) * | 2017-05-10 | 2017-09-12 | 广西师范大学 | A kind of method that quantum Haar wavelet transformations realize quantum wire design |
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| CN109165744A (en) * | 2018-08-15 | 2019-01-08 | 合肥本源量子计算科技有限责任公司 | A kind of Quantum logic gates operation optimization method |
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