JP3896057B2 - Quantum computer algorithm conversion apparatus and method, quantum computer algorithm conversion program, and recording medium recording the program - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method and apparatus for converting a quantum algorithm into an algorithm for a circular array type quantum computer.
[0002]
[Prior art]
Computers called “quantum computers” have been proposed that can solve problems much faster in principle than computers that are widely used today. Using the quantum superposition state, a phenomenon peculiar to the quantum world, expands the bit (unit expressing 0 or 1) in a classical computer and expresses 0 and 1 superposition in addition to 0 and 1 Is possible. Such an extended concept of bits is called a qubit, and a quantum computer is realized by a qubit operation. Since realization of quantum computers enables much faster computations than current computers for problems such as factorization, many research institutions around the world are developing them.
[0003]
Research on quantum computers is currently underway in two main directions. One is the development of quantum gates, which are the basic elements for performing quantum computer operations. The second is research on algorithms for quantum computers that operate when quantum gates are realized.
[0004]
The basic operations realized by quantum gates are expected to be completely different from those possible with conventional computers. Although it is desirable that the quantum algorithm is researched based on the basic operation of the developed quantum gate, the quantum gate is not developed yet, so the algorithm is studied based on the basic operation that seems to be valid at present. . As a basic operation, an operation called control NOT is often used.
[0005]
[Non-Patent Document 1]
S. Lloyd, "Science" 261, pp. 1569-1571 (1993)
[Non-Patent Document 2]
S. Lloyd, `` Programming Pulse Driven Quantum Computers, Technical Report '' http://arXiv.org/abs/quant-ph/9912086, LANL e-print, 1999.
[0006]
[Problems to be solved by the invention]
Unfortunately, the fact that quantum gates are not actually developed is not exactly what the basic operations on qubits will look like. The basic operation depends on the qubit implementation method, and a plurality of qubit implementation methods are currently proposed. Among these methods, the most promising method is the realization method using the nuclear spin of atoms. In this method, quantum operations are realized by using nuclear magnetic interaction between adjacent qubits. Furthermore, since the types of atoms suitable for such a method are limited, when a large-scale quantum computer is manufactured, there is a high possibility that the quantum computer has the same type of atoms repeatedly arranged. In such a quantum computer, operations between qubits at distant positions are virtually impossible, and it is almost impossible to execute the quantum algorithm described in the control NOT as it is.
[0007]
Therefore, it becomes necessary to convert the quantum algorithm described in the control NOT into a quantum algorithm suitable for such a quantum computer. Although conversion loss is also expected to occur due to conversion, such a conversion device is considered to be indispensable in quantum computers as well as a compiler that translates human-readable programs into machine language on conventional computers. It is done.
[0008]
S. In Lloyd, three types of qubits A, B, and C are like “... -A-B-C-A-B-C-A-B-C-A-B-C-. It has been shown that pool calculation can be performed using only operations between adjacent qubits on a repetitively arranged quantum computer (see Non-Patent Documents 1 and 2). However, there is no document describing a method for converting a quantum algorithm into a general circular array type quantum computer algorithm.
[0009]
An object of the present invention is to express a quantum algorithm described using control NOT as "Am-A1 -...- Am-A1 -...- Am-A1 -...- Am". It is an object of the present invention to provide a method and an apparatus for converting into an algorithm for a quantum computer (hereinafter referred to as a “circular array type quantum computer”) in which a certain qubit array “−A1-.
[0010]
[Means for Solving the Problems]
The present invention solves the above problem by replacing each operation of a given control NOT with a sequence of operations for a circular array type quantum computer.
[0011]
Definition of concepts necessary for algorithm description
First, a quantum algorithm is defined.
[0012]
Quantum algorithm
The concept of a quantum computer corresponding to a bit in a classical computer is called a qubit. Each qubit holds bit information of 1, 0, or an extension thereof (corresponding to a superposition of 1 and 0) in a classical computer. A quantum computer is composed of a finite number of qubits. Calculating with a quantum computer means giving each qubit an initial value, manipulating them, manipulating the bit information held by the qubit, and finally observing and extracting these bit information. To do. A series of operations on bit information performed on qubits is called a quantum algorithm. If the basic unit of operation performed on the qubit is defined, the quantum algorithm is described by this sequence of basic operations. In general, in a quantum algorithm, only the following operations are allowed on qubits.
[0013]
When the value of one qubit (assuming i) is 1 with respect to the control NOT 2 qubits i and j, the value of j is inverted (0 is changed to 1 or 1 is changed to 0), and i When the value of is 0, nothing is done. The qubit i is called a control bit, and the qubit j is called a target bit. This control NOT is expressed as (j, i).
The control NOT is illustrated as shown in FIG. The quantum algorithm is expressed by a sequence of control NOT. FIG. 5 is an example of the quantum algorithm (6, 2) (1, 5).
[0014]
Algorithms for circular array quantum computers
In the circular array type quantum computer, m types of qubits are formed by repeating the array "-A1-A2-... -Am-", and control NOT and control control NOT operations are performed only between adjacent qubits. It is a possible quantum computer. When qubits are realized by atomic nuclear spins, the interaction between qubits becomes very small, making it difficult to implement a normal quantum algorithm model as it is. The circular array type quantum computer is a model that is closer to reality than the model of a conventional quantum computer.
[0015]
There are two types of operation of qubits in a circular array type quantum computer: control NOT and control control NOT. The same operation is performed on the same kind of qubit array in one operation. Set the qubit types to A1, A2,. . . , Am.
[0016]
Control NOT Between two adjacent qubits (Ai and A (i + 1) or Am and A1), when the value of one (for example, Ai in Ai and A (i + 1), called control bit) is 1, the other bit An operation that inverts (called the target bit) and does nothing when it is 0. When the control bit is A and the target bit is B, the control NOT operation is expressed as (B, A).
[0017]
Control control NOT Between three adjacent qubits (Ai, A (i + 1), A (i + 2) or A (m-1), Am, A1 or Am, A1, A2), both ends (for example, Ai, A (i + 1) , A (i + 2) Ai and A (i + 2) (referred to as control bits) are both 1's, the bits between them (called target bits) are inverted, otherwise An operation that does nothing. When the control bits are A1 and A2 and the target bit is B, the control NOT operation is expressed as (B, A1, A2).
Symbols of these operations are shown in FIGS. 4 (b) and 4 (c).
[0018]
By combining the control NOT and the control control NOT, the following two types of operations can be made.
[0019]
Swap Operation to swap values between two adjacent qubits (Ai and A (i + 1) or Am and A1). When the two qubits are A and B, this operation is expressed as [A, B]. [A, B] is an abbreviation for (A, B) (B, A) (A, B).
[0020]
Control swap between adjacent 3 qubits (Ai, A (i + 1), A (i + 2) or A (m-1), Am, A1 or Am, A1, A2) at the end (eg Ai, A (i + 1), When the value of Ai (referred to as a control bit in A (i + 2)) is 1, the value of the remaining bits is replaced, and otherwise, nothing is performed. When 3 qubits are A, B, and C and A is a control bit, it is expressed as [C, B, A]. This is an abbreviation for (C, B) (B, A, C) (C, B).
[0021]
  An input quantum algorithm consisting of a series of control NOTsg=g1g2. . .gLet d. For all i (1 ≦ i ≦ d)gi isgIt can be expressed as i = (ti, ci). The number of qubits in this quantum algorithm is n. That is, for all i, 0 ≦ ti, ci <n. Further, the number of types of qubits in the circular quantum computer is m.
[0022]
  Variable for storing output algorithm is G ′, n + 1 variablesNameV is a variable name storage array for storing. The j-th element of V is denoted as V [j].
[0023]
  Less than,gEach quantum gateg1,g2,. . . ,gd from the frontZA method of obtaining a quantum algorithm for a circular array type quantum computer will be described with reference to FIG.
[0024]
Step 1. Initialize G 'and V
The initial value of V is V [0] = 0, s = 1,. . . , N
V [s] = [s + ((s-1) ÷ (m-1))]
And Here, [t] is the maximum integer not exceeding t (that is, [] is a Gaussian symbol). The initial value of G ′ is φ (empty set). The initial value of the variable i, which means the quantum gate number, is set to 1, and the following loop is executed from i = 1 to d.
[0025]
Step 2. Initialize i
[0026]
  Step 3. Conditional branch
  Control NOT gategLet i be (ti, ci). If | V [ti] -V [ci] | is not a multiple of m, the information held by the V [ti], V [ci], and V [0] -th qubits using the swap operation is the adjacent qubit. (Steps 5 to 6). However, when | V [ti] −V [ci] | is a multiple of m, the types of the V [ti] and V [ci] th qubits are the same, so that they can be converted into adjacent qubits only by swapping. Can not do it. Therefore, there are cases where | V [ti] −V [ci] | is a multiple of m. If | V [ti] −V [ci] | is a multiple of m, step 4 is executed. If not, skip step 4 and jump to step 5.
[0027]
Step 4. Definition of quantum algorithm G0
Hereinafter, the quantum algorithm G0 is defined. Also, V is changed based on G0. K, j, j ′, j ″, j ′ ″ and X1, X2, X3,. . . , Xm is defined as follows.
[0028]
Select the smaller of | V [ti] −V [0] | or | V [ci] −V [0] |. When | V [ti] −V [0] | is smaller, k = | V [ti] −V [0] | − [| V [ti] −V [0] | ÷ m] −2. . j, j ′, j ″, j ′ ″ are 1 ≦ j, j ′, j ″, j ′ ″ ≦ m, j = k mod m, J ′ = k + 1 mod m, J ″ = This is a value determined by k + 2 mod m, J ′ ″ = k + 3 mod m. X1, X2, X3,. . . , Xm is defined as follows depending on whether V [ti] -V [0] is positive or negative.
[0029]
When V [ti] -V [0] is negative
If V [ti] = 0 mod m, X1 = Am, X2 = A1,..., Xm = A (m-1).
If V [ti] = 1 mod m, X1 = A1, X2 = A2, ..., Xm = Am.
If V [ti] = 2 mod m, X1 = A2, X2 = A3, ..., Xm = A1.
...
If V [ti] = m-1 mod m, X1 = A (m-1), X2 = Am, ..., Xm = A (m-2).
[0030]
When V [ti] -V [0] is positive
If V [ti] = 0 mod m, X1 = Am, X2 = A (m-1), ..., Xm = A1.
If V [ti] = 1 mod m, X1 = A1, X2 = Am, ..., Xm = A2.
If V [ti] = 2 mod m, X1 = A2, X2 = A1, ..., Xm = A3.
...
If V [ti] = m-1 mod m, then X1 = A (m-1), X2 = A (m-2), ..., Xm = Am.
[0031]
On the other hand, when | V [ci] −V [0] | is smaller, k = | V [ci] −V [0] | − [| V [ci] −V [0] | ÷ m] −2 far. j, j ′, j ″, j ′ ″ are 1 ≦ j, j ′, j ″, j ′ ″ ≦ m, j = k mod m, J ′ = k + 1 mod m, J ″ = This is a value determined by k + 2 mod m, J ′ ″ = k + 3 mod m. X1, X2, X3,. . . , Xm is defined as follows depending on whether V [ci] -V [0] is positive or negative.
[0032]
When V [ci] -V [0] is negative
If V [ci] = 0 mod m, X1 = Am, X2 = A1,..., Xm = A (m-1).
If V [ci] = 1 mod m, X1 = A1, X2 = A2, ..., Xm = Am.
If V [ci] = 2 mod m, X1 = A2, X2 = A3, ..., Xm = A1.
...
If V [ci] = m-1 mod m, then X1 = A (m-1), X2 = Am, ..., Xm = A (m-2).
[0033]
When V [ci] -V [0] is positive
If V [ci] = 0 mod m, X1 = Am, X2 = A (m-1), ..., Xm = A1.
If V [ci] = 1 mod m, X1 = A1, X2 = Am, ..., Xm = A2.
If V [ci] = 2 mod m, X1 = A2, X2 = A1, ..., Xm = A3.
...
If V [ci] = m-1 mod m, then X1 = A (m-1), X2 = A (m-2), ..., Xm = Am.
G0 is defined as follows.
[0034]
If k ≦ 0,
G0 = [X1, X2, X3]
If 1 ≦ k,
G0 = [X1, X2] [X2, X3] ... [Xm, X1] [X1, X2] ... [Xj, Xj '] [Xj', Xj '', Xj '' ']
G'G0 can be defined by this G0. Here, G′G0 means an algorithm for executing the algorithm G0 after the algorithm G ′. Hereinafter, G′G0 is described as G ′ (in the memory, G0 is added after the array G ′). G0 is a column of swap and control swap S1S2. . . It is described by St. VG0 is recursively defined as follows from V currently obtained.
[0035]
S = [Aj, Aj ′] and
If V [s] = j mod m, then VS [s] = V [s] + (j'-j)
If V [s] = j 'mod m, then VS [s] = V [s] + (j-j')
S = [Aj, Aj ′, Aj ″] and
If V [0] = j '' mod m and V [s] = V [0] + (j'-j '')
VS [s] = V [0] + (j-j '')
If V [0] = j '' mod m and V [s] = V [0] + (j-j '')
VS [s] = V [0] + (j'-j '')
In all other cases,
VS [s] = V [s]
Here, S = S1,. . . , St.
Hereinafter, VG0 is described as V (that is, the value of the array of V on the memory is overwritten with the value of VG0).
[0036]
Step 5. Definition of quantum algorithm G1
The quantum algorithm G1 is defined as follows, and G ′ = G′G1.
[0037]
When the value of | V [ci] −V [0] | is 1, G1 is φ (empty set). Otherwise, k = | V [ci] −V [0] | − [| V [ci] −V [0] | ÷ m] −1
G1 = [X1, X2] [X2, X3] ... [Xm, X1] [X1, X2] ... [Xj, Xj ']
It is defined as Here, j and j ′ are values determined by 1 ≦ j, j ′ ≦ m, j = k mod m, and J ′ = k + 1 mod m. X1, X2, X3,. . . , Xm are defined as follows.
[0038]
When V [ci] -V [0] is negative
When V [ci] = 0 mod m, X1 = Am, X2 = A1,..., Xm = A (m-1).
When V [ci] = 1 mod m, X1 = A1, X2 = A2, ..., Xm = Am.
When V [ci] = 2 mod m, X1 = A2, X2 = A3,..., Xm = A1.
...
When V [ci] = m-1 mod m, X1 = A (m-1), X2 = Am,..., Xm = A (m-2).
[0039]
  When V [ci] -V [0] is positive
      When V [ci] = 0 mod m, X1 = Am, X2 = A (m−1),..., Xm = A1.
      When V [ci] = 1 mod m, X1 = A1, X2 = Am,..., Xm = A2.
      When V [ci] = 2 mod m, X1 = A2, X2 = A1, ..., Xm = A3.
      ...
      When V [ci] = m-1 mod m X1 = A (m-1), X2 = A (m-2), ..., Xm = Am.
Also, according to this algorithm G1,Like VG0VG1 can be defined. Hereinafter, VG1 is described as V.
[0040]
Step 6. Definition of quantum algorithm G2
The quantum algorithm G2 is defined as follows, and G ′ = G′G2.
[0041]
When the value of | V [ti] −V [0] | is 1, G2 is φ (empty set). Otherwise, k = | V [ti] −V [0] | − [| V [ti] −V [0] | ÷ m] −1,
G2 = [X1, X2] [X2, X3] ... [Xm, X1] [X1, X2] ... [Xj, Xj ']
It is defined as Here, j and j ′ are values determined by 1 ≦ j, j ′ ≦ m, j = k mod m, and J ′ = k + 1 mod m. X1, X2, X3,. . . , Xm are defined as follows.
[0042]
When V [ti] -V [0] is negative
When V [ti] = 0 mod m, X1 = Am, X2 = A1,..., Xm = A (m-1).
When V [ti] = 1 mod m, X1 = A1, X2 = A2, ..., Xm = Am.
When V [ti] = 2 mod m, X1 = A2, X2 = A3, ..., Xm = A1.
...
When V [ti] = m-1 mod m, X1 = A (m-1), X2 = Am,..., Xm = A (m-2).
[0043]
  When V [ti] -V [0] is positive
      When V [ti] = 0 mod m, X1 = Am, X2 = A (m−1),..., Xm = A1.
      When V [ti] = 1 mod m, X1 = A1, X2 = Am,..., Xm = A2.
      When V [ti] = 2 mod m, X1 = A2, X2 = A1,..., Xm = A3.
      ...
      When V [ti] = m-1 mod m, X1 = A (m-1), X2 = A (m-2), ..., Xm = Am.
Also, according to this algorithm G2,Like VG0VG2 can be defined. Hereinafter, VG2 is described as V.
[0044]
  Step 7. Definition of quantum algorithm G3
  G3 is defined as follows, and G ′ = G′G3.
When V [ci], V [0] ≦ V [ti]
              G3 = [X3, X2] (X2, X1, X3)
However,
      When V [ti] = 0 mod m, X1 = A (m-2), X2 = A (m-1), and X3 = Am.
      When V [ti] = 1 mod m, X1 = A (m−1), X2 = Am, and X3 = A1.
      When V [ti] = 2 mod m, X1 = Am, X2 = A1, X3 = A2.
      ...
      When V [ti] = m−1 mod m, X1 = A (m−3), X2 = A (m−2), and X3 = A (m−1).
When V [ti] ≦ V [ci], V [0]
              G3 = [X1, X2] (X2, X1, X3)
However,
      When V [ti] = 0 mod m X1 = Am, X2 = A1, X3 = A2.
      When V [ti] = 1 mod m, X1 = A1, X2 = A2, X3 = A3.
      When V [ti] = 2 mod m, X1 = A2, X2 = A3, X3 = A4.
      ...
      When V [ti] = m−1 mod m, X1 = A (m−1), X2 = Am, and X3 = A1.
Otherwise
              G3 = (X2, X1, X3)
However,
      When V [ti] = 0 mod m, X1 = A (m-1), X2 = Am, X3 = A1.
      When V [ti] = 1 mod m, X1 = Am, X2 = A1, X3 = A2.
      When V [ti] = 2 mod m X1 = A1, X2 = A2, X3 = A3.
      ...
      When V [ti] = m−1 mod m, X1 = A (m−2), X2 = A (m−1), and X3 = Am.
Also, according to this algorithm G3,Like VG0VG3 can be defined. Hereinafter, VG3 is described as V.
[0045]
Step 8. increment i
Step 9. Conditional branch
If i> d, G ′ and V are output and the algorithm is terminated. If i ≦ d, return to Step 3.
[0046]
Let s be an arbitrary natural number of n bits, and i be an integer. The i-th bit of s is expressed as s (i). t is a function from integer to {0,1}
t (0) = 1,
t ([i + (i ÷ m)]) = s (i−1), where i = 1, 2,..., n
T (j) = 0 for all other cases
It is defined as One suitable qubit is selected from Am constituting the circular array type quantum computer, and an integer is assigned to all qubits, such as 0th, A1 next to it, and the like. Let G ′ (t) be the calculation result of the circular array type quantum algorithm G ′ when the initial value t (i) is input to the i-th qubit.
[0047]
  G ′ and V output by the present invention and the original quantum algorithmgIt can be seen that the following relational expression holds between
[0048]
      gI−1th bit of (s) = V [i] th bit of G ′ (t) where i = 1, 2,. . . , N. For this reason, the quantum algorithm described in the conventional control NOTgsogInstead of calculating (s), if G ′ and V obtained by the present invention are executed on a cyclic quantum computer and G ′ (t) is observed, the desired calculation result can be obtained.
[0049]
  Example of calculation
  To show a specific calculation example,g= (6,2) shows a calculation for converting a quantum algorithm of (1,5) into an algorithm for a circular array type quantum computer of m = 3. In this case, since the number of input qubits is 6, n = 6. Of course, the input is not limited to this example.
[0050]
Step 1. By definition, V [0] = 0, V [1] = 1, V [2] = 2, V [3] = 4, V [4] = 5, V [5] = 7, V [6] = 8. The output variable G ′ is initialized so that G ′ = φ (empty set).
[0051]
Step 3. Since the first gate is (t1, c1) = (6, 2), V [0] = 0, V [t1] = 8, and V [c1] = 2. Since | V [ti] −V [c1] | = 6 and a multiple of 3, step 4 is executed.
[0052]
Step 4. Since | V [c1] −V [0] | = 2 and | V [ti] −V [0] | = 8, the smaller one is the former. By definition, k = 0. Since V [c1] -V [0] is positive and V [c1] = 2 mod 3, X1 = A2, X2 = A1, X3 = A3. Therefore, G0 = [A2, A1, A3]. Since G ′ is an empty set, G′G0 = [A2, A1, A3]. Hereinafter, G′G0 is referred to as G ′. That is, G ′ = [A2, A1, A3].
Since V [0] = 0, V [0] = 0 mod 3. Therefore, when S = [A2, A1, A3], VS [1] = 2 from V [1] = 1, and VS [2] = 1 from V [2] = 2. In all cases where s is other than 1 and 2, VS [s] = V [s]. Hereinafter, VS is assumed to be V. Specifically, V [0] = 0, V [1] = 2, V [2] = 1, V [3] = 4, V [4] = 5, V [5] = 7, V [ 6] = 8.
[0053]
Step 5. Since V [0] = 0 and V [c1] = 1, | V [c1] −V [0] | = 1, G1 is φ (empty set). Therefore, G'G1 is equal to G '= [A2, A1, A3]. In this case, V does not change.
[0054]
Step 6. Since V [0] = 0 and V [t1] = 8, | V [t1] −V [0] | = 8, k = 5, j = 2, and j ′ = 3. From V [t1] = 2 mod 3, X1 = A2, X2 = A1, X3 = A3. Therefore, G1 = [A2, A1] [A1, A3] [A3, A2] [A2, A1] [A1, A3]. Therefore, G'G1 is [A2, A1, A3] [A2, A1] [A1, A3] [A3, A2] [A2, A1] [A1, A3]. Hereinafter, G′G1 is referred to as G ′. If S1 = [A2, A1], S2 = [A1, A3], and S3 = [A3, A2], then G1 = S1S2S3S1S2, and so when calculated in order, VS1 [0] = 0, VS1 [1] = 1 , VS1 [2] = 2, VS1 [3] = 5, VS1 [4] = 4, VS1 [5] = 8, VS1 [6] = 7,
VS1S2 [0] = 1, VS1S2 [1] = 0, VS1S2 [2] = 2, VS1S2 [3] = 5, VS1S2 [4] = 3, VS1S2 [5] = 8, VS1S2 [6] = 6,
VS1S2S3 [0] = 1, VS1S2S3 [1] =-1, VS1S2S3 [2] = 3, VS1S2S3 [3] = 6, VS1S2S3 [4] = 2, VS1S2S3 [5] = 9, VS1S2S3 [6] = 5,
VS1S2S3S1 [0] = 2, VS1S2S3S1 [1] =-2, VS1S2S3S1 [2] = 3, VS1S2S3S1 [3] = 6, VS1S2S3S1 [4] = 1, VS1S2S3S1 [5] = 9, VS1S2S3S1 [4] is there. Therefore, VG1 [0] = 2, VG1 [1] =-3, VG1 [2] = 4, VG1 [3] = 7, VG1 [4] = 0, VG1 [5] = 10, VG1 [6] = 3. VG1 is written as V in the future.
[0055]
Step 7. Since V [c1] = 4, V [t1] = 3, and V [0] = 2, this corresponds to other cases. By definition, X1 = A2, X2 = A3, X3 = A1, and G3 = (A3, A2, A1). Therefore, G'G3 is [A2, A1, A3] [A2, A1] [A1, A3] [A3, A2] [A2, A1] [A1, A3] (A3, A2, A1). Hereinafter, G′G3 is referred to as G ′. V does not change by G3.
[0056]
Step 8. i = 2
Step 9. Since i = d, return to Step 3.
[0057]
Step 3. Since the next gate is (t2, c2) = (1, 5), V [0] = 2, V [t2] = − 3, and V [c2] = 10. Since | V [t2] −V [c2] | = 13 and not a multiple of 3, step 5 is executed.
[0058]
Step 5. Since | V [c2] −V [0] | = 8, k = 5, j = 2, and J ′ = 3. From V [c2] = 1 mod 3, X1 = A1, X2 = A3, X3 = A2. Therefore, G1 = [A1, A3] [A3, A2] [A2, A1] [A1, A3] [A3, A2]. G′G1 is [A2, A1, A3] [A2, A1] [A1, A3] [A3, A2] [A2, A1] [A1, A3] (A3, A2, A1) [A1, A3] [A3 , A2] [A2, A1] [A1, A3] [A3, A2]. Hereinafter, G′G1 is referred to as G ′. When VG1 is calculated, VG1 [0] = 4, VG1 [1] = 0, VG1 [2] =-1, VG1 [3] = 2, VG1 [4] = 3, VG1 [5] = 5, VG1 [ 6] = 6. Let VG1 be V.
[0059]
Step 6. Since | V [t2] −V [0] | = 4, k = 2, j = 2, and J ′ = 3. From V [t2] = 0 mod 3, Z1 = A3, Z2 = A1, Z3 = A2. Therefore, G2 = [A3, A1] [A1, A2]. Therefore, G′G2 is [A2, A1, A3] [A2, A1] [A1, A3] [A3, A2] [A2, A1] [A1, A3] (A3, A2, A1) [A1, A3]. [A3, A2] [A2, A1] [A1, A3] [A3, A2] [A3, A1] [A1, A2]. Hereinafter, G′G2 is referred to as G ′. When VG2 is calculated, VG2 [0] = 3, VG2 [1] = 2, VG2 [2] =-2, VG2 [3] = 1, VG2 [4] = 5, VG2 [5] = 4, VG2 [ 6] = 8. Let VG2 be V.
[0060]
Step 7. Since V [c2] = 4, V [t2] = 2, and V [0] = 3, this corresponds to the case of V [t2] ≦ V [c2], V [n]. By definition, X1 = A2, X2 = A3, X3 = A1, and G3 = [A2, A3] (A3, A2, A1). G′G3 is [A2, A1, A3] [A2, A1] [A1, A3] [A3, A2] [A2, A1] [A1, A3] (A3, A2, A1) [A1, A3] [A3 , A2] [A2, A1] [A1, A3] [A3, A2] [A3, A1] [A1, A2] [A2, A3] (A3, A2, A1). Hereinafter, G′G3 is referred to as G ′. When VG3 is calculated, VG3 [0] = 2, VG3 [1] = 3, VG3 [2] =-3, VG3 [3] = 1, VG3 [4] = 6, VG3 [5] = 4, VG3 [ 6] = 9. Let VG3 be V.
[0061]
Step 8. i = 3
Step 9. Since i> d, G ′ and V are output and the algorithm is terminated.
[0062]
DETAILED DESCRIPTION OF THE INVENTION
Next, embodiments of the present invention will be described with reference to the drawings.
[0063]
FIG. 2 is a configuration diagram of a quantum computer algorithm conversion apparatus according to an embodiment of the present invention.
[0064]
The quantum computer algorithm conversion apparatus according to the present embodiment includes an operation unit 11 and a storage unit 12, and the storage unit 12 includes an input algorithm storage unit 13, an output algorithm storage unit 14, and a variable name array storage unit 15. As shown in FIG. 2, the calculation unit 11 and the input unit 20, an initialization unit 21 that performs the processing of steps 11 to 17 in FIG. 3, a processing determination unit 22, processing units 23, 24, 25, 26, end determination / An output unit 27 is included.
[0065]
The quantum algorithm is input to the apparatus by the input unit 20 and stored in the input algorithm storage unit 13. Next, in the initialization unit 21, the output algorithm storage unit 14 and the variable name array storage unit 15 are initialized. Thereafter, the processing from the processing determination unit 22 to the calculation unit 26 is repeated according to the input algorithm. During this time, the output algorithm storage unit 14 and the variable name array storage unit 15 are updated for each step. Finally, the contents of the output algorithm storage unit 14 and the variable name storage unit 15 are output from the end determination / output unit 27 as calculation results.
[0066]
The quantum computer algorithm conversion method of the present invention is recorded on a computer-readable recording medium and a program for realizing its function in addition to that realized by dedicated hardware. The program may be read by a computer system and executed. The computer-readable recording medium refers to a recording medium such as a floppy disk, a magneto-optical disk, a CD-ROM, or a storage device such as a hard disk device built in the computer system. Furthermore, a computer-readable recording medium is a server that dynamically holds a program (transmission medium or transmission wave) for a short period of time as in the case of transmitting a program via the Internet, and a server in that case Some of them hold programs for a certain period of time, such as volatile memory inside computer systems.
[0067]
【The invention's effect】
As described above, according to the present invention, it is not necessary to directly describe a quantum algorithm for a circular array type quantum computer, and if a normal quantum algorithm is described, the machine converts this into a quantum algorithm for a circular array type quantum computer. (For example, instead of manually writing the algorithm shown in FIG. 5, the algorithm shown in FIG. 4 may be written instead), the manufacturing efficiency of the algorithm is dramatically increased. .
[Brief description of the drawings]
FIG. 1 is a flowchart showing a quantum computer algorithm conversion method of the present invention.
FIG. 2 is a configuration diagram of a quantum computer algorithm conversion apparatus according to an embodiment of the present invention.
3 is a configuration diagram of a calculation unit 11 in FIG. 2;
FIG. 4 is a diagrammatic representation of an algorithm.
FIG. 5 is a diagram showing an example of an input quantum algorithm and its graphical representation.
FIG. 6 is a diagram showing an example of an output quantum algorithm and its representation in the figure.
[Explanation of symbols]
1-9 steps
11 Calculation unit
12 Storage unit
13 Input algorithm storage
14 Output algorithm storage
15 Variable name array storage
20 Input section
21 Initialization section
22 Process determination unit
23 to 26 processing section
27 End determination / output section

Claims (4)

An input algorithm storage unit that stores an input quantum algorithm that is described using a control NOT and is a series of operations on bit information applied to qubits;
An output algorithm storage section for storing the quantum algorithm that outputs,
A variable name storage unit for storing variable names;
Performs writing and reading of information to and from these storage unit, converts the inputted quantized algorithm algorithm for cycle sequencing quantum computers, have a computing unit for outputting,
The calculation unit sets the input quantum algorithm as g = g1g2... Gd,
A first means for initializing a variable name storage array V for storing an output algorithm storage variable G ′ and n (n is the number of qubits) +1 variable names;
The controlled-NOT gate g i as (ti, ci), | and multiples determining whether the second unit type number m qubit circulation quantum computer, | V [ti] -V [ ci]
When | V [ti] −V [ci] | is a multiple of m, a quantum algorithm G0 is defined, G ′ = G′G0, and a third means for changing the variable name storage array V based on G0 When,
| V [ti] -V [ci ] | if is not a multiple of m, defining the quantum algorithm G1, G '= G' and G1, the fourth means for changing the variable name memory array V based on the G1 When,
Define a quantum algorithm G2, and G '= G' G2, and fifth means for changing the variable name memory array V based on the G2,
Define a quantum algorithm G3, and G '= G' G3, having a sixth means for changing the variable name memory array V based on G3,
The second to sixth means are sequentially executed while increasing i by 1 from i = 1 to i = d.
Algorithm conversion device. An input algorithm storage unit that stores an input quantum algorithm that is described as a series of operations on bit information that is described using control NOT and is applied to a qubit, and an output algorithm storage unit that stores the output quantum algorithm A variable name storage unit that stores variable names, and an operation that writes and reads information between these storage units, converts the input quantum algorithm into an algorithm for a circular array type quantum computer, and outputs it Quantum computer algorithm for converting input quantum algorithm g (= g 1 g 2... G d), which is performed by an algorithm conversion device having a unit and described using control NOT, into an algorithm for circular array type quantum A conversion method,
The computing unit is
A first step of initializing a variable name storage array V for storing an output algorithm storage variable G ′ and n (n is the number of qubits) +1 variable name ;
The controlled-NOT gate g i as (ti, ci), | and multiples if the second step of determining whether the number of types m of the qubit circulation quantum computer, | V [ti] -V [ ci]
When | V [ti] −V [ci] | is a multiple of m, the quantum algorithm G0 is defined, G ′ = G′G0, and the variable name storage array V is changed based on G0. When,
If | V [ti] −V [ci] | is not a multiple of m, the quantum algorithm G1 is defined, G ′ = G′G1, and the variable name storage array V is changed based on G1. When,
Defining a quantum algorithm G2, setting G ′ = G′G2, and changing the variable name storage array V based on G2 ,
Defining a quantum algorithm G3, setting G ′ = G′G3, and changing the variable name storage array V based on G3 ,
The second to sixth steps are sequentially executed while increasing i by 1 from i = 1 to i = d.
Quantum computer algorithm conversion method. The computer is described using a control NOT, accumulates the input algorithm storage section for storing the input quantized algorithm is a series of operations on bit information applied on qubits, the quantum algorithm outputs Information is written to and read from the output algorithm storage unit, variable name storage unit that stores variable names, and these storage units, and the input quantum algorithm is converted into an algorithm for a circular array type quantum computer. , Function as an algorithm conversion device having an arithmetic unit for output, and convert the input quantum algorithm g (= g 1 g 2... G d) described using the control NOT into an algorithm for a circular array type quantum A quantum computer algorithm conversion program,
The computing unit is
First procedure for initializing variable G ′ for storing output algorithm and variable name storage array V that stores n (n is the number of qubits) +1 variable name
Run
The controlled-NOT gate g i as (ti, ci), | a circulation type quantum computer qubit number of types m multiple of determining whether the second procedure, | V [ti] -V [ ci]
When | V [ti] −V [ci] | is a multiple of m, the quantum procedure G0 is defined, G ′ = G′G0, and the variable name storage array V is changed based on G0 When,
If | V [ti] −V [ci] | is not a multiple of m, a quantum algorithm G1 is defined, G ′ = G′G1, and the variable name storage array V is changed based on G1 . Procedure and
Defining a quantum algorithm G2, setting G ′ = G′G2, and changing the variable name storage array V based on G2 ,
A sixth procedure that defines a quantum algorithm G3, sets G ′ = G′G3, and changes the variable name storage array V based on G3 ;
The Do Increase i by 1 to order from the next run from i = 1 to i = d,
Quantum computer algorithm conversion program. The recording medium which recorded the quantum computer algorithm conversion program of Claim 3 .

Images