Quantum circuit with quick search

Abstract

The oracle is used to mark a solution to the search problem, wherein the output of the Dicke state unit is applied to the oracle. The second register has a qubit that serves as the output of the oracle. The third register has n qubits and is used to reflect the superposition of the solutions to the search problem marked by the oracle.

Description

[Technical Field]

[0001] This invention relates to a quantum circuit, and more particularly to a fast quantum search circuit. [Previous Technology]

[0002] Quantum computing is based on the principles of quantum mechanics to perform information calculations. One of the fundamental characteristics of quantum computing is the use of quantum bits (qubits) as information units for computation. Qubits can be particles like electrons or other quasi-particles in a state of elementary excitation. Taking electrons as an example, an electron with spin up represents state 1, and an electron with spin down represents state 0. A quantum state in which electron spin is both up and down is called a superposition state. A small number of particles in a superposition state can carry a large amount of information. The superposition state of just 100 particles can simultaneously represent numbers from 0 to (2^100) - 1.

[0003] In the field of existing quantum computing, Grover's algorithm is a quantum search algorithm that can find a target data item from N unstructured or unsorted data. Specifically, Grover's algorithm aims to find the target input or solution from N unstructured input instances by repeating the oracle and diffuser 0() times, thereby identifying the target input with a high probability.

[0004] Figure 1 shows a block diagram of the quantum circuit of the Groove algorithm, in which the oracle (Uf) and diffuser 11 form the Groove iterator 13. When there are n qubits, the Groove iterator will iterate 0() times, where N=2n. Since a diffuser is an operation that inverts the probability amplitude of a quantum state around its mean, the Grover algorithm iteratively modifies the qubit states. In other words, initially, the qubit states are in uniform superposition. Then, an oracle Uf is applied to invert the phase of the qubit state corresponding to the solution, creating a negative probability amplitude. Next, diffuser 11 is applied to perform an inversion-around-amplitude-mean operation to amplify the probability amplitude of the target solution. After the Grover iterator 13 is repeated 0() times, the amplitude of the qubit state corresponding to the solution becomes very large, while the amplitude of each non-solution qubit state becomes very small or even close to zero. This allows the Grover algorithm to find the target solution with a high probability. However, in the Grover algorithm, the Grover iterator 13 needs to be repeated 0() times to obtain the target solution, i.e., the oracle needs to be called 0() times, making it difficult to improve the computational speed.

[0005] Therefore, it is urgent to propose an improved quantum circuit to eliminate or mitigate the above problems. [Summary of the Invention]

[0006] The purpose of this disclosure is to provide a fast quantum search circuit that only requires calling the oracle once and uses the Dick state quantum search method, which has a solution search space of only C(n,k) states, thus greatly improving the speed of quantum search.

[0007] To achieve the aforementioned objective, the fast search quantum circuit disclosed herein includes: a Dick state unit; a first register having n qubits, wherein the n qubits of the first register are applied to the Dick state unit, where n is an integer greater than 0; an oracle for marking the solution to the search problem, wherein the output of the Dick state unit is applied to the oracle; a second register having one qubit, used as the output of the oracle; and a third register having n qubits for reflecting the superposition state of the solution to the search problem marked by the oracle.

[0008] Other objects, advantages and novel features of the present invention will become more apparent from the following detailed description with reference to the drawings. [Simplified Explanation of the Diagram]

[0027] Figure 1 shows a block diagram of the quantum circuitry of the Grover algorithm.

[0028] Figure 2 shows a block diagram of a fast quantum circuit using the Dick state quantum search (DSQS) method.

[0029] Figure 3A shows a given undirected graph G=(V,E), where V={v0,v1,v2,v3,v4} and E={e0,e1,e2,e3}.

[0030] Figure 3B shows an undirected graph G=(V,E) and a vertex cover with two vertices.

[0031] Figure 3C shows an undirected graph G=(V,E) and its other vertex cover with two vertices.

[0032] Figure 4 shows the experiment performed on the IBM quantum computer simulator using the IBM Qiskit kit to realize the fast search for quantum circuits disclosed in this paper using the Dick state quantum search method to solve the k-vertex cover problem.

[0033] Figure 5 shows a histogram to illustrate the statistical results of multiple measurements of the fast search quantum circuit of this disclosure using the Dick state quantum search method to solve the k-vertex cover problem.

[0034] Figure 6 shows a block diagram of the dual quantum flags.

Implementation Method

[0009] The following provides different embodiments of the present invention. These embodiments are used to illustrate the technical content of the present invention, and are not intended to limit the scope of the present invention. A feature of one embodiment may be applied to other embodiments through suitable modifications, substitutions, combinations, or separations.

[0010] It should be noted that, unless otherwise specified herein, having "a" element is not limited to having a single element, but may include one or more elements.

[0011] In this document, unless otherwise specified, the term "characteristic A" or "and / or" and "characteristic B" means that A exists alone, B exists alone, or A and B exist simultaneously; the term "characteristic A" and "and" or "and" or "and" and "characteristic B" means that A and B exist simultaneously; the terms "including", "containing", "having", and "containing" refer to, but are not limited to, these.

[0012] Furthermore, in this document, the terms “up,” “down,” “front,” “back,” or “between” are used only to describe the relative positions between multiple elements and can be extended to include translation, rotation, or mirroring.

[0013] In addition, unless otherwise specified herein, the phrase "an element on another element" or similar statements do not necessarily indicate that the element is in contact with the other element.

[0014] Furthermore, unless otherwise specified herein, a numerical value may cover a range of ±10% of the value, and in particular a range of ±5% of the value. Unless otherwise specified, a numerical range consists of multiple subranges defined by the smaller endpoint, the smaller quartile, the median, the larger quartile, and the larger endpoint.

[0015] In one embodiment of this disclosure, a fast-search quantum circuit is provided. Figure 2 shows a block diagram of the proposed fast-search quantum circuit using the Dicke State Quantum Search (DSQS) method. As shown in Figure 2, the quantum circuit has an oracle (Uf) 23, a first register REG-x, a second register REG-y, a third register REG-x', a Dicke state unit 21, and multiple multi-controlled NOT gates. gate)25, multiple measurement program units 27, wherein the first register REG-x has n qubits, which serve as working qubits, so that the first register REG-x can use n working qubits to form a solution search space of multiple states (e.g., C(n,k) states), where n is an integer greater than 0; the second register REG-y has one qubit, which serves as a response qubit and is used as a response or output of oracle 23; the third register REG-x' has n qubits, which serve as auxiliary qubits and are used to reflect the superposition state of the solution to the relevant search problem.

[0016] The n working qubits of the aforementioned first temporary register REG-x are applied to the Dick state unit 21. Therefore, the state of the n qubits before processing through the oracle is the Dick state. In the DSQS method using the Dick state unit 21, the function of the Dick state unit 21 is to generate the Dick state |〉. The state of the Dick state unit 21 is to restrict the search space by the Dick state, where exactly k qubits out of the n qubits are in the quantum state |1〉, and the remaining qubits are in the quantum state |0〉, where k is an integer greater than 0 and k is less than or equal to n.

[0017] The output of the Dicke state unit 21 described above is applied to the oracle 23, which can be regarded as a black box and usually has an input function for marking the solution to the search problem. In the present invention, n qubits of the first register REG-x are used as the input, and 1 qubit of the second register REG-y is used as the output. The oracle 23 is defined as follows:

[0018] Where T is the set of all target inputs or solutions. If the first register REG-x is a solution or target input in T, then the oracle 23 sets the second register REG-y to the state |1〉; otherwise, the oracle 23 sets the second register REG-y to the state |0〉.

[0019] The output of the oracle 23 is applied to a plurality of multi-controlled NOT gates 25. Each multi-controlled NOT gate 25 includes a plurality of control bits 251 and 252 and a target bit 253. By applying a bit of the register REG-x to the control bit 251 and the output of the oracle 23 (i.e., the single bit of the register REG-y) to the control bit 252, the corresponding target bit 253 is obtained, and the quantum state of 0 or 1 is measured by the measurement program unit 27 corresponding to the target bit 253. All the target bits 253 are reflected by n auxiliary qubits of the third register REG-x' in the superposition state of the solution to the relevant search problem.

[0020] To further illustrate the Dicke state unit 21, please still refer to FIG. 2. If not specified, the initial state of all qubits is |0〉. Since the Dicke state unit 21 described above uses the Dicke state to limit the search space to the quantum state where exactly k qubits among n qubits are in the state |1〉 and the remaining qubits are in the state |0〉, the size of the solution search space is C(n,k), and the probability that the solution is finally measured is 1 / C(n,k), where C(n,k)=n(n - 1)...(n - k + 1) / k! (when 0 < k << n / 2, C(n,k)=O(n^k), that is, approximately the k-th power of n). And due to the limitation of the Dicke state, in the oracle 23 of the DSQS method, all counters that count the number of qubits in the state |1〉 being k can be omitted. Therefore, the design of the quantum circuit of the oracle 23 can be further simplified.

[0021] That is, the function of the Dick State Quantum Search (DSQS) method is to use Oracle 23 to check the solution (i.e., the target input) of the search problem in the quantum superposition state of the n qubits x0,...,xn-1 of the first temporary register REG-x. The result is that the n qubits x'0,...,x'n-1 of the third temporary register REG-x' present a superposition state of the solution (i.e., the target input), and the probability density of each state is 1 / C(n,k), which is the probability amplitude.

[0022] Figures 3A-3C, 4 and 5 show an example of the Dicke State Quantum Search (DSQS) method for fast quantum circuit search according to the present invention. This example uses the Dicke State Quantum Search (DSQS) method to solve the k-vertex cover problem (k-VCP). Figure 3A shows a given undirected graph G=(V,E), where V={v0,v1,v2,v3,v4} and E={e0,e1,e2,e3}. If the value of k is set to 2, then the undirected graph G has a total of two vertex covers with two vertices. Figure 3B shows the undirected graph G=(V,E) and one of its vertex covers with two vertices ({v0,v3}). Figure 3C shows the undirected graph G=(V,E) and another vertex cover with two vertices ({v1,v3}).

[0023] Figure 4 shows the experiment performed on the IBM quantum computer simulator using the IBM Qiskit kit to realize the fast quantum circuit search of the present invention using the Dick state quantum search (DSQS) method to solve the k-VCP, where x0~x4 represent the 5 qubits of the first temporary register REG-x, y represents the 1 qubit of the second temporary register REG-y, x'0~x'4 represent the 5 qubits of the third temporary register REG-x', f0~f7 represent the 8 auxiliary bits of Oracle 23, c represents the classical bit (bits 0~4, a total of 5 bits), e0~e3 represent the check procedure, check represents the overall check procedure, sol. represents the solution procedure, and measure represents the measurement procedure. As shown in Figure 4, the qubits x0~x4 of the first temporary register REG-x are applied to the Dick state unit 21; the checking procedure (e0~e3) is performed using dual quantum flags 41, where the block diagram of dual quantum flag 41 is shown in Figure 6, illustrating that dual quantum flag 41 can be used to check whether the condition (control bit xi is |1> and / or control bit xj is |1>) is met. If the condition is met, fh is |1>, otherwise fh is |0>, where h = 0, 2, 4, 6, and 0i,j4; the overall checking procedure is performed using a multi-controlled NOT gate, with f0, f2, f4 and f6 are control bits, and the qubit y of the second temporary register REG-y is used as the target bit; the solution program (sol.) uses multiple multi-controlled NOT gates, with the qubits x0~x4 of the first temporary register REG-x as control bits, and the qubit y of the second temporary register REG-y as control bits, and the qubits x'0~x'4 of the third temporary register REG-x' as outputting the target bit 253; the measurement program (measure) uses the measurement program unit 27 to measure whether the quantum state corresponding to the target bit 253 is 0 or 1, and generates the classical bit (c). Figure 5 shows a histogram illustrating the statistical results of multiple measurements of the k-VCP quantum circuit instance solved by the DSQS method. It lists the quasi-probabilities corresponding to bits 0 to 4 of the classical bits being 00000, 01001, and 01010, respectively, which are 0.801, 0.099, and 0.101 (because the quasi-probabilities are calculated independently for different measurement results, their sum is not necessarily exactly equal to 1).

[0024] In summary, the fast quantum search circuit of the present invention only requires calling the oracle once, and adopts the Dick state quantum search method with only C(n,k) states for the solution search space. Compared with the conventional method that requires calling the oracle 0() times and has a solution search space of up to 2n states, the size of the quantum search space can be greatly reduced. In addition, due to the limitation of the Dick state, the counters with k states of all counting working qubits in the oracle being |1> can be omitted, which can further simplify the design of the quantum circuit of the oracle.

[0025] Although the present invention has been described through various embodiments, it should be understood that many other possible modifications and variations may be made without departing from the spirit of the present invention and the claims made in the patent application.

Claims

1. A fast quantum search circuit, comprising: A Dick state unit is used to generate Dick states; A first register with n qubits, the n qubits of which are applied to the Dick state unit, where n is an integer greater than 0; an oracle for marking the solution to the search problem, wherein the output of the Dick state unit is applied to the oracle; a second register with one qubit, used as the output of the oracle; and a third register with n qubits, used to reflect the superposition state of the solution to the search problem marked by the oracle.

2. The fast quantum search circuit as described in claim 1 further includes: Multiple control gates, each control gate including multiple control bits and one target bit, wherein the output of the oracle is applied to the control bits of the control gates to obtain the corresponding target bit.

3. The fast quantum search circuit as described in claim 2, wherein, All the target bits are represented by the superposition state of the solution to the search problem by the n qubits of the third register.

4. The fast quantum search circuit as described in claim 2 further includes: A plurality of measurement procedure units, corresponding to the target bits, and each measurement procedure unit is used to measure the quantum state of the corresponding target bit as 0 or 1.

5. The fast quantum search circuit as described in claim 1, wherein, The oracle defines the second register as follows: if the first register is a solution or target input in the set of all target inputs or solutions, then the second register is set to state |1⟩; otherwise, the second register is set to state |0⟩.

6. A fast quantum search circuit as described in claim 1, wherein, The Dick state unit is a state in which the search space is restricted by the Dick state. The state is |1⟩ of exactly k qubits out of n qubits, and the rest are |0⟩, where k is an integer greater than 0 and k is less than or equal to n.

7. A fast quantum search circuit as described in claim 1, wherein, This Dick state unit forms a solution search space of C(n,k) states.

8. A fast quantum search circuit as described in claim 7, wherein, The probability of the final measured value of this solution is 1 / C(n,k).

9. A fast quantum search circuit as described in claim 7, wherein, The oracle is used to check the superposition state of the solution to the search problem in the quantum superposition state of the n qubits of the first temporary register, and to make the solution superposition state appear in the n qubits of the third temporary register.

10. The fast quantum search circuit as described in claim 4, wherein, After the quantum state of the target bit corresponding to the measurement is 0 or 1, the majority of measurement procedure units generate classical bits.

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