Distributed quantum computation has gained extensive attention since small-qubit quantum computers seem to be built more practically in the noisy intermediate-scale quantum (NISQ) era. In this paper, we give a distributed Bernstein-Vazirani algorithm (DBVA) with $t$ computing nodes, and a distributed exact Grover's algorithm (DEGA) that solve the search problem with only one target item in the unordered databases. Though the designing techniques are simple in the light of BV algorithm, Grover's algorithm, the improved Grover's algorithm by Long, and the distributed Grover's algorithm by Qiu et al, in comparison to BV algorithm, the circuit depth of DBVA is not greater than $2^{\text{max}(n_0, n_1, \cdots, n_{t-1})}+3$ instead of $2^{n}+3$ , and the circuit depth of DEGA is $8(n~\text{mod}~2)+9$ , which is less than the circuit depth of Grover's algorithm, $1 + 8\left\lfloor \fracπ{4}\sqrt{2^n} \right\rfloor$ . In particular, we provide situations of our DBVA and DEGA on MindQuantum (a quantum software) to validate the correctness and practicability of our methods. By simulating the algorithms running in the depolarized channel, it further illustrates that distributed quantum algorithm has superiority of resisting noise.Distributed quantum computation has gained extensive attention since small-qubit quantum computers seem to be built more practically in the noisy intermediate-scale quantum (NISQ) era. In this paper, we give a distributed Bernstein-Vazirani algorithm (DBVA) with $t$ computing nodes, and a distributed exact Grover's algorithm (DEGA) that solve the search problem with only one target item in the unordered databases. Though the designing techniques are simple in the light of BV algorithm, Grover's algorithm, the improved Grover's algorithm by Long, and the distributed Grover's algorithm by Qiu et al, in comparison to BV algorithm, the circuit depth of DBVA is not greater than $2^{\text{max}(n_0, n_1, \cdots, n_{t-1})}+3$ instead of $2^{n}+3$, and the circuit depth of DEGA is $8(n~\text{mod}~2)+9$, which is less than the circuit depth of Grover's algorithm, $1 + 8\left\lfloor \fracπ{4}\sqrt{2^n} \right\rfloor$. In particular, we provide situations of our DBVA and DEGA on MindQuantum (a quantum software) to validate the correctness and practicability of our methods. By simulating the algorithms running in the depolarized channel, it further illustrates that distributed quantum algorithm has superiority of resisting noise.

arXiv:2303.10670Mar 19, 20232 citations

Grover Algorithm

Ray LaPierre

The Materials Research Society seriesJan 1, 20212 citations

Distributed exact multi-objective quantum search algorithm

Hao Li, Daowen Qiu, Le Luo

Multi-objective search means searching for any one of several objectives in an unstructured database. Grover's algorithm has quadratic acceleration in multi-objection search than classical ones. Iterated operator in Grover's algorithm is a key element and plays an important role in amplitude amplification. In this paper, we design two distributed iterated operators and therefore two new distributed Grover's algorithms are obtained with the following advantages: (1) Compared to Grover's algorithm and the modified Grover's algorithm by Long, our distributed algorithms require fewer qubits; (2) Compared to the distributed Grover's algorithm proposed by Qiu et al., one of our distributed algorithms is exact. Of course, both our distributed algorithms require quite quantum communication and involve a number of more complicated unitary operators as cost, but there still may have certain advantage of physical realizability in the Noisy Intermediate-Scale Quantum (NISQ) era.Multi-objective search means searching for any one of several objectives in an unstructured database. Grover's algorithm has quadratic acceleration in multi-objection search than classical ones. Iterated operator in Grover's algorithm is a key element and plays an important role in amplitude amplification. In this paper, we design two distributed iterated operators and therefore two new distributed Grover's algorithms are obtained with the following advantages: (1) Compared to Grover's algorithm and the modified Grover's algorithm by Long, our distributed algorithms require fewer qubits; (2) Compared to the distributed Grover's algorithm proposed by Qiu et al., one of our distributed algorithms is exact. Of course, both our distributed algorithms require quite quantum communication and involve a number of more complicated unitary operators as cost, but there still may have certain advantage of physical realizability in the Noisy Intermediate-Scale Quantum (NISQ) era.

arXiv:2409.04039Sep 6, 20240 citations

Distributed exact Grover’s algorithm

Xu Zhou, Daowen Qiu, Le Luo

Distributed quantum computation has gained extensive attention. In this paper, we consider a search problem that includes only one target item in the unordered database. After that, we propose a distributed exact Grover’s algorithm (DEGA), which decomposes the original search problem into ⌊n/2⌋ parts. Specifically, (i) our algorithm is as exact as the modified version of Grover’s algorithm by Long, which means the theoretical probability of finding the objective state is 100%; (ii) the actual depth of our circuit is 8(n mod 2) + 9, which is less than the circuit depths of the original and modified Grover’s algorithms, $1 + 8\left\lfloor {{\pi \over 4}\sqrt {{2^n}} } \right\rfloor$ and $9 + 8\left\lfloor {{\pi \over 4}\sqrt {{2^n}} - {1 \over 2}} \right\rfloor$ , respectively. It only depends on the parity of n, and it is not deepened as n increases; (iii) we provide particular situations of the DEGA on MindQuantum (a quantum software) to demonstrate the practicality and validity of our method. Since our circuit is shallower, it will be more resistant to the depolarization channel noise.Distributed quantum computation has gained extensive attention. In this paper, we consider a search problem that includes only one target item in the unordered database. After that, we propose a distributed exact Grover’s algorithm (DEGA), which decomposes the original search problem into ⌊n/2⌋ parts. Specifically, (i) our algorithm is as exact as the modified version of Grover’s algorithm by Long, which means the theoretical probability of finding the objective state is 100%; (ii) the actual depth of our circuit is 8(n mod 2) + 9, which is less than the circuit depths of the original and modified Grover’s algorithms, $$1 + 8\left\lfloor {{\pi \over 4}\sqrt {{2^n}} } \right\rfloor $$ and $$9 + 8\left\lfloor {{\pi \over 4}\sqrt {{2^n}} - {1 \over 2}} \right\rfloor $$ , respectively. It only depends on the parity of n, and it is not deepened as n increases; (iii) we provide particular situations of the DEGA on MindQuantum (a quantum software) to demonstrate the practicality and validity of our method. Since our circuit is shallower, it will be more resistant to the depolarization channel noise.

Frontiers of PhysicsAug 14, 202323 citations

t

computing nodes, and a distributed exact Grover's algorithm (DEGA) that solve the search problem with only one target item in the unordered databases. Though the designing techniques are simple in the light of BV algorithm, Grover's algorithm, the improved Grover's algorithm by Long, and the distributed Grover's algorithm by Qiu et al, in comparison to BV algorithm, the circuit depth of DBVA is not greater than

2^{\text{max}(n_0, n_1, \cdots, n_{t-1})}+3

instead of

2^{n}+3

, and the circuit depth of DEGA is

8(n~\text{mod}~2)+9

, which is less than the circuit depth of Grover's algorithm,

1 + 8\left\lfloor \fracπ{4}\sqrt{2^n} \right\rfloor

. In particular, we provide situations of our DBVA and DEGA on MindQuantum (a quantum software) to validate the correctness and practicability of our methods. By simulating the algorithms running in the depolarized channel, it further illustrates that distributed quantum algorithm has superiority of resisting noise.

1 + 8\left\lfloor {{\pi \over 4}\sqrt {{2^n}} } \right\rfloor

and

9 + 8\left\lfloor {{\pi \over 4}\sqrt {{2^n}} - {1 \over 2}} \right\rfloor

, respectively. It only depends on the parity of n, and it is not deepened as n increases; (iii) we provide particular situations of the DEGA on MindQuantum (a quantum software) to demonstrate the practicality and validity of our method. Since our circuit is shallower, it will be more resistant to the depolarization channel noise.