Incoherent quantum algorithm dynamics of an open system with near-term devices

Mahdian, M.; Yeganeh, Hojatollah

doi:10.1007/s11128-020-02800-8

Cited by 6 publications

(4 citation statements)

References 52 publications

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“…Two of representative VQAs are the variations quantum eigensolver (VQE) which is a hybrid algorithm to approximate the ground state eigenvalues for chemical systems [14,15] and the quantum approximate optimization algorithm (QAOA) for finding an approximate solution of an optimization problem [4,16]. Also, VQAs have been introduced for other promising applications such as simulation open quantum system dynamics [17][18][19][20][21], which allows us to have a better understanding of the nonequilibrium dynamics of many-body quantum systems [10,22].…”

Section: Introductionmentioning

confidence: 99%

Single entanglement connection architecture between multi-layer bipartite hardware efficient ansatz

Zhang,

Qin,

Zhou

et al. 2024

New J. Phys.

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Variational quantum algorithms (VQAs) are among the most promising algorithms to achieve quantum advantages in the NISQ era. One important challenge in implementing such algorithms is to construct an effective parameterized quantum circuit (also called an ansatz). In this work, we propose a single entanglement connection architecture (SECA) for a bipartite hardware-efficient ansatz (HEA) by balancing its expressibility, entangling capability, and trainability. Numerical simulations with a one-dimensional Heisenberg model and quadratic unconstrained binary optimization (QUBO) issues were conducted. Our results indicate the superiority of SECA over the common full entanglement connection architecture (FECA) in terms of computational performance. Furthermore, combining SECA with gate-cutting technology to construct distributed quantum computation (DQC) can efficiently expand the size of NISQ devices under low overhead. We also demonstrated the effectiveness and scalability of the DQC scheme. Our study is a useful indication for understanding the characteristics associated with an effective training circuit.

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Section: Introductionmentioning

confidence: 99%

Single entanglement connection architecture between multi-layer bipartite hardware efficient ansatz

Zhang,

Qin,

Zhou

et al. 2024

New J. Phys.

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“…The role of coherence in quantum algorithms has attracted considerable attention in recent years [59][60][61][62][63][64][65][66]. It has been found that the Deutsch-Jozsa algorithm relies on coherence during the processing, and its precision is directly related to the recoverable coherence [67,68].…”

Section: Introductionmentioning

confidence: 99%

Tsallis relative α entropy of coherence dynamics in Grover′s search algorithm

Fei

2023

Commun. Theor. Phys.

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Quantum coherence plays a central role in Grover's search algorithm. We study the Tsallis relative $\alpha$ entropy of coherence dynamics of the evolved state in Grover's search algorithm. We prove that the Tsallis relative $\alpha$ entropy of coherence decreases with the increase of the success probability, and derive the complementarity relations between the coherence and the success probability. We show that the operator coherence of the first $H^{\otimes n}$ relies on the size of the database $N$, the success probability and the target states for $\alpha\in(1,2]$. Moreover, we illustrate the relations between the coherence and the entanglement of the superposition state of targets, as well as the coherence producing and deleting in the Grover iterations.

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“…Among the different approaches to quantum computing, NISQ devices, which include relatively low-depth quantum circuits by hybrid variational quantumclassical algorithms, have recently received a lot of attention. Hybrid algorithms have been designed in a way that uses resources such as quantum and classical to solve problems specific optimization tasks that are not accessible to traditional classical computers [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. One of the most important advantages of this method is that it requires a small number of qubits (contain from 10 to 10 3 of qubits) to run with high gate fidelity and not fault-tolerant error correction [37].…”

Section: Introductionmentioning

confidence: 99%

“…One of the most important advantages of this method is that it requires a small number of qubits (contain from 10 to 10 3 of qubits) to run with high gate fidelity and not fault-tolerant error correction [37]. Also, these algorithms have been introduced for other applications such as finding ground and excited states [38,43,53] and simulation system dynamics [51,52,54,55]. In this paper, we design the variational hybrid quantum-classical algorithm for calculating quantum and classical correlations.…”

Section: Introductionmentioning

confidence: 99%

Toward a quantum computing algorithm to quantify classical and quantum correlation of system states

Mahdian,

Yeganeh

2021

Preprint

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Optimal measurement is required to obtain the quantum and classical correlations of a quantum state, and the crucial difficulty is how to acquire the maximal information about one system by measuring the other part; in other words, getting the maximum information corresponds to preparing the best measurement operators. Within a general setup, we designed a variational hybrid quantum-classical (VHQC) algorithm to achieve classical and quantum correlations for system states under the Noisy-Intermediate Scale Quantum (NISQ) technology. To employ, first, we map the density matrix to the vector representation, which displays it in a doubled Hilbert space, and it's converted to a pure state. Then we apply the measurement operators to a part of the subsystem and use variational principle and a classical optimization for the determination of the amount of correlation. We numerically test the performance of our algorithm at finding a correlation of some density matrices, and the output of our algorithm is compatible with the exact calculation.

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Incoherent quantum algorithm dynamics of an open system with near-term devices

Cited by 6 publications

References 52 publications

Single entanglement connection architecture between multi-layer bipartite hardware efficient ansatz

Single entanglement connection architecture between multi-layer bipartite hardware efficient ansatz

Tsallis relative α entropy of coherence dynamics in Grover′s search algorithm

Toward a quantum computing algorithm to quantify classical and quantum correlation of system states

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