A quantum algorithm for evolving open quantum dynamics on quantum computing devices

Abstract

Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.

Characterization of Quantum States Based on Creation Complexity

“…Quantum computing has seen enormous progress in both the theoretical and the experimental fronts. [1][2][3][4][5][6] From the early proposals of the phase estimation algorithm, [7] the Shor's factorization algorithm [8] and the Harrow-Hassidim-Lloyd algorithm for linear systems, [9] to the more recent ones like the variational quantum eigensolver, [10] the quantum machine learning algorithms, [11,12] and quantum algorithm for open quantum dynamics, [13,14] the potential of quantum algorithms to outperform their classical counterparts in numerous tasks become increasingly realistic with the rapid development of quantum computing hardware. [15][16][17][18] However, the design of quantum DOI: 10.1002/qute.202000043 algorithms so far remains an accidental process because there is no systematic way to look for algorithms that scale efficiently.…”

“…Equation (13) means that even if K 1 ≪ 2 n , with a very large number N of trials all being successful, the probability of K ≤ K 1 can still be an appreciable number. For example, if we have 50 qubits (n = 50), "polynomial" is defined as K ≤ K 1 = 2 30 ≪ 2 50 , for a given (n) we have N = 10 7 trials all being successful, then we can conclude with 1 − 10 −4 confidence probability that (n) is polynomial.…”

Strategies to simulate dephasing-assisted quantum transport on digital quantum computers

“…To study the interplay of unitary quantum evolution and decoherence in digital quantum simulations we need to face the inherent difficulty of mapping non-unitary evolution into the framework of unitary gates. General strategies to tackle this problem have been developed, mostly based on dilation of the Hilbert space of the system [28,29] and variational principles [30]. Dilation of the Hilbert space allows one to obtain the non-unitary dynamics of the system of interest by simulating the unitary dynamics of a larger system.…”

Universal quantum simulation of single-qubit nonunitary operators using duality quantum algorithm

“…Several efforts have been made to simulate dissipative-quantum systems. For examples, Barreiro et al experimentally implement open-system dynamics through the dissipative map 32 ; Hu et al propose and demonstrate a general quantum algorithm to evolve open quantum by simulating Kraus maps 33 ; Rost et al simulate condensed matter system 34 ; Viyuela et al prepare topological thermal states to simulate a topological insulator open system for the topological-Uhlmann-phase measurement 35 . In recent years, non-Hermitian quantum mechanics and related systems are investigated massively.…”