Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression

Berthusen, Noah F.; Trevisan, Thaís V.; Iadecola, Thomas; Orth, Peter P.

doi:10.48550/arxiv.2112.12654

Cited by 5 publications

(10 citation statements)

References 50 publications

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“…However, it is unstable, whereas Richardson extrapolation is not very effective but stable for our particular quantum circuits [48]. As discussed in reference [47] and shown recently in reference [63], the joint implementation of RC and ZNE increases the effectiveness of these quantum error mitigation techniques with respect to their individual application.…”

Section: State Initialization Qubit Measurement and Quantum Error Mit...mentioning

confidence: 71%

“…The simulations performed with these decomposition techniques typically require long coherence times in the current NISQ computers in order to produce faithful results. Therefore, one may instead simulate the closed Hamil-tonian dynamics via hybrid quantum-classical methods, such as the Variational Quantum Simulator [20,35], Variational Fast-Forwarding methods [36,37] or variational compressed Trotter techniques [38,39].…”

Section: Revisiting the Tedopamentioning

confidence: 99%

See 1 more Smart Citation

Efficient method to simulate non-perturbative dynamics of an open quantum system using a quantum computer

Guimarães¹,

Vasilevskiy²,

Barbosa³

2022

Preprint

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Classical non-perturbative simulations of open quantum systems dynamics face several scalability problems, namely, exponential scaling as a function of either the time length of the simulation or the size of the open system. In this work, we propose a quantum computational method which we term as Quantum Time Evolving Density operator with Orthogonal Polynomials Algorithm (Q-TEDOPA), based on the known TEDOPA technique, avoiding any exponential scaling in simulations of non-perturbative dynamics of open quantum systems on a quantum computer. By performing an exact transformation of the Hamiltonian, we obtain only local nearest-neighbour interactions, making this algorithm suitable to be implemented in the current Noisy-Intermediate Scale Quantum (NISQ) devices. We show how to implement the Q-TEDOPA using an IBM quantum processor by simulating the exciton transport between two light-harvesting molecules in the regime of moderate coupling strength to a non-Markovian harmonic oscillator environment. Applications of the Q-TEDOPA span problems which can not be solved by perturbation techniques belonging to different areas, such as dynamics of quantum biological systems and strongly correlated condensed matter systems.

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Section: State Initialization Qubit Measurement and Quantum Error Mit...mentioning

confidence: 71%

Section: Revisiting the Tedopamentioning

confidence: 99%

Efficient method to simulate non-perturbative dynamics of an open quantum system using a quantum computer

Guimarães¹,

Vasilevskiy²,

Barbosa³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…This algorithm regards the quantum device as a co-processor that measures the energy of a quantum system and its derivatives, evaluated for a set of variational states, and the optimization of the parameters in the variational manifold is carried by a classical co-processor. Motivated by this algorithm, several variational algorithms for quantum dynamics simulations (VQDS) [10][11][12][13][14][15][16][17][18][19][20][21][22] have been proposed to solve the problem of time-evolving the state of an isolated quantum system using quantum computers.…”

Section: Introductionmentioning

confidence: 99%

Variational quantum algorithms for simulation of Lindblad dynamics

Watad,

Lindner

2024

Quantum Sci. Technol.

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We introduce a variational hybrid classical-quantum algorithm to simulate the Lindblad master equation and its adjoint for time-evolving Markovian open quantum systems and quantum observables. Our method is based on a direct representation of density matrices and quantum observables as quantum superstates. We design and optimize low-depth variational quantum circuits that efficiently capture the unitary and non-unitary dynamics of the solutions. We benchmark and test the algorithm on different models and system sizes, showing its potential for utility with near-future hardware.

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“…Another promising approach is to use the framework of variational quantum algorithms [24]. They are exemplified by variational quantum simulation [25][26][27][28][29][30][31], and quantum compilations FIG. 1.…”

Section: Introductionmentioning

confidence: 99%

Local variational quantum compilation of a large-scale Hamiltonian dynamics

Mizuta¹,

Nakagawa²,

Mitarai³

et al. 2022

Preprint

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Implementing time evolution operators on quantum circuits is important for quantum simulation. However, the standard way, Trotterization, requires a huge numbers of gates to achieve desirable accuracy. Here, we propose a local variational quantum compilation (LVQC) algorithm, which allows to accurately and efficiently compile a time evolution operators on a large-scale quantum system by the optimization with smaller-size quantum systems. LVQC utilizes a subsystem cost function, which approximates the fidelity of the whole circuit, defined for each subsystem as large as approximate causal cones brought by the Lieb-Robinson (LR) bound. We rigorously derive its scaling property with respect to the subsystem size, and show that the optimization conducted on the subsystem size leads to the compilation of whole-system time evolution operators. As a result, LVQC runs with limited-size quantum computers or classical simulators that can handle such smaller quantum systems. For instance, finite-ranged and short-ranged interacting L-size systems can be compiled with O(L 0 )-or O(log L)-size quantum systems depending on observables of interest. Furthermore, since this formalism relies only on the LR bound, it can efficiently construct time evolution operators of various systems in generic dimension involving finite-, short-, and long-ranged interactions. We also numerically demonstrate the LVQC algorithm for one-dimensional systems. Employing classical simulation by time-evolving block decimation, we succeed in compressing the depth of a time evolution operators up to 40 qubits by the compilation for 20 qubits. LVQC not only provides classical protocols for designing large-scale quantum circuits, but also will shed light on applications of intermediate-scale quantum devices in implementing algorithms in larger-scale quantum devices.

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Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression

Cited by 5 publications

References 50 publications

Efficient method to simulate non-perturbative dynamics of an open quantum system using a quantum computer

Efficient method to simulate non-perturbative dynamics of an open quantum system using a quantum computer

Variational quantum algorithms for simulation of Lindblad dynamics

Local variational quantum compilation of a large-scale Hamiltonian dynamics

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