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arXiv:2210.12138 · Physical Review A

Quantum algorithm for solving open-system dynamics on quantum computers using noise

Juha Leppäkangas, Nicolas Vogt, Keith R. Fratus, Kirsten Bark, Jesse A. Vaitkus, Pascal Stadler, Jan-Michael Reiner, Sebastian Zanker, Michael Marthaler

Published Dec 22, 2023• 22 citations
arXivHTMLPDF

Abstract

In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy bath qubits represent the system and the bath of the open quantum system. All incoherent qubit noise can be mapped to bath spectral functions. The form of the spectral functions can be tuned digitally, allowing for the time evolution of a wide range of open-system models at finite temperature. We study the feasibility of this approach with a focus on the solution of the spin-boson model and assume intrinsic qubit noise that is dominated by damping and dephasing. We find that classes of open quantum systems exist where our algorithm performs very well, even with gate errors as high as 1%. In general the presented algorithm performs best if the system-bath interactions can be decomposed into native gates.

DOI
10.1103/physreva.108.062424

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In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy bath qubits represent the system and the bath of the open quantum system. All incoherent qubit noise can be mapped to bath spectral functions. The form of the spectral functions can be tuned digitally, allowing for the time evolution of a wide range of open-system models at finite temperature. We study the feasibility of this approach with a focus on the solution of the spin-boson model and assume intrinsic qubit noise that is dominated by damping and dephasing. We find that classes of open quantum systems exist where our algorithm performs very well, even with gate errors as high as 1%. In general the presented algorithm performs best if the system-bath interactions can be decomposed into native gates.
Abstract Quantum simulation represents the most promising quantum application to demonstrate quantum advantage on near-term noisy intermediate-scale quantum (NISQ) computers, yet available quantum simulation algorithms are prone to errors and thus difficult to realize with limited circuit depth on nowadays quantum devices. Herein, we propose a novel scheme to utilize intrinsic gate errors of NISQ devices to enable controllable simulation of open quantum system dynamics without ancillary qubits or explicit bath engineering, thus turning unwanted quantum noises into useful quantum resources. Specifically, we simulate the energy transfer process in a photosynthetic dimer system on IBM-Q cloud. By employing tailored decoherence-inducing gates, we show that quantum dissipative dynamics can be simulated efficiently across coherent-to-incoherent regimes with results comparable to those of the numerically exact classical method. Moreover, we demonstrate a calibration routine that enables consistent and predictive simulations of open-quantum system dynamics in the intermediate coupling regime. This work provides a new direction for quantum advantage in the NISQ era.
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.
Dephasing decoherence induced by interaction of one qubit with a quantum bath can be simulated classically by random unitary evolution without the need for a bath and this random unitary evolution is equivalent to the quantum case. For a general dephasing model and a single-qubit system, we explicitly construct the noise functional and completely specify the random unitary evolution. To demonstrate the technique, we applied our results to three paradigmatic models: spin-boson, central spin, and quantum impurity. For multiple qubits, we identify a class of generalized quantum dephasing models that can be simulated classically. Finally we show that depolarizing quantum models can be simulated classically for all dimensionalities of the principal system.
We introduce multipulse quantum noise spectroscopy protocols for spectral estimation of the noise affecting multiple qubits coupled to Gaussian dephasing environments including both classical and quantum sources. Our protocols are capable of reconstructing all the noise auto- and cross-correlation spectra entering the multiqubit dynamics, providing access, in particular, to the asymmetric spectra associated with nonclassical environments. Our result relies on (i) an exact analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control; (ii) the use of specific timing symmetries, which allow for a frequency comb to be engineered for all filter functions of interest, and for the spectra to be related to experimentally accessible observables. We show that quantum spectra have distinctive dynamical signatures, which we explore in two paradigmatic open-system models describing spin and charge qubits coupled to bosonic environments. Complete noise spectroscopy is demonstrated numerically in a realistic setting consisting of two-exciton qubits coupled to a phonon bath. The estimated spectra allow us to accurately predict the exciton dynamics as well as extract the temperature and spectral density of the quantum environment.
Accurate models of the dynamics of quantum circuits are essential for optimizing and advancing quantum devices. Since first-principles models of environmental noise and dissipation in real quantum systems are often unavailable, deriving accurate models from measured time-series data is critical. However, identifying open quantum systems poses significant challenges: powerful methods from systems engineering can perform poorly beyond weak damping (as we show) because they fail to incorporate essential constraints required for quantum evolution (e.g., positivity). Common methods that can include these constraints are typically multi-step, fitting linear models to physically grounded master equations, often resulting in non-convex functions in which local optimization algorithms get stuck in local extrema (as we show). In this work, we solve these problems by formulating quantum system identification directly from data as a polynomial optimization problem, enabling the use of recently developed global optimization methods. These methods are essentially guaranteed to reach global optima, allowing us for the first time to efficiently obtain the most accurate Markovian model for a given system. In addition to its practical importance, this allows us to take the error of these Markovian models as an alternative (operational) measure of the non-Markovianity of a system. We test our method with the spin-boson model -- a two-level system coupled to a bath of harmonic oscillators -- for which we obtain the exact evolution using matrix-product-state techniques. We show that polynomial optimization using moment/sum-of-squares approaches significantly outperforms traditional optimization algorithms, and we show that even for strong damping Lindblad-form master equations can provide accurate models of the spin-boson system.
Digital quantum simulation on quantum systems require algorithms that can be implemented using finite quantum resources. Recent studies have demonstrated digital quantum simulation of open quantum systems on Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we develop quantum circuits for optimal simulation of Markovian and Non-Markovian open quantum systems. The circuits use ancilla qubits to simulate the environment, and memory effects are induced by storing information about the system on extra qubits. We simulate the amplitude damping channel and dephasing channel as examples of the framework and infer (Non-)Markovianity from the (non-)monotonic behaviour of the dynamics. Further, we develop a method to optimize simulations by decomposing complex open quantum dynamics into smaller parts, that can be simulated using a small number of qubits. We show that this optimization reduces quantum space complexity from O(l)O(l)O(l) to O(1)O(1)O(1) for simulating the environment.