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arXiv:2302.14592 · PRX Quantum

Noise-Assisted Digital Quantum Simulation of Open Systems Using Partial Probabilistic Error Cancellation

José D. Guimarães, James Lim, Mikhail I. Vasilevskiy, Susana F. Huelga, Martin Bodo Plenio

Published Nov 21, 2023• 53 citations
arXivHTMLPDF

Abstract

Quantum systems are inherently open and susceptible to environmental noise, which can have both detrimental and beneficial effects on their dynamics.This phenomenon has been observed in biomolecular systems, where noise enables novel functionalities, making the simulation of their dynamics a crucial target for digital and analog quantum simulation.Nevertheless, the computational capabilities of current quantum devices are often limited due to their inherent noise.In this work, we present a novel approach that capitalizes on the intrinsic noise of quantum devices to reduce the computational resources required for simulating open quantum systems.Our approach combines quantum noise characterization methods with quantum error mitigation techniques, enabling us to manipulate and control the intrinsic noise in a quantum circuit.Specifically, we selectively enhance or reduce decoherence rates in the quantum circuit to achieve the desired simulation of open-system dynamics.We provide a detailed description of our methods and report on the results of noise characterization and quantum error mitigation experiments conducted on both real and emulated IBM Quantum computers.Additionally, we estimate the experimental resource requirements for our techniques.Our approach holds the potential to unlock new simulation techniques in noisy intermediate-scale quantum devices, harnessing their intrinsic noise to enhance quantum computations.

DOI
10.1103/prxquantum.4.040329

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Quantum systems are inherently open and susceptible to environmental noise, which can have both detrimental and beneficial effects on their dynamics.This phenomenon has been observed in biomolecular systems, where noise enables novel functionalities, making the simulation of their dynamics a crucial target for digital and analog quantum simulation.Nevertheless, the computational capabilities of current quantum devices are often limited due to their inherent noise.In this work, we present a novel approach that capitalizes on the intrinsic noise of quantum devices to reduce the computational resources required for simulating open quantum systems.Our approach combines quantum noise characterization methods with quantum error mitigation techniques, enabling us to manipulate and control the intrinsic noise in a quantum circuit.Specifically, we selectively enhance or reduce decoherence rates in the quantum circuit to achieve the desired simulation of open-system dynamics.We provide a detailed description of our methods and report on the results of noise characterization and quantum error mitigation experiments conducted on both real and emulated IBM Quantum computers.Additionally, we estimate the experimental resource requirements for our techniques.Our approach holds the potential to unlock new simulation techniques in noisy intermediate-scale quantum devices, harnessing their intrinsic noise to enhance quantum computations.
Noise in quantum devices is generally considered detrimental to computational accuracy. However, the recent proposal of noise-assisted simulation has demonstrated that noise can be an asset in digital quantum simulations of open systems on noisy intermediate-scale quantum (NISQ) devices. In this context, we introduce an optimized decoherence rate control scheme that can significantly reduce computational requirements by multiple orders of magnitude, in comparison to the original noise-assisted simulation. We further extend this approach to encompass Lindblad equations with time-dependent coefficients, using only quantum error characterization and mitigation techniques. This extension allows for the perturbative simulation of non-Markovian dynamics on NISQ devices, eliminating the need for ancilla qubits or midcircuit measurements. Our contributions are validated through numerical experiments on an emulated IBM Quantum device. Overall, our paper offers valuable optimizations that bring current quantum processors closer to effectively simulating realistic open systems.
Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate, the assumptions are inappropriate for describing realistic noise that may have strong gate dependence and complicated nonlocal effects, and general computing models such as analog quantum simulators. To address these challenges, we first extend the scenario, where each computation process, being either digital or analog, is described by a continuous time evolution. For noise from imperfections of the engineered Hamiltonian or additional noise operators, we show it can be effectively suppressed by a stochastic QEM method. Since our method assumes only accurate single qubit controls, it is applicable to all digital quantum computers and various analog simulators. Meanwhile, errors in the mitigation procedure can be suppressed by leveraging the Richardson extrapolation method. As we numerically test our method with various Hamiltonians under energy relaxation and dephasing noise and digital quantum circuits with additional two-qubit crosstalk, we show an improvement of simulation accuracy by 2 orders. We assess the resource cost of our scheme and conclude the feasibility of accurate quantum computing with NISQ devices.
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.
Quantum simulation of dynamics is an important goal in the noisy intermediate-scale quantum era, within which quantum error mitigation may be a viable path towards modifying or eliminating the effects of noise. Most studies on quantum error mitigation have focused on the resource cost due to its exponential scaling in the circuit depth. Methods such as probabilistic error cancellation rely on discretizing the evolution into finite time steps and applying the mitigation layer after each time step, modifying only the noise part without any Hamiltonian dependence. This may lead to Trotter-like errors in the simulation results even if the error mitigation is implemented ideally, which means that the number of samples is taken as infinite. Here we analyze the aforementioned errors which have been largely neglected before. We show that they are determined by the commutating relations between the superoperators of the unitary part, the device noise part, and the noise part of the open dynamics to be simulated. We include both digital quantum simulation and analog quantum simulation setups and consider defining the ideal error mitigation map both by exactly inverting the noise channel and by approximating it to first order in the time step. We use single-qubit toy models to numerically demonstrate our findings. Our results illustrate fundamental limitations of applying probabilistic error cancellation in a stepwise manner to continuous dynamics, thus motivating the investigations of truly time-continuous error cancellation methods. Published by the American Physical Society 2024
Analog quantum simulation has been proposed as an efficient approach for probing classically intractable many-body physics. In contrast to digital, gate-based quantum simulation, the analog approach involves configuring the quantum hardware to directly mimic the physics of the target system. This reduces the level of control required and can offer a degree of inherent robustness, but it comes at the cost that known error-handling techniques may be inapplicable. Accumulation of error is thus a major challenge facing medium-scale and large-scale analog quantum simulation with current and near-term noisy quantum (NISQ) devices. Here we propose a hybrid error mitigation scheme that can suppress general local Markovian noise in analog quantum simulators. We employ stochastic error mitigation for physical noise and use Richardson extrapolation to compensate for model estimation error. We numerically test the error mitigation scheme for an Ising-type Hamiltonian with energy relaxation and dephasing noise, and show an improvement of simulation accuracy by two orders. We assess the resource cost of our error mitigation scheme and conclude that analog quantum simulation at scale is feasible with NISQ hardware.
As quantum devices continue to improve in scale and precision, a central challenge is how to effectively utilize noisy hardware for meaningful computation. Most existing approaches aim to recover noiseless circuit outputs from noisy ones through error mitigation or correction. Here, we show that noisy quantum devices can be directly leveraged as computational resources to enhance the classical simulation of quantum circuits. We introduce the Noisy-device-enhanced Classical Simulation (NDE-CS) protocol, which improves stabilizer-based classical Monte Carlo simulation methods by incorporating data obtained from noisy quantum hardware. Specifically, NDE-CS uses noisy executions of a target circuit together with noisy Clifford circuits to learn how the target circuit can be expressed in terms of Clifford circuits under realistic noise. The same learned relation can then be reused in the noiseless Clifford limit, enabling accurate estimation of ideal expectation values with substantially reduced sampling cost. Numerical simulations on Trotterized Ising circuits demonstrate that NDE-CS achieves orders-of-magnitude reductions in sampling cost compared to the underlying purely classical Monte Carlo approaches from which it is derived, while maintaining the same accuracy. We also compare NDE-CS with Sparse Pauli Dynamics (SPD), a powerful classical framework capable of simulating quantum circuits at previously inaccessible scales, and provide an example where the cost of SPD scales exponentially with system size, while NDE-CS scales much more favorably. These results establish NDE-CS as a scalable hybrid simulation approach for quantum circuits, where noise can be harnessed as a computational asset.