Simulating the dynamic evolution of physical and molecular systems in a quantum computer is of fundamental interest in many applications.The implementation of dynamics simulation requires efficient quantum algorithms....Simulating the dynamic evolution of physical and molecular systems in a quantum computer is of fundamental interest in many applications.The implementation of dynamics simulation requires efficient quantum algorithms.The Lie-Trotter-Suzuki approximation algorithm,also known as the Trotterization,is basic in Hamiltonian dynamics simulation.A multi-product algorithm that is a linear combination of multiple Trotterizations has been proposed to improve the approximation accuracy.However,implementing such multiproduct Trotterization in quantum computers remains challenging due to the requirements of highly controllable and precise quantum entangling operations with high success probability.Here,we report a programmable integrated-photonic quantum simulator based on a linear combination of unitaries,which can be tailored for implementing the linearly combined multiple Trotterizations,and on the simulator we benchmark quantum simulation of Hamiltonian dynamics.We modify the multi-product algorithm by integrating it with oblivious amplitude amplification to simultaneously reach high simulation precision and high success probability.The quantum simulator is devised and fabricated on a large-scale silicon-photonic quantum chip,which allows the initialization,manipulation,and measurement of arbitrary four-qubit states and linearly combined unitary gates.As an example,the quantum simulator is reprogrammed to emulate the dynamics of an electron spin and nuclear spin coupled system.This work promises the practical dynamics simulations of real-world physical and molecular systems in future large-scale quantum computers.展开更多
In the noisy intermediate-scale quantum era,emerging classical-quantum hybrid optimization algorithms,such as variational quantum algorithms(VQAs),can leverage the unique characteristics of quantum devices to accelera...In the noisy intermediate-scale quantum era,emerging classical-quantum hybrid optimization algorithms,such as variational quantum algorithms(VQAs),can leverage the unique characteristics of quantum devices to accelerate computations tailored to specific problems with shallow circuits.However,these algorithms encounter biases and iteration difficulties due to significant noise in quantum processors.These difficulties can only be partially addressed without error correction by optimizing hardware,reducing circuit complexity,or fitting and extrapolating.A compelling solution is applying probabilistic error cancellation(PEC),a quantum error mitigation technique that enables unbiased results without full error correction.Traditional PEC is challenging to apply in VQAs due to its variance amplification,contradicting iterative process assumptions.This paper proposes a novel noise-adaptable strategy that combines PEC with the quantum approximate optimization algorithm(QAOA).It is implemented through invariant sampling circuits(invariant-PEC,or IPEC)and substantially reduces iteration variance.This strategy marks the first successful integration of PEC and QAOA,resulting in efficient convergence.Moreover,we introduce adaptive partial PEC(APPEC),which modulates the error cancellation proportion of IPEC during iteration.We experimentally validate this technique on a superconducting quantum processor,cutting sampling cost by 90.1%.Notably,we find that dynamic adjustments of error levels via APPEC can enhance the ability to escape from local minima and reduce sampling costs.These results open promising avenues for executing VQAs with large-scale,low-noise quantum circuits,paving the way for practical quantum computing advancements.展开更多
基金Innovation Program for Quantum Science and Technology(2021ZD0301500)Key R&D Program of Guangdong Province(2018B030329001)+2 种基金Beijing Natural Science Foundation(Z190005,Z220008)National Natural Science Foundation of China(12325410,61975001,62235001)National Key Research and Development Program of China(2019YFA0308702)。
文摘Simulating the dynamic evolution of physical and molecular systems in a quantum computer is of fundamental interest in many applications.The implementation of dynamics simulation requires efficient quantum algorithms.The Lie-Trotter-Suzuki approximation algorithm,also known as the Trotterization,is basic in Hamiltonian dynamics simulation.A multi-product algorithm that is a linear combination of multiple Trotterizations has been proposed to improve the approximation accuracy.However,implementing such multiproduct Trotterization in quantum computers remains challenging due to the requirements of highly controllable and precise quantum entangling operations with high success probability.Here,we report a programmable integrated-photonic quantum simulator based on a linear combination of unitaries,which can be tailored for implementing the linearly combined multiple Trotterizations,and on the simulator we benchmark quantum simulation of Hamiltonian dynamics.We modify the multi-product algorithm by integrating it with oblivious amplitude amplification to simultaneously reach high simulation precision and high success probability.The quantum simulator is devised and fabricated on a large-scale silicon-photonic quantum chip,which allows the initialization,manipulation,and measurement of arbitrary four-qubit states and linearly combined unitary gates.As an example,the quantum simulator is reprogrammed to emulate the dynamics of an electron spin and nuclear spin coupled system.This work promises the practical dynamics simulations of real-world physical and molecular systems in future large-scale quantum computers.
基金supported by the Innovation Program for Quantum Science and Technology(Grant Nos.2021ZD0301702,and 2024ZD0302000)the Natural Science Foundation of Jiangsu Province(Grant No.BK20232002)+1 种基金the National Natural Science Foundation of China(Grant Nos.U21A20436,and 12074179)the Natural Science Foundation of Shandong Province(Grant No.ZR2023LZH002)。
文摘In the noisy intermediate-scale quantum era,emerging classical-quantum hybrid optimization algorithms,such as variational quantum algorithms(VQAs),can leverage the unique characteristics of quantum devices to accelerate computations tailored to specific problems with shallow circuits.However,these algorithms encounter biases and iteration difficulties due to significant noise in quantum processors.These difficulties can only be partially addressed without error correction by optimizing hardware,reducing circuit complexity,or fitting and extrapolating.A compelling solution is applying probabilistic error cancellation(PEC),a quantum error mitigation technique that enables unbiased results without full error correction.Traditional PEC is challenging to apply in VQAs due to its variance amplification,contradicting iterative process assumptions.This paper proposes a novel noise-adaptable strategy that combines PEC with the quantum approximate optimization algorithm(QAOA).It is implemented through invariant sampling circuits(invariant-PEC,or IPEC)and substantially reduces iteration variance.This strategy marks the first successful integration of PEC and QAOA,resulting in efficient convergence.Moreover,we introduce adaptive partial PEC(APPEC),which modulates the error cancellation proportion of IPEC during iteration.We experimentally validate this technique on a superconducting quantum processor,cutting sampling cost by 90.1%.Notably,we find that dynamic adjustments of error levels via APPEC can enhance the ability to escape from local minima and reduce sampling costs.These results open promising avenues for executing VQAs with large-scale,low-noise quantum circuits,paving the way for practical quantum computing advancements.
