Improving quantum algorithms run-time performance involves several strategies such as reducing the quantum gate counts, decreasing the number of measurements, advancement in QPU technology for faster gate operations, or optimizing the classical processing. This work focuses on the latter, specifically reducing classical processing and compilation time via hardware-assisted parameterized circuit execution (PCE) for computing dynamical properties of quantum systems. PCE was previously validated for QCVV protocols, which leverages structural circuit equivalencies. We demonstrate the applicability of this approach to computing dynamical properties of quantum many-body systems using structurally equivalent time evolution circuits, specifically calculating correlation functions of spin models using constant-depth circuits generated via Cartan decomposition. Implementing this for spin-spin correlation functions in Transverse field XY (up to 6-sites) and Heisenberg spin models (up to 3-sites), we observed a run-time reduction of up to $\mathbf{5 0 \%}$ compared to standard compilation methods. This highlights the adaptability of time-evolution circuit with hardware-assisted PCE to potentially mitigate the classical bottlenecks in near-term quantum algorithms.Improving quantum algorithms run-time performance involves several strategies such as reducing the quantum gate counts, decreasing the number of measurements, advancement in QPU technology for faster gate operations, or optimizing the classical processing. This work focuses on the latter, specifically reducing classical processing and compilation time via hardware-assisted parameterized circuit execution (PCE) for computing dynamical properties of quantum systems. PCE was previously validated for QCVV protocols, which leverages structural circuit equivalencies. We demonstrate the applicability of this approach to computing dynamical properties of quantum many-body systems using structurally equivalent time evolution circuits, specifically calculating correlation functions of spin models using constant-depth circuits generated via Cartan decomposition. Implementing this for spin-spin correlation functions in Transverse field XY (up to 6-sites) and Heisenberg spin models (up to 3-sites), we observed a run-time reduction of up to$\mathbf{5 0 \%}$compared to standard compilation methods. This highlights the adaptability of time-evolution circuit with hardware-assisted PCE to potentially mitigate the classical bottlenecks in near-term quantum algorithms.

IEEE International Conference on Quantum Computing and Engineering (QCE)Aug 30, 20250 citations

Some aspects of the dynamics of many-body systems

Irene D’Amico

Jan 1, 20000 citations

Variational Quantum Simulation of General Processes

Suguru Endo, Jinzhao Sun, Ying Li +2 more

Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks-generalized time evolution with a non-Hermitian Hamiltonian, linear algebra problems, and open quantum system dynamics. The algorithm for generalized time evolution provides a unified framework for variational quantum simulation. In particular, we show its application in solving linear systems of equations and matrix-vector multiplications by converting these algebraic problems into generalized time evolution. Meanwhile, assuming a tensor product structure of the matrices, we also propose another variational approach for these two tasks by combining variational real and imaginary time evolution. Finally, we introduce variational quantum simulation for open system dynamics. We variationally implement the stochastic Schrödinger equation, which consists of dissipative evolution and stochastic jump processes. We numerically test the algorithm with a 6-qubit 2D transverse field Ising model under dissipation.Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks-generalized time evolution with a non-Hermitian Hamiltonian, linear algebra problems, and open quantum system dynamics. The algorithm for generalized time evolution provides a unified framework for variational quantum simulation. In particular, we show its application in solving linear systems of equations and matrix-vector multiplications by converting these algebraic problems into generalized time evolution. Meanwhile, assuming a tensor product structure of the matrices, we also propose another variational approach for these two tasks by combining variational real and imaginary time evolution. Finally, we introduce variational quantum simulation for open system dynamics. We variationally implement the stochastic Schrödinger equation, which consists of dissipative evolution and stochastic jump processes. We numerically test the algorithm with a 6-qubit 2D transverse field Ising model under dissipation.

arXiv:1812.08778Physical Review LettersJun 29, 2020237 citations

On the time evolution of large systems: A soluble model with two-body interactions

Hans Jürgen Kreuzer, ANTON Z. CAPRI

Physica A Statistical Mechanics and its ApplicationsJan 1, 19755 citations

Exclusive-or encoded algebraic structure for efficient quantum dynamics

Lukas Broers, Ludwig Mathey

Abstract We propose a formalism that captures the algebraic structure of many-body two-level quantum systems, and directly motivates an efficient numerical method. This formalism is based on the binary representation of the enumeration-indices of the elements of the corresponding Lie algebra. The action of arbitrarily large elements of that algebra reduces to a few bit-wise exclusive-or operations. This formalism naturally produces sparse representations of many-body density operators, the size of which we control through a dynamic truncation method. We demonstrate how this formalism applies to real-time evolution, dissipative Lindblad action, imaginary-time evolution, and projective measurement processes. We find that this approach to calculating quantum dynamics scales close to linearly with the number of non-zero components in the density operator. We refer to this exclusive-or represented quantum algebra as ORQA. As a proof of concept, we provide a numerical demonstration of this formalism by simulating quantum annealing processes for the maximum independent set problem for up to 22 two-level systems.Abstract We propose a formalism that captures the algebraic structure of many-body two-level quantum systems, and directly motivates an efficient numerical method. This formalism is based on the binary representation of the enumeration-indices of the elements of the corresponding Lie algebra. The action of arbitrarily large elements of that algebra reduces to a few bit-wise exclusive-or operations. This formalism naturally produces sparse representations of many-body density operators, the size of which we control through a dynamic truncation method. We demonstrate how this formalism applies to real-time evolution, dissipative Lindblad action, imaginary-time evolution, and projective measurement processes. We find that this approach to calculating quantum dynamics scales close to linearly with the number of non-zero components in the density operator. We refer to this exclusive-or represented quantum algebra as ORQA. As a proof of concept, we provide a numerical demonstration of this formalism by simulating quantum annealing processes for the maximum independent set problem for up to 22 two-level systems.

arXiv:2404.09312New Journal of PhysicsApr 1, 20262 citations

\mathbf{5 0 \%}

compared to standard compilation methods. This highlights the adaptability of time-evolution circuit with hardware-assisted PCE to potentially mitigate the classical bottlenecks in near-term quantum algorithms.