Quantum trajectory methods for simulating solid-state qubit systems

We present a theoretical framework for the evolution of the internal state of a fast highly charged one-electron ion traversing an amorphous solid. We employ an open quantum system approach which incorporates the complex array of collisions with electrons and ionic cores in the solid within the framework of system-reservoir interactions. Interactions with the solid environment and the radiation field are treated on the same footing and the quantum master equation for the reduced density matrix of the electronic state of the ion is approximated by a Lindblad equation. The latter allows the solution of this multistate problem in terms of Monte Carlo sampling of quantum trajectories. Similarities and extensions to methods used in quantum optics and previously employed in ion-solid interactions are discussed. Our focus is on the transient buildup and destruction of coherences by stochastic processes. We apply our method to the study of coherence properties of the internal state of a fast ${\mathrm{Kr}}^{35+}$ ion traversing carbon foils. Simulations exhibit clear signatures of partially coherent transitions and are found to be in good agreement with experimental data.We present a theoretical framework for the evolution of the internal state of a fast highly charged one-electron ion traversing an amorphous solid. We employ an open quantum system approach which incorporates the complex array of collisions with electrons and ionic cores in the solid within the framework of system-reservoir interactions. Interactions with the solid environment and the radiation field are treated on the same footing and the quantum master equation for the reduced density matrix of the electronic state of the ion is approximated by a Lindblad equation. The latter allows the solution of this multistate problem in terms of Monte Carlo sampling of quantum trajectories. Similarities and extensions to methods used in quantum optics and previously employed in ion-solid interactions are discussed. Our focus is on the transient buildup and destruction of coherences by stochastic processes. We apply our method to the study of coherence properties of the internal state of a fast ${\mathrm{Kr}}^{35+}$ ion traversing carbon foils. Simulations exhibit clear signatures of partially coherent transitions and are found to be in good agreement with experimental data.

Physical Review AFeb 28, 200325 citations

Qubit-based Model for Simulation of Discrete Quantum Systems

Steven Peil

Bulletin of the American Physical SocietyMay 21, 20090 citations

Augmenting Simulated Noisy Quantum Data Collection by Orders of Magnitude Using Pre-Trajectory Sampling with Batched Execution

Taylor L. Patti, Thien Nguyen, Justin G. Lietz +2 more

Classically simulating quantum systems is challenging, as even noiseless n-qubit quantum states scale as 2n. The complexity of noisy quantum systems is even greater, requiring 2n × 2n-dimensional density matrices. Various approximations reduce density matrix overhead, including quantum trajectory-based methods, which instead use an ensemble of m ≪ 2n noisy states. While this method is dramatically more efficient, current implementations use unoptimized sampling, redundant state preparation, and single-shot data collection. In this manuscript, we present the Pre-Trajectory Sampling technique, increasing the efficiency and utility of trajectory simulations by tailoring error types, batching sampling without redundant computation, and collecting error information. We demonstrate the effectiveness of our method with both a mature statevector simulation of a 35-qubit quantum error-correction code and a preliminary tensor network simulation of 85 qubits, yielding speedups of up to 106x and 16x, as well as generating massive datasets of one trillion and one million shots, respectively.Classically simulating quantum systems is challenging, as even noiseless n-qubit quantum states scale as 2n. The complexity of noisy quantum systems is even greater, requiring 2n × 2n-dimensional density matrices. Various approximations reduce density matrix overhead, including quantum trajectory-based methods, which instead use an ensemble of m ≪ 2n noisy states. While this method is dramatically more efficient, current implementations use unoptimized sampling, redundant state preparation, and single-shot data collection. In this manuscript, we present the Pre-Trajectory Sampling technique, increasing the efficiency and utility of trajectory simulations by tailoring error types, batching sampling without redundant computation, and collecting error information. We demonstrate the effectiveness of our method with both a mature statevector simulation of a 35-qubit quantum error-correction code and a preliminary tensor network simulation of 85 qubits, yielding speedups of up to 106x and 16x, as well as generating massive datasets of one trillion and one million shots, respectively.

arXiv:2504.16297International Conference for High Performance Computing, Networking, Storage and Analysis (SC)Nov 12, 20251 citation

Coupling hybrid quantum systems: from atomic to solid-state qubits

Jacob M. Taylor

Bulletin of the American Physical SocietyMay 28, 20100 citations

On the scheme of cavity photon elimination in multi-qubit circuit-quantum electrodynamics system

Meng Jian-Yu, Wang Pei-Yue, Feng Wei +2 more

Solid-state superconducting circuit-quantum electrodynamics (QED) system is a promising candidate for quantum information processing and an ideal platform for quantum measurement and quantum control studies. As an extension to our previous simulation for single qubit circuit-QED, in this work we simulate the quantum measurement and control of multi-qubit system. Particularly, we consider the deterministic generation of a two-qubit Bell state. In this context we examine the validity conditions of two cavity-photon-elimination scheme. On the level of quantum trajectory simulation, we find that, owing to the qubit flip caused by feedback, the advanced polaron-transformation scheme is no longer applicable if the measurement is not weak, which also makes meaningless the elegant effective measurement operator.Solid-state superconducting circuit-quantum electrodynamics (QED) system is a promising candidate for quantum information processing and an ideal platform for quantum measurement and quantum control studies. As an extension to our previous simulation for single qubit circuit-QED, in this work we simulate the quantum measurement and control of multi-qubit system. Particularly, we consider the deterministic generation of a two-qubit Bell state. In this context we examine the validity conditions of two cavity-photon-elimination scheme. On the level of quantum trajectory simulation, we find that, owing to the qubit flip caused by feedback, the advanced polaron-transformation scheme is no longer applicable if the measurement is not weak, which also makes meaningless the elegant effective measurement operator.

Acta Physica SinicaJan 1, 20120 citations

{\mathrm{Kr}}^{35+}

ion traversing carbon foils. Simulations exhibit clear signatures of partially coherent transitions and are found to be in good agreement with experimental data.