Related Experiment Video
Updated: May 31, 2026
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Dimension reduction by balanced truncation: application to light-induced control of open quantum systems
Boris Schäfer-Bung1, Carsten Hartmann, Burkhard Schmidt
1Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany. boris.schaefer-bung@fu-berlin.de
The Journal of Chemical Physics
|July 13, 2011
Summary
Balanced truncation effectively reduces the complexity of open quantum systems. This control method, applied to quantum dynamics, achieves significant dimension reduction based on system parameters.
Area of Science:
- Quantum Control
- Quantum Dynamics
- Control Theory
Background:
- Balanced truncation is a standard technique for reducing the state-space dimension in linear control systems.
- Open quantum systems are often modeled using the Liouville-von Neumann equation within the Lindblad formalism.
- Controlling quantum systems requires addressing bilinear terms arising from control field coupling.
Purpose of the Study:
- To apply balanced truncation for the first time to control open quantum systems.
- To generalize linear balanced truncation theory for bilinear quantum control.
- To investigate the accuracy and efficiency of dimension reduction in a specific quantum system.
Main Methods:
- Generalizing linear balanced truncation for bilinear terms in quantum systems.
- Modeling dissipative quantum dynamics using the Liouville-von Neumann equation and Lindblad formalism.
- Applying the method to a particle in an asymmetric double well potential driven by an external field.
Main Results:
- Demonstrated efficient dimension reduction for open quantum system control.
- Investigated the accuracy of the truncated model by comparing population dynamics.
- Showed that the degree of dimension reduction is dependent on temperature and relaxation rate.
Conclusions:
- Balanced truncation is a viable and effective technique for simplifying the control of open quantum systems.
- The generalized method accurately represents the system's dynamics after dimension reduction.
- System parameters like temperature and relaxation rate influence the efficiency of the reduction.
Related Concept Videos
01:22Block Diagram Reduction
The process of deriving the transfer function of a control system often involves reducing its block diagram to a single block. This simplification can be achieved through a series of strategic operations, including relocating branch points and comparators. These operations preserve the overall function of the system while allowing for easier manipulation and combination of blocks.
The first step in this process is the identification and relocation of a branch point. A branch point, where a...
The first step in this process is the identification and relocation of a branch point. A branch point, where a...
01:25Deactivation Processes: Jablonski Diagram
Luminescence, the emission of light by a substance that has absorbed energy, is a process that involves the interaction of molecules with light. The energy-level diagram, or Jablonski diagram, is a graphical representation of these interactions, illustrating the various states and transitions a molecule can undergo. In a typical Jablonski diagram, the lowest horizontal line represents the ground-state energy of the molecule, which is usually a singlet state. This state represents the energies...
01:16Conservation of Mass in Finite Cotrol Volume
The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
01:20Downsampling
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
01:34Woodward–Hoffmann Selection Rules and Microscopic Reversibility
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
01:14Conservation of Energy in Control Volume
Consider a turbine operating under steady-flow conditions. The control volume is drawn around the turbine, with fluid entering at one point and exiting at another. The turbine extracts energy from the fluid, which performs mechanical work (shaft work).
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to:
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to: