Related Experiment Video
Updated: Jul 7, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Entropy scaling and simulability by matrix product states
Norbert Schuch1, Michael M Wolf, Frank Verstraete
1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, Germany.
Physical Review Letters
|February 1, 2008
Summary
We explore how block entropies relate to simulating quantum systems with matrix product states (MPSs). Notably, even states with area laws aren't always MPS-approximable, impacting quantum computing simulations.
Area of Science:
- Quantum Information Theory
- Computational Physics
Background:
- Matrix product states (MPSs) are a powerful tool for simulating quantum many-body systems.
- Block entropies quantify entanglement and are crucial for understanding system complexity.
Purpose of the Study:
- To investigate the relationship between block entropy scaling and MPS approximability.
- To clarify this connection for both von Neumann and Rényi entropies.
- To assess the implications for quantum computation's advantage over classical simulation.
Main Methods:
- Analysis of block entropy scaling in quantum many-body systems.
- Theoretical investigation of MPS approximation capabilities.
- Application of entropy scaling results to quantum simulation scenarios.
Main Results:
- Established a precise connection between block entropy scaling and MPS approximability for von Neumann and Rényi entropies.
- Demonstrated that states obeying a strict area law for von Neumann entropy are not necessarily MPS-approximable.
- Identified conditions under which quantum computers may outperform classical computers in simulating quantum systems.
Conclusions:
- The efficiency of MPS simulations is intricately linked to block entropy scaling.
- Area laws alone do not guarantee MPS approximability, challenging some assumptions in condensed matter physics.
- Quantum computers hold potential for simulating complex quantum dynamics, even for translationally invariant systems.
Related Concept Videos
01:21State Space to Transfer Function
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
01:23Transfer Function to State Space
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
In an RLC...
01:27State Space Representation
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Consider an RLC circuit, a...
01:25Multimachine Stability
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
01:22Multi-input and Multi-variable systems
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
In the absence of...
01:26Scaling
In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...