Related Experiment Video
Updated: Jul 2, 2026
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Quantum simulation of many-body Hamiltonians using perturbation theory with bounded-strength interactions
Sergey Bravyi1, David P DiVincenzo, Daniel Loss
1IBM Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598 , USA.
Physical Review Letters
|September 4, 2008
Summary
This study presents a method to map complex quantum Hamiltonians with k-body interactions onto simpler two-body interaction systems. This technique ensures the ground-state energy remains accurate for quantum simulations.
Area of Science:
- Quantum physics
- Computational chemistry
- Many-body physics
Background:
- Simulating complex quantum systems is computationally demanding.
- Quantum Hamiltonians with k-body interactions are difficult to model directly.
- Effective low-energy Hamiltonians are crucial for simplifying quantum simulations.
Purpose of the Study:
- To develop a method for mapping n-qubit target Hamiltonians with k-body interactions to simulator Hamiltonians with only two-body interactions.
- To ensure the ground-state energy of the target and simulator Hamiltonians are equivalent within a controlled error.
- To provide a scalable approach for quantum simulations independent of the number of qubits (n).
Main Methods:
- Utilizing a novel derivation of effective low-energy Hamiltonians.
- Applying the Schrieffer-Wolff transformation from many-body physics.
- Mapping k-body interactions to two-body interactions with bounded strength.
Main Results:
- A successful mapping of n-qubit target Hamiltonians to simulator Hamiltonians with two-body interactions.
- Ground-state energy equivalence achieved with an error of O(epsilon n) for arbitrary small epsilon.
- Simulator Hamiltonian interaction strength is independent of n, depending only on epsilon and k.
Conclusions:
- The developed method offers an efficient way to simulate complex quantum systems.
- This approach reduces the complexity of quantum simulations by converting k-body interactions to two-body interactions.
- The findings have significant implications for quantum computing and condensed matter physics research.
Related Concept Videos
02:45The Quantum-Mechanical Model of an Atom
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
04:08The Uncertainty Principle
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
01:23Equilibrium Conditions for a Particle
When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
02:32The de Broglie Wavelength
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
01:21Linear Approximation in Time Domain
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...