Related Experiment Video
Updated: Jun 28, 2026
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Size dependence of the minimum excitation gap in the quantum adiabatic algorithm
A P Young1, S Knysh, V N Smelyanskiy
1Department of Physics, University of California, Santa Cruz, CA 95064, USA. peter@physics.ucsc.edu
Physical Review Letters
|November 13, 2008
Summary
The quantum adiabatic algorithm demonstrates polynomial complexity for the exact cover problem, outperforming classical algorithms for larger problem sizes. This quantum approach offers a significant advantage in computational efficiency.
Area of Science:
- Quantum computing
- Computational complexity theory
- Algorithm analysis
Background:
- The exact cover problem is a fundamental challenge in computer science.
- Classical algorithms like Davis-Putnam exhibit exponential complexity for this problem.
- Understanding quantum algorithm performance is crucial for future computational advancements.
Purpose of the Study:
- To investigate the computational complexity of the quantum adiabatic algorithm for the exact cover problem.
- To analyze the scaling behavior of the minimum gap for larger problem instances.
- To identify performance bottlenecks in the quantum adiabatic approach.
Main Methods:
- Utilizing quantum Monte Carlo simulations to study the minimum gap.
- Analyzing the median value of the minimum gap for varying problem sizes (N <= 128).
- Comparing the complexity of quantum and classical algorithms.
Main Results:
- The quantum adiabatic algorithm exhibits polynomial median complexity for the exact cover problem.
- Classical Davis-Putnam algorithm shows exponential median complexity for the same problem.
- An isolated avoided-crossing point of Landau-Zener type was identified as a key bottleneck.
Conclusions:
- The quantum adiabatic algorithm offers a more efficient solution for the exact cover problem compared to classical methods.
- The identified bottleneck suggests areas for potential algorithmic optimization.
- This study provides insights into the scalability and limitations of quantum algorithms for complex problems.
Related Concept Videos
01:10Entropy Change in Reversible Processes
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
01:26Reaction Mechanisms: The Steady-State Approximation
The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
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...
03:25Free Energy Changes for Nonstandard States
The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
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...