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Related Experiment Video

Updated: Jul 7, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Quantum simulators, continuous-time automata, and translationally invariant systems.

K G H Vollbrecht¹, J I Cirac

¹Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Str. 1, Garching, D-85748, Germany.

Physical Review Letters

|February 1, 2008

Summary

Finding the ground state energy of quantum systems is difficult, even for quantum computers. This study demonstrates this hardness for 1D translationally invariant systems and shows a quantum computer can be built within them.

Related Experiment Videos

Last Updated: Jul 7, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

Quantum computing
Condensed matter physics
Computational complexity

Background:

Finding the ground state energy of lattice Hamiltonians is a computationally challenging problem, even for quantum computers.
This difficulty extends to translationally invariant systems in one dimension (1D).

Purpose of the Study:

To demonstrate the computational hardness of finding ground state energies for 1D translationally invariant lattice Hamiltonians.
To show the feasibility of constructing a quantum computer within such a 1D system.

Main Methods:

Theoretical analysis of 1D lattice Hamiltonians.
Investigating the computational complexity of ground state energy determination.
Proposing a model for quantum computation using nearest-neighbor interactions in a 1D chain.

Main Results:

The problem of finding the ground state energy for 1D translationally invariant systems is confirmed to be computationally hard.
A quantum computer can be realized within a 1D chain with a fixed, translationally invariant Hamiltonian.
The computation yields results with high probability within a specified time.

Conclusions:

The computational hardness of ground state energy determination in 1D is established.
1D translationally invariant systems can serve as a platform for building quantum computers.
This research opens possibilities for quantum computation in constrained physical systems.