Probing Entanglement in Adiabatic Quantum Optimization with Trapped Ions
Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of col...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2015-04-01
|
| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fphy.2015.00021/full |
| _version_ | 1811196596455473152 |
|---|---|
| author | Philipp eHauke Philipp eHauke Lars eBonnes Markus eHeyl Markus eHeyl Wolfgang eLechner Wolfgang eLechner |
| author_facet | Philipp eHauke Philipp eHauke Lars eBonnes Markus eHeyl Markus eHeyl Wolfgang eLechner Wolfgang eLechner |
| author_sort | Philipp eHauke |
| collection | DOAJ |
| description | Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms. |
| first_indexed | 2024-04-12T01:01:29Z |
| format | Article |
| id | doaj.art-ad1056dae8f742c58986c117b408ad40 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-04-12T01:01:29Z |
| publishDate | 2015-04-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-ad1056dae8f742c58986c117b408ad402022-12-22T03:54:26ZengFrontiers Media S.A.Frontiers in Physics2296-424X2015-04-01310.3389/fphy.2015.00021130258Probing Entanglement in Adiabatic Quantum Optimization with Trapped IonsPhilipp eHauke0Philipp eHauke1Lars eBonnes2Markus eHeyl3Markus eHeyl4Wolfgang eLechner5Wolfgang eLechner6Institute for Quantum Optics and Quantum Information, InnsbruckUniversity of InnsbruckUniversity of InnsbruckInstitute for Quantum Optics and Quantum Information, InnsbruckUniversity of InnsbruckInstitute for Quantum Optics and Quantum Information, InnsbruckUniversity of InnsbruckAdiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.http://journal.frontiersin.org/Journal/10.3389/fphy.2015.00021/fullentanglementtrapped ionsadiabatic quantum optimizationNP complete problemsnoise engineering |
| spellingShingle | Philipp eHauke Philipp eHauke Lars eBonnes Markus eHeyl Markus eHeyl Wolfgang eLechner Wolfgang eLechner Probing Entanglement in Adiabatic Quantum Optimization with Trapped Ions Frontiers in Physics entanglement trapped ions adiabatic quantum optimization NP complete problems noise engineering |
| title | Probing Entanglement in Adiabatic Quantum Optimization with Trapped Ions |
| title_full | Probing Entanglement in Adiabatic Quantum Optimization with Trapped Ions |
| title_fullStr | Probing Entanglement in Adiabatic Quantum Optimization with Trapped Ions |
| title_full_unstemmed | Probing Entanglement in Adiabatic Quantum Optimization with Trapped Ions |
| title_short | Probing Entanglement in Adiabatic Quantum Optimization with Trapped Ions |
| title_sort | probing entanglement in adiabatic quantum optimization with trapped ions |
| topic | entanglement trapped ions adiabatic quantum optimization NP complete problems noise engineering |
| url | http://journal.frontiersin.org/Journal/10.3389/fphy.2015.00021/full |
| work_keys_str_mv | AT philippehauke probingentanglementinadiabaticquantumoptimizationwithtrappedions AT philippehauke probingentanglementinadiabaticquantumoptimizationwithtrappedions AT larsebonnes probingentanglementinadiabaticquantumoptimizationwithtrappedions AT markuseheyl probingentanglementinadiabaticquantumoptimizationwithtrappedions AT markuseheyl probingentanglementinadiabaticquantumoptimizationwithtrappedions AT wolfgangelechner probingentanglementinadiabaticquantumoptimizationwithtrappedions AT wolfgangelechner probingentanglementinadiabaticquantumoptimizationwithtrappedions |