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Geometric analysis of minimum time trajectories for a two-level quantum system
Quantum Physics · Submitted 18 Oct 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The analysis is performed in any regime: controlled dynamics stronger, of the same magnitude or weaker than the drift term, and gives a method to synthesize quantum logic operations on a two-level system in minimum time.
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The abstract, sentence by sentence
We consider the problem of controlling in minimum time a two-level quantum system which can be subject to a drift. The control is assumed to be bounded in magnitude, and to affect two or three independent generators of the dynamics. We describe the time optimal trajectories in $SU(2)$, the Lie group of possible evolutions for the system, by means of a particularly simple parametrization of the group. A key ingredient of our analysis is the introduction of the optimal front line. This tool allows us to fully characterize the time-evolution of the reachable sets, and to derive the worst-case operators and the corresponding times. The analysis is performed in any regime: controlled dynamics stronger, of the same magnitude or weaker than the drift term, and gives a method to synthesize quantum logic operations on a two-level system in minimum time.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider the problem of controlling in minimum time a two-level quantum system which can be subject to a drift. | background 0.90 | 0.40 | 0.05 | asserted 0.72 |
| s1 | The control is assumed to be bounded in magnitude, and to affect two or three independent generators of the dynamics. | background 0.81 | 0.14 | 0.03 | asserted 0.96 |
| s2 | We describe the time optimal trajectories in $SU(2)$, the Lie group of possible evolutions for the system, by means of a particularly simple parametrization of the group. | method 0.75 | 0.93 | 0.13 | asserted 1.00 |
| s3 | A key ingredient of our analysis is the introduction of the optimal front line. | method 0.53 | 0.90 | 0.08 | asserted 1.00 |
| s4 | This tool allows us to fully characterize the time-evolution of the reachable sets, and to derive the worst-case operators and the corresponding times. | result 0.47 | 0.93 | 0.21 | asserted 0.99 |
| s5 | The analysis is performed in any regime: controlled dynamics stronger, of the same magnitude or weaker than the drift term, and gives a method to synthesize quantum logic operations on a two-level system in minimum time. | contribution 0.60 | 0.90 | 0.53 | asserted 1.00 |
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Original abstract
We consider the problem of controlling in minimum time a two-level quantum system which can be subject to a drift. The control is assumed to be bounded in magnitude, and to affect two or three independent generators of the dynamics. We describe the time optimal trajectories in $SU(2)$, the Lie group of possible evolutions for the system, by means of a particularly simple parametrization of the group. A key ingredient of our analysis is the introduction of the optimal front line. This tool allows us to fully characterize the time-evolution of the reachable sets, and to derive the worst-case operators and the corresponding times. The analysis is performed in any regime: controlled dynamics stronger, of the same magnitude or weaker than the drift term, and gives a method to synthesize quantum logic operations on a two-level system in minimum time.
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What it cites · 3 sentences without a confident label
Builds on 1 paper
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From a mathematical point of view, we introduce some new key tools which enable a simple and comprehensive treatment of the system, and the extension of the results in [ref] .
Minimum Time Optimal Synthesis for a Control System on SU(2) · Introduction · 1.00
Cites as background 1 paper
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For its fundamental role, the control of this system has been studied in several works, under many different assumptions (see for example [ref] and references therein).
Minimum Time Optimal Synthesis for a Control System on SU(2) · Introduction · 0.99
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