2006 Fiscal Year Final Research Report Summary
Black Hole and Quantum Information
| Project/Area Number |
15540258
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
HOSOYA Akio Tokyo Institute of Technology, Department of Physics, Professor (80028258)
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| Co-Investigator(Kenkyū-buntansha) |
KOIKE Tatsuhiko Keio University, Department of Physics, Assistant professor (40286646)
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| Project Period (FY) |
2003 – 2006
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| Keywords | quantum comnutation / variational princinle / unitary transformation / mixed state / quantum brachistochrone equation / measurement |
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| Research Abstract |
We have given a general frame work to find an optimal quantum evolution for given initial final states in quantum mechanics in analogy to brachistochrone in classical mechanics. The formulation is based on variational principle, in which the Hamiltonian is regarded as a dynamical variable as well as the quantum state. The available Hamiltonian is constrained by natural law or experimental set-up etc and taken care of as the constraints. A few simple examples are demonstrated.
This method is extended to the case of arbitrary initial state so as to be relevant to quantum computation. We demonstrated it in typical two qubit gates. To scale-up to many qubits, we have developed a powerful numerical methods. The method is extended to mixed state cases by using measurement. In some cases, the quantum trajectory which passes mixed state is more efficient.
We hope our method is useful for quantum computation algorithm, quantum control and Making efficient quantum devices.
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