dorsal/arxiv
View SchemaLocal control theory for unitary transformations: Application to quantum computing without leakage
| Authors | Shlomo E. Sklarz, David J. Tannor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0404081 |
| URL | https://arxiv.org/abs/quant-ph/0404081 |
Abstract
We present a local optimal control strategy to produce desired unitary transformations. Unitary transformations are central to all quantum computational algorithms. Many realizations of quantum computation use a submanifold of states, comprising the quantum register, coupled by an external driving field to a collection of additional mediating excited states. Previous attempts to apply control theory to induce unitary transformations on the quantum register, while successful, produced pulses that drive the population out of the computational register at intermediate times. Leakage of population from the register is undesirable since often the states outside the register are prone to decay and decoherence, and populating them causes a decrease in the final fidelity. In this work we devise a local optimal control method for achieving target unitary transformations on a quantum register, while avoiding intermediate leakage out of the computational submanifold. The technique exploits a phase locking of the field to the system such as to eliminate the undesirable excitation. This method is then applied to produce an SU(6) Fourier transform on the vibrational levels of the ground electronic state of the Na$_2$ molecule. The emerging mechanism uses two photon resonances to create a transformation on the quantum register while blocking one photon resonances to excited states.
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"abstract": "We present a local optimal control strategy to produce desired unitary\ntransformations. Unitary transformations are central to all quantum\ncomputational algorithms. Many realizations of quantum computation use a\nsubmanifold of states, comprising the quantum register, coupled by an external\ndriving field to a collection of additional mediating excited states. Previous\nattempts to apply control theory to induce unitary transformations on the\nquantum register, while successful, produced pulses that drive the population\nout of the computational register at intermediate times. Leakage of population\nfrom the register is undesirable since often the states outside the register\nare prone to decay and decoherence, and populating them causes a decrease in\nthe final fidelity. In this work we devise a local optimal control method for\nachieving target unitary transformations on a quantum register, while avoiding\nintermediate leakage out of the computational submanifold. The technique\nexploits a phase locking of the field to the system such as to eliminate the\nundesirable excitation. This method is then applied to produce an SU(6) Fourier\ntransform on the vibrational levels of the ground electronic state of the\nNa$_2$ molecule. The emerging mechanism uses two photon resonances to create a\ntransformation on the quantum register while blocking one photon resonances to\nexcited states.",
"arxiv_id": "quant-ph/0404081",
"authors": [
"Shlomo E. Sklarz",
"David J. Tannor"
],
"categories": [
"quant-ph"
],
"title": "Local control theory for unitary transformations: Application to quantum computing without leakage",
"url": "https://arxiv.org/abs/quant-ph/0404081"
},
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