dorsal/arxiv
View SchemaGate simulation and lower bounds on the simulation time
| Authors | Robert Zeier, Markus Grassl, Thomas Beth |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403082 |
| URL | https://arxiv.org/abs/quant-ph/0403082 |
| DOI | 10.1103/PhysRevA.70.032319 |
| Journal | Physical Review A 70, 032319 (2004) |
Abstract
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common versions of this task are known as Hamiltonian simulation and gate simulation, where Hamiltonian simulation can be seen as an infinitesimal version of the general task of gate simulation. We present a Lie-theoretic approach to Hamiltonian simulation and gate simulation. From this, we derive lower bounds on the time complexity in the n-qubit case, generalizing known results to both even and odd n. To achieve this we develop a generalization of the so-called magic basis for two-qubits. As a corollary, we note a connection to entanglement measures of concurrence-type.
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"abstract": "Unitary operations are the building blocks of quantum programs. Our task is\nto design effcient or optimal implementations of these unitary operations by\nemploying the intrinsic physical resources of a given n-qubit system. The most\ncommon versions of this task are known as Hamiltonian simulation and gate\nsimulation, where Hamiltonian simulation can be seen as an infinitesimal\nversion of the general task of gate simulation. We present a Lie-theoretic\napproach to Hamiltonian simulation and gate simulation. From this, we derive\nlower bounds on the time complexity in the n-qubit case, generalizing known\nresults to both even and odd n. To achieve this we develop a generalization of\nthe so-called magic basis for two-qubits. As a corollary, we note a connection\nto entanglement measures of concurrence-type.",
"arxiv_id": "quant-ph/0403082",
"authors": [
"Robert Zeier",
"Markus Grassl",
"Thomas Beth"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.70.032319",
"journal_ref": "Physical Review A 70, 032319 (2004)",
"title": "Gate simulation and lower bounds on the simulation time",
"url": "https://arxiv.org/abs/quant-ph/0403082"
},
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