dorsal/arxiv
View SchemaQuantum universality by state distillation
| Authors | Ben W. Reichardt |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608085 |
| URL | https://arxiv.org/abs/quant-ph/0608085 |
| Journal | Quantum Inf. Comput. 9:1030-1052, 2009 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? This "magic states distillation" question is closely related to quantum fault tolerance. Lower bounds on the noise tolerable on the ancilla help give lower bounds on the tolerable noise rate threshold for fault-tolerant computation. Upper bounds show the limits of threshold upper-bound arguments based on the Gottesman-Knill theorem. We extend the range of single-qubit mixed states that are known to give universality, by using a simple parity-checking operation. For applications to proving threshold lower bounds, certain practical stability characteristics are often required, and we also show a stable distillation procedure. No distillation upper bounds are known beyond those given by the Gottesman-Knill theorem. One might ask whether distillation upper bounds reduce to upper bounds for single-qubit ancilla states. For multi-qubit pure states and previously considered two-qubit ancilla states, the answer is yes. However, we exhibit two-qubit mixed states that are not mixtures of stabilizer states, but for which every postselected stabilizer reduction from two qubits to one outputs a mixture of stabilizer states. Distilling such states would require true multi-qubit state distillation methods.
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"abstract": "Quantum universality can be achieved using classically controlled stabilizer\noperations and repeated preparation of certain ancilla states. Which ancilla\nstates suffice for universality? This \"magic states distillation\" question is\nclosely related to quantum fault tolerance. Lower bounds on the noise tolerable\non the ancilla help give lower bounds on the tolerable noise rate threshold for\nfault-tolerant computation. Upper bounds show the limits of threshold\nupper-bound arguments based on the Gottesman-Knill theorem.\n We extend the range of single-qubit mixed states that are known to give\nuniversality, by using a simple parity-checking operation. For applications to\nproving threshold lower bounds, certain practical stability characteristics are\noften required, and we also show a stable distillation procedure.\n No distillation upper bounds are known beyond those given by the\nGottesman-Knill theorem. One might ask whether distillation upper bounds reduce\nto upper bounds for single-qubit ancilla states. For multi-qubit pure states\nand previously considered two-qubit ancilla states, the answer is yes. However,\nwe exhibit two-qubit mixed states that are not mixtures of stabilizer states,\nbut for which every postselected stabilizer reduction from two qubits to one\noutputs a mixture of stabilizer states. Distilling such states would require\ntrue multi-qubit state distillation methods.",
"arxiv_id": "quant-ph/0608085",
"authors": [
"Ben W. Reichardt"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Inf. Comput. 9:1030-1052, 2009",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Quantum universality by state distillation",
"url": "https://arxiv.org/abs/quant-ph/0608085"
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