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Surface code implementation of block code state distillation.

Fowler AG, Devitt SJ, Jones C - Sci Rep (2013)

Bottom Line: Until recently, the lowest overhead method of distilling states produced a single improved [formula: see text] state given 15 input copies.New block code state distillation methods can produce k improved [formula: see text] states given 3k + 8 input copies, potentially significantly reducing the overhead associated with state distillation.We find that, using the best available techniques, for parameters of practical interest, block code state distillation does not always lead to lower overhead, and, when it does, the overhead reduction is typically less than a factor of three.

View Article: PubMed Central - PubMed

Affiliation: Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Victoria 3010, Australia. austingfowler@gmail.com

ABSTRACT
State distillation is the process of taking a number of imperfect copies of a particular quantum state and producing fewer better copies. Until recently, the lowest overhead method of distilling states produced a single improved [formula: see text] state given 15 input copies. New block code state distillation methods can produce k improved [formula: see text] states given 3k + 8 input copies, potentially significantly reducing the overhead associated with state distillation. We construct an explicit surface code implementation of block code state distillation and quantitatively compare the overhead of this approach to the old. We find that, using the best available techniques, for parameters of practical interest, block code state distillation does not always lead to lower overhead, and, when it does, the overhead reduction is typically less than a factor of three.

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Extendable quantum circuit for block code state distillation.This circuit takes 3k + 8 copies of /A〉, each with probability p of error, and producing k copies, each with approximate probability (3k + 1)p2 of error. In the figure, k = 4. The repeating unit cell is highlighted. Note that k must be even. A box encircles output numbers. Each T gate consumes one /A〉 state as shown in Figure 2.
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f1: Extendable quantum circuit for block code state distillation.This circuit takes 3k + 8 copies of /A〉, each with probability p of error, and producing k copies, each with approximate probability (3k + 1)p2 of error. In the figure, k = 4. The repeating unit cell is highlighted. Note that k must be even. A box encircles output numbers. Each T gate consumes one /A〉 state as shown in Figure 2.

Mentions: Figure 1 illustrates a quantum circuit to implement the block code state distillation protocol of Jones23. This protocol uses a delayed application of T gates to eliminate X errors as illustrated in Figure 2. Details of the state distillation protocol can be found in the methods section.


Surface code implementation of block code state distillation.

Fowler AG, Devitt SJ, Jones C - Sci Rep (2013)

Extendable quantum circuit for block code state distillation.This circuit takes 3k + 8 copies of /A〉, each with probability p of error, and producing k copies, each with approximate probability (3k + 1)p2 of error. In the figure, k = 4. The repeating unit cell is highlighted. Note that k must be even. A box encircles output numbers. Each T gate consumes one /A〉 state as shown in Figure 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3672884&req=5

f1: Extendable quantum circuit for block code state distillation.This circuit takes 3k + 8 copies of /A〉, each with probability p of error, and producing k copies, each with approximate probability (3k + 1)p2 of error. In the figure, k = 4. The repeating unit cell is highlighted. Note that k must be even. A box encircles output numbers. Each T gate consumes one /A〉 state as shown in Figure 2.
Mentions: Figure 1 illustrates a quantum circuit to implement the block code state distillation protocol of Jones23. This protocol uses a delayed application of T gates to eliminate X errors as illustrated in Figure 2. Details of the state distillation protocol can be found in the methods section.

Bottom Line: Until recently, the lowest overhead method of distilling states produced a single improved [formula: see text] state given 15 input copies.New block code state distillation methods can produce k improved [formula: see text] states given 3k + 8 input copies, potentially significantly reducing the overhead associated with state distillation.We find that, using the best available techniques, for parameters of practical interest, block code state distillation does not always lead to lower overhead, and, when it does, the overhead reduction is typically less than a factor of three.

View Article: PubMed Central - PubMed

Affiliation: Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Victoria 3010, Australia. austingfowler@gmail.com

ABSTRACT
State distillation is the process of taking a number of imperfect copies of a particular quantum state and producing fewer better copies. Until recently, the lowest overhead method of distilling states produced a single improved [formula: see text] state given 15 input copies. New block code state distillation methods can produce k improved [formula: see text] states given 3k + 8 input copies, potentially significantly reducing the overhead associated with state distillation. We construct an explicit surface code implementation of block code state distillation and quantitatively compare the overhead of this approach to the old. We find that, using the best available techniques, for parameters of practical interest, block code state distillation does not always lead to lower overhead, and, when it does, the overhead reduction is typically less than a factor of three.

Show MeSH