Universal resource-efficient topological measurement-based quantum
computation via color-code-based cluster states
- URL: http://arxiv.org/abs/2106.07530v3
- Date: Tue, 17 Aug 2021 03:31:46 GMT
- Title: Universal resource-efficient topological measurement-based quantum
computation via color-code-based cluster states
- Authors: Seok-Hyung Lee and Hyunseok Jeong
- Abstract summary: Topological measurement-based quantum computation (MBQC) enables one to carry out universal fault-tolerant quantum computation via single-qubit Pauli measurements.
We show that all the logical Clifford gates including the CNOT, Hadamard, and phase gates can be implemented fault-tolerantly without state distillation.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Topological measurement-based quantum computation (MBQC) enables one to carry
out universal fault-tolerant quantum computation via single-qubit Pauli
measurements with a family of large entangled states called cluster states as
resources. Raussendorf's three-dimensional cluster states (RTCSs) based on the
surface codes are mainly considered for topological MBQC. In such schemes,
however, the fault-tolerant implementation of the logical Hadamard, phase
($Z^{1/2}$), and $T$ ($Z^{1/4}$) gates which are essential for building up
arbitrary logical gates has not been achieved to date without using state
distillation, while the controlled-NOT (CNOT) gate does not require it, to best
of our knowledge. State distillation generally consumes many ancillary logical
qubits, thus it is a severe obstacle against practical quantum computing. To
solve this problem, we suggest an MBQC scheme via a family of cluster states
called color-code-based cluster states (CCCSs) based on the two-dimensional
color codes instead of the surface codes. We define logical qubits, construct
elementary logical gates, and describe error correction schemes. We show that
all the logical Clifford gates including the CNOT, Hadamard, and phase gates
can be implemented fault-tolerantly without state distillation, although the
fault-tolerant $T$ gate still requires it. We further prove that the minimal
number of physical qubits per logical qubit in a CCCS is at most approximately
1.8 times smaller than the case of an RTCS. We lastly show that the error
threshold of MBQC via CCCSs for logical-$Z$ errors is 2.7-2.8%, which is
comparable to the value for RTCSs, assuming a simple error model where physical
qubits have $X$-measurement or $Z$ errors independently with the same
probability.
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