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The promise of quantum computing with imperfect qubits relies on the ability of a quantum computing system to scale cheaply through error correction and fault-tolerance.
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In this work we use the standard definitions of average gate infidelity as 1 − ℱ ( 𝒰 , 𝒰 ~ ) 1-\mathcal{F}({\mathcal{U}},\tilde{{\mathcal{U}}}) , with average gate fidelity ℱ \mathcal{F} defined as Nielsen 2002 ℱ ( 𝒰 , 𝒰 ~ ) = tr 𝒰 ~ 𝒰 † + d d 2 + d \displaystyle\mathcal{F}({\mathcal{U}},\tilde{{\mathcal{U}}})=\frac{\tr~\tilde{{\mathcal{U}}}{\mathcal{U}}^{\dagger}+d}{d^{2}+d}
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The diamond distance between two processes Kitaev et al. 2002 ; Watrous 2009 is defined as 𝒟 ⋄ = 1 2 ‖ 𝒰 ~ − 𝒰 ‖ ⋄ = sup ρ 1 2 ‖ ( 𝒰 ~ ⊗ ℐ d − 𝒰 ⊗ ℐ d ) ( ρ ) ‖ 1 , \displaystyle\mathcal{D}_{\diamond}=\frac{1}{2}||\tilde{{\mathcal{U}}}-{\mathcal{U}}||_{\diamond}=\mathop{{\rm sup}}_{\rho}\frac{1}{2}||(\tilde{{\mathcal{U}}}\otimes{\mathcal{I}}_{d}-{\mathcal{U}}\otimes{\mathcal{I}}_{d})(\rho)||_{1}, with d d being the total system dimension
2009
Cited alongside, same era.
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2016
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2016
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Joel J. Wallman and Joseph Emerson, “Noise tailoring for scalable quantum computation via randomized compiling,” Physical Review A 94
2016
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The number of randomizations could be much lower Wallman and Emerson 2016 , or, equivalently, more measurement shots could be collected per randomized sequences, but we chose to take the extreme limit of one shot per randomized sequence to avoid any subtle questions about how many shots would be safe to take per randomized sequence before correlations became significant
2016
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2017
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David Poulin, “Surprising facts about quantum error correction,” (2017), Sydney Quantum Information Theory Workshop, Coogee, Australia
2017
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2017
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Robin Blume-Kohout, John King Gamble, Erik Nielsen, Kenneth Rudinger, Jonathan Mizrahi, Kevin Fortier, and Peter Maunz, “Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography,” Nature Communications 8
2017
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2017
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2017
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2017
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Colm A. Ryan, Blake R. Johnson, Diego Ristè, Brian Donovan, and Thomas A. Ohki, “Hardware for dynamic quantum computing,” Review of Scientific Instruments 88
2017
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David C. McKay, Christopher J. Wood, Sarah Sheldon, Jerry M. Chow, and Jay M. Gambetta, “Efficient z z gates for quantum computing,” Phys. Rev. A 96
2017
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M. A. Rol, C. C. Bultink, T. E. O’Brien, S. R. de Jong, L. S. Theis, X. Fu, F. Luthi, R. F. L. Vermeulen, J. C. de Sterke, A. Bruno, D. Deurloo, R. N. Schouten, F. K. Wilhelm, and L. DiCarlo, “Restless tuneup of high-fidelity qubit gates,” Phys. Rev. Applied 7
2017
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Pavithran Iyer and David Poulin, “A small quantum computer is needed to optimize fault-tolerant protocols,” Quantum Science and Technology 3
2018
Closest in time.
Joel J. Wallman, “Randomized benchmarking with gate-dependent noise,” Quantum 2
2018
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Matthew Ware, Guilhem Ribeill, Diego Ristè, Colm A. Ryan, Blake Johnson, and Marcus P. da Silva, “Dataset and analysis for for ”experimental pauli-frame randomization on a superconducting qubit”,” (2020)
2020
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