Qutrit and ququint magic states

Jain, Akalank; Prakash, Soam

doi:10.1103/physreva.102.042409

Cited by 20 publications

(34 citation statements)

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“…The pure states saturating these bounds are of interest because they are non-stabilizer Clifford eigenstates and candidates for the terminus of magic distillation [16,[49][50][51]. Of all the knots we considered in this paper, we did not find a single instance of framing saturating either bound.…”

Section: Jhep04(2021)090 5 Discussionmentioning

confidence: 84%

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Knots, links, and long-range magic

Fliss

2021

J. High Energ. Phys.

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We study the extent to which knot and link states (that is, states in 3d Chern-Simons theory prepared by path integration on knot and link complements) can or cannot be described by stabilizer states. States which are not classical mixtures of stabilizer states are known as “magic states” and play a key role in quantum resource theory. By implementing a particular magic monotone known as the “mana” we quantify the magic of knot and link states. In particular, for SU(2)k Chern-Simons theory we show that knot and link states are generically magical. For link states, we further investigate the mana associated to correlations between separate boundaries which characterizes the state’s long-range magic. Our numerical results suggest that the magic of a majority of link states is entirely long-range. We make these statements sharper for torus links.

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Section: Jhep04(2021)090 5 Discussionmentioning

confidence: 84%

“…One potentially JHEP04(2021)090 interesting feature, though counter to the interpretation of mana as lower bound, is the maximum mana over framings. One reason is the following: for qutrit and ququint single party states it is known that mana is bounded above by (respectively) [49]…”

Section: Jhep04(2021)090 5 Discussionmentioning

confidence: 99%

Knots, links, and long-range magic

Fliss

2021

J. High Energ. Phys.

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“…In particular, it can be shown [28,33] that the Hadamard gate H = VĤ acts on Pauli operators via HXH † = Z and HZH † = X −1 and therefore corresponds to the SL (2…”

Section: (A) Qudit Pauli and Clifford Operatorsmentioning

confidence: 99%

“…The discrete Wigner functions for false|S⟩ and false|N⟩ are plotted in figure 1. The symmetries of these and other qutrit Clifford eigenstates are discussed in detail in [33]. Any of these states can be used to implement a non-Clifford gate via state injection, as we review in appendix A, which closely follows [10].…”

Section: The Strange State and The Norell Statementioning

confidence: 99%

“…In particular, it can be shown [28,33] that the Hadamard gate H=VHfalse^ acts on Pauli operators via HXH†=Z and HZH†=X−1 and therefore corresponds to the SLfalse(2,double-struckZdfalse) transformation, Hfalse^=(0−110). Let us define another Clifford operator N=VNfalse^ to correspond to the SLfalse(2,double-struckZdfalse) transformation, Nfalse^=(−10−1−1). Explicitly, N acts on qutrit Pauli operators via NXN†=ω2X2Z2 and <...>…”

Section: Introductionmentioning

confidence: 99%

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Magic state distillation with the ternary Golay code

Prakash

2020

Proc. R. Soc. A.

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The ternary Golay code—one of the first and most beautiful classical error-correcting codes discovered—naturally gives rise to an 11-qutrit quantum error correcting code. We apply this code to magic state distillation, a leading approach to fault-tolerant quantum computing. We find that the 11-qutrit Golay code can distil the ‘most magic’ qutrit state—an eigenstate of the qutrit Fourier transform known as the strange state —with cubic error suppression and a remarkably high threshold. It also distils the ‘second-most magic’ qutrit state, the Norell state, with quadratic error suppression and an equally high threshold to depolarizing noise.

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Predicting the Lattice Thermal Conductivity in Nitride Perovskite LaWN₃ from ab initio Lattice Dynamics

et al. 2023

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Using a density functional theory‐based thermal transport model, which includes the effects of temperature (T)‐dependent potential energy surface, lattice thermal expansion, force constant renormalization, and higher‐order quartic phonon scattering processes, it is found that the recently synthesized nitride perovskite LaWN3 displays strong anharmonic lattice dynamics manifested into a low lattice thermal conductivity (κL) and a non‐standard κL∝T−0.491 dependence. At high T, the departure from the standard κL∝T−1 law originates in the dual particle‐wave behavior of the heat carrying phonons, which includes vibrations tied to the N atoms. While the room temperature κL=2.98 W mK‐1 arises mainly from the conventional particle‐like propagation of phonons, there is also a significant atypical wave‐like phonon tunneling effect, leading to a 20% glass‐like heat transport contribution. The phonon broadening effect lowers the particle‐like contribution but increases the glass‐like one. Upon T increase, the glass‐like contribution increases and dominates above T = 850 K. Overall, the low κL with a weak T‐dependence points to a new utility for LaWN3 in energy technology applications, and motivates synthesis and exploration of nitride perovskites.

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Qutrit and ququint magic states

Cited by 20 publications

References 57 publications

Knots, links, and long-range magic

Knots, links, and long-range magic

Magic state distillation with the ternary Golay code

Predicting the Lattice Thermal Conductivity in Nitride Perovskite LaWN₃ from ab initio Lattice Dynamics

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Qutrit and ququint magic states

Cited by 20 publications

References 57 publications

Knots, links, and long-range magic

Knots, links, and long-range magic

Magic state distillation with the ternary Golay code

Predicting the Lattice Thermal Conductivity in Nitride Perovskite LaWN3 from ab initio Lattice Dynamics

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Product

Resources

About

Predicting the Lattice Thermal Conductivity in Nitride Perovskite LaWN₃ from ab initio Lattice Dynamics