From 82816d290c8a94fec3563b5f17ad627d5130e7bd Mon Sep 17 00:00:00 2001 From: VVA2024 Date: Thu, 10 Oct 2024 22:04:32 -0400 Subject: [PATCH] refs --- codes/quantum/oscillators/oscillators.yml | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/codes/quantum/oscillators/oscillators.yml b/codes/quantum/oscillators/oscillators.yml index ca038177b..0c6e424c9 100644 --- a/codes/quantum/oscillators/oscillators.yml +++ b/codes/quantum/oscillators/oscillators.yml @@ -70,8 +70,9 @@ features: general_gates: - 'Displacement operations form a group called the Heisenberg-Weyl group, the oscillator analogue to the \hyperref[topic:pauli]{Pauli group}. Analogues of (non-Pauli) Clifford-group transformations are the \textit{Gaussian unitary transformations} (a.k.a. symplectic, Bogoliubov-Valatin, or linear canonical transformations) \cite{doi:10.1063/1.1665805,arxiv:1110.3234,manual:{Wagner, M. Unitary transformations in solid state physics. Netherlands.}}, which are unitaries generated by quadratic polynomials in positions and momenta. The Gaussian unitary transformation group permutes displacement operators amognst themselves, and, up to any phases, is equivalent to the symplectic group \(Sp(2n,\mathbb{R})\).' - - 'Computing using Gaussian states and Gaussian unitaries only can be efficiently simulated on a classical computer \cite{arxiv:quant-ph/0109047,arxiv:1210.1783,arxiv:1208.3660}. This remains true even if superpositions of Gaussian states are considered \cite{arxiv:2010.14363,arxiv:2403.19059}, but is no longer the case when the number of modes scales exponentially \cite{arxiv:2407.06290}. A cubic phase gate is required to make a universal gate set on the oscillator \cite{arxiv:quant-ph/9810082,arxiv:quant-ph/0410100}; other gates are possible, but cubic or higher versions of squeezing are not well defined \cite{doi:10.1103/PhysRevD.29.1107}. More generally, controllability has been proven when the normalizable state space is restricted to Schwartz space \cite{arxiv:quant-ph/0505063}.' - - 'Measurements can be performed by homodyne and generalized homodyne measurements \cite{arxiv:quant-ph/0511044}.' + - 'Computing using Gaussian states and Gaussian unitaries only can be efficiently simulated on a classical computer \cite{arxiv:quant-ph/0109047,arxiv:1210.1783,arxiv:1208.3660}. This remains true even if superpositions of Gaussian states are considered \cite{arxiv:2010.14363,arxiv:2403.19059}, but is no longer the case when the number of modes scales exponentially \cite{arxiv:2407.06290}. A cubic phase gate is required to make a universal gate set on the oscillator \cite{arxiv:quant-ph/9810082,arxiv:quant-ph/0410100}; other gates are possible, but cubic or higher versions of squeezing are not well defined \cite{doi:10.1103/PhysRevD.29.1107}. See Ref. \cite{arxiv:2410.04274} for bosonic computational complexity classes.' + - 'Controllability of bosonic states has been proven when the normalizable state space is restricted to Schwartz space \cite{arxiv:quant-ph/0505063}.' + - 'Measurements can be performed by homodyne, heterodyne, and generalized homodyne measurements \cite{arxiv:quant-ph/0511044}.' - 'The number-phase interpretation allows for the mapping of rotor Clifford gates into the oscillator, some of which become non-unitary (e.g., conditional occupation number addition) \cite{arxiv:2311.07679}.' - 'ZX calculus has been extended to bosonic codes for both Gaussian operators \cite{arxiv:2405.07246} and Fock-state based operators \cite{arxiv:2406.02905}. An earlier graphical calculus exists for Gaussian pure states \cite{arxiv:1007.0725}.'