01707nas a2200133 4500008004100000245007300041210006900114260001500183520128600198100001401484700001501498700002301513856003701536 2023 eng d00aClifford operations and homological codes for rotors and oscillators0 aClifford operations and homological codes for rotors and oscilla c11/13/20233 a
We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the group of bosonic Gaussian operations inherited by the rotor. This n-rotor Clifford group, U(1)n(n+1)/2⋊GLn(Z), is represented by continuous U(1) gates generated by polynomials quadratic in angular momenta, as well as discrete GLn(Z) momentum sign-flip and sum gates. We classify homological rotor error-correcting codes [arXiv:2303.13723] and various rotor states based on equivalence under Clifford operations.
Reversing direction, we map homological rotor codes and rotor Clifford operations back into oscillators by interpreting occupation-number states as rotor states of non-negative angular momentum. This yields new multimode homological bosonic codes protecting against dephasing and changes in occupation number, along with their corresponding encoding and decoding circuits. In particular, we show how to non-destructively measure the oscillator phase using conditional occupation-number addition and post selection. We also outline several rotor and oscillator varieties of the GKP-stabilizer codes [arXiv:1903.12615].
We consider a class of holographic tensor networks that are efficiently contractible variational ansatze, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. In the case when the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem, and the desirability of local contractibility for an efficient variational ansatz, we provide guidelines for constructing networks consisting of multiple types of tensors that can support power-law correlation. We also provide an explicit construction of one such network, which approximates the holographic HaPPY pentagon code in the limit where variational parameters are taken to be small.
1 aCao, ChunJun1 aPollack, Jason1 aWang, Yixu uhttps://arxiv.org/abs/2103.0863101128nas a2200145 4500008004100000245008100041210006900122260001400191520066400205100002100869700002100890700001900911700001500930856003700945 2020 eng d00aApproximate recovery and relative entropy I. general von Neumann subalgebras0 aApproximate recovery and relative entropy I general von Neumann c6/14/20203 aWe prove the existence of a universal recovery channel that approximately recovers states on a v. Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I v. Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary v. Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda Lp norms. We comment on applications to the quantum null energy condition.
1 aFaulkner, Thomas1 aHollands, Stefan1 aSwingle, Brian1 aWang, Yixu uhttps://arxiv.org/abs/2006.0800201128nas a2200145 4500008004100000245008100041210006900122260001400191520066400205100002100869700002100890700001900911700001500930856003700945 2020 eng d00aApproximate recovery and relative entropy I. general von Neumann subalgebras0 aApproximate recovery and relative entropy I general von Neumann c6/14/20203 aWe prove the existence of a universal recovery channel that approximately recovers states on a v. Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I v. Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary v. Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda Lp norms. We comment on applications to the quantum null energy condition.
1 aFaulkner, Thomas1 aHollands, Stefan1 aSwingle, Brian1 aWang, Yixu uhttps://arxiv.org/abs/2006.0800201255nas a2200133 4500008004100000245006300041210006100104260000900165490000800174520086800182100001901050700001501069856003701084 2018 eng d00aHolographic Complexity of Einstein-Maxwell-Dilaton Gravity0 aHolographic Complexity of EinsteinMaxwellDilaton Gravity c20180 v1063 aWe study the holographic complexity of Einstein-Maxwell-Dilaton gravity using the recently proposed "complexity = volume" and "complexity = action" dualities. The model we consider has a ground state that is represented in the bulk via a so-called hyperscaling violating geometry. We calculate the action growth of the Wheeler-DeWitt patch of the corresponding black hole solution at non-zero temperature and find that, in the presence of violations of hyperscaling, there is a parametric enhancement of the action growth rate. We partially match this behavior to simple tensor network models which can capture aspects of hyperscaling violation. We also exhibit the switchback effect in complexity growth using shockwave geometries and comment on a subtlety of our action calculations when the metric is discontinuous at a null surface.
1 aSwingle, Brian1 aWang, Yixu uhttps://arxiv.org/abs/1712.0982601111nas a2200109 4500008004100000245004900041210004900090520079100139100001900930700001500949856003700964 2018 eng d00aRecovery Map for Fermionic Gaussian Channels0 aRecovery Map for Fermionic Gaussian Channels3 aA recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. We also discuss subtleties arising from the singularities of the involved matrices.
1 aSwingle, Brian1 aWang, Yixu uhttps://arxiv.org/abs/1811.04956