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Register a new userQuantum simulation of $phi^4$ theories in qudit systems
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We discuss the implementation of quantum algorithms for lattice $Phi^4$ theory on circuit quantum electrodynamics (cQED) system. The field is represented on qudits in a discretized field amplitude basis. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates. Considering the set of universal gates formed by the single-qudit phase gate and the displacement gate, we address initial state preparation and single-qudit gate synthesis with variational methods.
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Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a task of utmost significance. One such strategy of broadcasting is through the application of cloning machines. In this article, broadcasting of quantum resources beyond $2 otimes 2$ systems is investigated. In particular, in $2otimes3$ dimension, a class of states not useful for broadcasting of entanglement is characterized for a choice of optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states (MEMS) and two parameter class of states (TPCS) are obtained to exemplify our protocol. A significant derivative of the protocol is the generation of entangled states with positive partial transpose in $3 otimes 3$ dimension and states which are absolutely separable in $2 otimes 2$ dimension. Moving beyond entanglement, in $2 otimes d$ dimension, the impossibility to optimally broadcast quantum correlations beyond entanglement (QCsbE) (discord) and quantum coherence ($l_{1}$-norm) is established. However, some significant illustrations are provided to highlight that non-optimal broadcasting of QCsbE and coherence are still possible.
We describe the simulation of dihedral gauge theories on digital quantum computers. The nonabelian discrete gauge group $D_N$ -- the dihedral group -- serves as an approximation to $U(1)timesmathbb{Z}_2$ lattice gauge theory. In order to carry out such a lattice simulation, we detail the construction of efficient quantum circuits to realize basic primitives including the nonabelian Fourier transform over $D_N$, the trace operation, and the group multiplication and inversion operations. For each case the required quantum resources scale linearly or as low-degree polynomials in $n=log N$. We experimentally benchmark our gates on the Rigetti Aspen-9 quantum processor for the case of $D_4$. The fidelity of all $D_4$ gates was found to exceed $80%$.
My previous work [arXiv:1902.00977] studied the dynamics of Renyi entanglement entropy $R_alpha$ in local quantum circuits with charge conservation. Initializing the system in a random product state, it was proved that $R_alpha$ with Renyi index $alpha>1$ grows no faster than diffusively (up to a sublogarithmic correction) if charge transport is not faster than diffusive. The proof was given only for qubit or spin-$1/2$ systems. In this note, I extend the proof to qudit systems, i.e., spin systems with local dimension $dge2$.
We examine, in correlated mixed states of qudit-qubit systems, the set of all conditional qubit states that can be reached after local measurements at the qudit based on rank-1 projectors. While for a similar measurement at the qubit, the conditional post-measurement qudit states lie on the surface of an ellipsoid, for a measurement at the qudit we show that the set of post-measurement qubit states can form more complex solid regions. In particular, we show the emergence, for some classes of mixed states, of sets which are the convex hull of solid ellipsoids and which may lead to cone-like and triangle-like shapes in limit cases. We also analyze the associated measurement dependent conditional entropy, providing a full analytic determination of its minimum and of the minimizing local measurement at the qudit for the previous states. Separable rank-2 mixtures are also discussed.
A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single qubit quantum channels ${T_t}$ specified by a generator $mathcal{L}$. This algorithm requires only $mathcal{O}big((||mathcal{L}||_{(1rightarrow 1)} t)^{3/2}/epsilon^{1/2} big)$ single qubit and CNOT gates and approximates the channel $T_t = e^{tmathcal{L}}$ up to chosen accuracy $epsilon$. Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilised which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a non-unitary single-qubit quantum channel.
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