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1. Uncertainties in quantum measurements: a quantum tomography

   https://doi.org/10.1088/1751-8121/ac6a2c  

   Balachandran, A P; Calderón, F; Nair, V P; Pinzul, Aleksandr; Reyes-Lega, A F; Vaidya, S (May 2022, Journal of Physics A: Mathematical and Theoretical)

   Abstract The observables associated with a quantum system S form a non-commutative algebra A S . It is assumed that a density matrix ρ can be determined from the expectation values of observables. But A S admits inner automorphisms a ↦ u a u − 1 , a , u ∈ A S , u * u = u u * = 1 , so that its individual elements can be identified only up to unitary transformations. So since Tr  ρ ( uau *) = Tr( u * ρu ) a , only the spectrum of ρ , or its characteristic polynomial, can be determined in quantum mechanics. In local quantum field theory, ρ cannot be determined at all, as we shall explain. However, abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables in abelian algebras A M ⊂ A S ( M for measurement, S for system). We study the uncertainties in extending ρ | A M to ρ | A S (the determination of which means measurement of A S ) and devise a protocol to determine ρ | A S ≡ ρ by determining ρ | A M for different choices of A M . The problem we formulate and study is a generalization of the Kadison–Singer theorem. We give an example where the system S is a particle on a circle and the experiment measures the abelian algebra of a magnetic field B coupled to S . The measurement of B gives information about the state ρ of the system S due to operator mixing. Associated uncertainty principles for von Neumann entropy are discussed in the appendix, adapting the earlier work by Białynicki-Birula and Mycielski (1975 Commun. Math. Phys. 44 129) to the present case. 

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2. Quantum Phases in a Quantum Rabi Triangle

   https://doi.org/10.1103/PhysRevLett.127.063602  

   Zhang, Yu-Yu; Hu, Zi-Xiang; Fu, Libin; Luo, Hong-Gang; Pu, Han; Zhang, Xue-Feng (August 2021, Physical Review Letters)
3. A quantum walk control plane for distributed quantum computing in quantum networks

   https://doi.org/10.1109/QCE52317.2021.00048  

   de Andrade, Matheus Guedes; Dai, Wenhan; Guha, Saikat; Towsley, Don (November 2021, 2021 IEEE International Conference on Quantum Computing and Engineering (QCE))

   Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum computation among quantum computers. In this work, we describe a quantum walk protocol to perform distributed quantum computing in a quantum network. The protocol uses a quantum walk as a quantum control signal to perform distributed quantum operations. We consider a generalization of the discrete-time coined quantum walk model that accounts for the interaction between a quantum walker system in the network graph with quantum registers inside the network nodes. The protocol logically captures distributed quantum computing, abstracting hardware implementation and the transmission of quantum information through channels. Control signal transmission is mapped to the propagation of the walker system across the network, while interactions between the control layer and the quantum registers are embedded into the application of coin operators. We demonstrate how to use the quantum walker system to perform a distributed CNOT operation, which shows the universality of the protocol for distributed quantum computing. Furthermore, we apply the protocol to the task of entanglement distribution in a quantum network. 

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4. Landau-Forbidden Quantum Criticality in Rydberg Quantum Simulators

   https://doi.org/10.1103/PhysRevLett.131.083601  

   Lee, Jong Yeon; Ramette, Joshua; Metlitski, Max A.; Vuletić, Vladan; Ho, Wen Wei; Choi, Soonwon (August 2023, Physical Review Letters)
5. Boosting quantum amplitude exponentially in variational quantum algorithms

   https://doi.org/10.1088/2058-9565/acf4ba  

   Kyaw, Thi Ha; Soley, Micheline B; Allen, Brandon; Bergold, Paul; Sun, Chong; Batista, Victor S; Aspuru-Guzik, Alán (October 2023, Quantum Science and Technology)

   Abstract We introduce a family of variational quantum algorithms, which we coin as quantum iterative power algorithms (QIPAs), and demonstrate their capabilities as applied to global-optimization numerical experiments. Specifically, we demonstrate the QIPA based on a double exponential oracle as applied to ground state optimization of theH₂molecule, search for the transmon qubit ground-state, and biprime factorization. Our results indicate that QIPA outperforms quantum imaginary time evolution (QITE) and requires a polynomial number of queries to reach convergence even with exponentially small overlap between an initial quantum state and the final desired quantum state, under some circumstances. We analytically show that there exists an exponential amplitude amplification at every step of the variational quantum algorithm, provided the initial wavefunction has non-vanishing probability with the desired state and that the unique maximum of the oracle is given by ${\lambda }_1>0$, while all other values are given by the same value $0<{\lambda }_2<{\lambda }_1$(hereλcan be taken as eigenvalues of the problem Hamiltonian). The generality of the global-optimization method presented here invites further application to other problems that currently have not been explored with QITE-based near-term quantum computing algorithms. Such approaches could facilitate identification of reaction pathways and transition states in chemical physics, as well as optimization in a broad range of machine learning applications. The method also provides a general framework for adaptation of a class of classical optimization algorithms to quantum computers to further broaden the range of algorithms amenable to implementation on current noisy intermediate-scale quantum computers. 

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