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1. Reductive quantum phase estimation

   https://doi.org/10.1103/PhysRevResearch.6.033051  

   Papadopoulos, Nicholas_J C; Reilly, Jarrod T; Wilson, John Drew; Holland, Murray J (July 2024, Physical Review Research)

   Estimating a quantum phase is a necessary task in a wide range of fields of quantum science. To accomplish this task, two well-known methods have been developed in distinct contexts, namely, Ramsey interferometry (RI) in atomic and molecular physics and quantum phase estimation (QPE) in quantum computing. We demonstrate that these canonical examples are instances of a larger class of phase estimation protocols, which we call reductive quantum phase estimation (RQPE) circuits. Here, we present an explicit algorithm that allows one to create an RQPE circuit. This circuit distinguishes an arbitrary set of phases with a smaller number of qubits and unitary applications, thereby solving a general class of quantum hypothesis testing to which RI and QPE belong. We further demonstrate a tradeoff between measurement precision and phase distinguishability, which allows one to tune the circuit to be optimal for a specific application. Published by the American Physical Society2024 

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2. Phase-engineered bosonic quantum codes

   https://doi.org/10.1103/PhysRevA.103.062427  

   Li, Linshu; Young, Dylan J.; Albert, Victor V.; Noh, Kyungjoo; Zou, Chang-Ling; Jiang, Liang (June 2021, Physical Review A)
3. Statistical approach to quantum phase estimation

   https://doi.org/10.1088/1367-2630/ac320d  

   Moore, Alexandria J.; Wang, Yuchen; Hu, Zixuan; Kais, Sabre; Weiner, Andrew M. (November 2021, New Journal of Physics)

   Abstract We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown eigenstate–eigenphase pair from a given unitary matrix utilizing a simplified version of the hardware intended for the iterative PEA (IPEA). This is achieved by treating the probabilistic output of an IPEA-like circuit as an eigenstate–eigenphase proximity metric, using this metric to estimate the proximity of the input state and input phase to the nearest eigenstate–eigenphase pair and approaching this pair via a variational process on the input state and phase. This method may search over the entire computational space, or can efficiently search for eigenphases (eigenstates) within some specified range (directions), allowing those with some prior knowledge of their system to search for particular solutions. We show the simulation results of the method with the Qiskit package on the IBM Q platform and on a local computer. 

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4. Quantum computation of phase transition in interacting scalar quantum field theory

   https://doi.org/10.1007/s11128-023-04149-0  

   Thompson, Shane; Siopsis, George (November 2023, Quantum Information Processing)
5. Decoherent quench dynamics across quantum phase transitions

   https://doi.org/10.21468/SciPostPhys.11.4.084  

   Kuo, Wei-Ting; Arovas, Daniel; Vishveshwara, Smitha; You, Yi-Zhuang (January 2021, SciPost Physics)

   We present a formulation for investigating quench dynamics acrossquantum phase transitions in the presence of decoherence. We formulatedecoherent dynamics induced by continuous quantum non-demolitionmeasurements of the instantaneous Hamiltonian. We generalize thewell-studied universal Kibble-Zurek behavior for linear temporal driveacross the critical point. We identify a strong decoherence regimewherein the decoherence time is shorter than the standard correlationtime, which varies as the inverse gap above the groundstate. In thisregime, we find that the freeze-out time \bar{t}\sim\tau^{{2\nu z}/({1+2\nu z})} t - ∼ τ 2 ν z / ( 1 + 2 ν z ) for when the system falls out of equilibrium and the associatedfreeze-out length \bar{\xi}\sim\tau^{\nu/({1+2\nu z})} ξ ‾ ∼ τ ν / ( 1 + 2 ν z ) show power-law scaling with respect to the quench rate 1/\tau 1 / τ ,where the exponents depend on the correlation length exponent \nu ν and the dynamical exponent z z associated with the transition. The universal exponents differ fromthose of standard Kibble-Zurek scaling. We explicitly demonstrate thisscaling behavior in the instance of a topological transition in a Cherninsulator system. We show that the freeze-out time scale can be probedfrom the relaxation of the Hall conductivity. Furthermore, onintroducing disorder to break translational invariance, we demonstratehow quenching results in regions of imbalanced excitation densitycharacterized by an emergent length scale which also shows universalscaling. We perform numerical simulations to confirm our analyticalpredictions and corroborate the scaling arguments that we postulate asuniversal to a host of systems. 

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