Unitary Matrix Completion-Based DOA Estimation of Noncircular Signals in Nonuniform Noise by Xianpeng Wang, Yanghui Zhu, Mengxing Huang, Jingjing Wang, Liangtian Wan, Guoan Bi

“…Then, the virtual complex-valued covariance matrix with the unknown nonuniform noise is transformed into the real-valued one by utilizing the unitary transformation to improve the computational efficiency. …”
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Unitary matrix completion-based DOA estimation of noncircular signals in nonuniform noise by Wang, Xianpeng, Zhu, Yanghui, Huang, Mengxing, Wang, Jingjing, Wan, Liangtian, Bi, Guoan

“…Then, the virtual complex-valued covariance matrix with the unknown nonuniform noise is transformed into the real-valued one by utilizing the unitary transformation to improve the computational efficiency. …”
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Multi-parameter estimation with multi-mode Ramsey interferometry by Xinwei Li, Jia-Hao Cao, Qi Liu, Meng Khoon Tey, Li You

“…In such an interferometer, the first beam splitter represented by unitary transformation U generates a quantum phase sensing superposition state, while the second beam splitter U ^−1 recombines the phase encoded paths to realize interferometric sensing in terms of population measurements. …”
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Geometric Quantum Computation by Ekert, A, Ericsson, M, Hayden, P, Inamori, H, Jones, J, Oi, D, Vedral, V

“…Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. …”

Orbit classification of qutrit via the Gram matrix. by Tay, Buang Ann, Zainuddin, Hishamuddin

“…We classify the orbits generated by unitary transformation on the density matrices of the three-state quantum systems (qutrits) via the Gram matrix. …”
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Supertranslation-invariant dressed Lorentz charges by Reza Javadinezhad, Uri Kol, Massimo Porrati

“…Key to the construction is the use of infrared regularizations and of a unitary transformation that makes observables commute with the soft degrees of freedom. …”
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Quantum machines powered by correlated baths by Gabriele De Chiara, Mauro Antezza

“…In our framework, two reservoir particles, initially prepared in a thermal state, are correlated through a unitary transformation and afterward interact locally with the two quantum subsystems which form the working fluid. …”
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Hamiltonian transformability, fast adiabatic dynamics and hidden adiabaticity by Lian-Ao Wu, Dvira Segal

“…Abstract We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. …”
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Using an imperfect photonic network to implement random unitaries by Burgwal, R, Clements, W, Smith, D, Gates, J, Kolthammer, W, Renema, J, Walmsley, I

“…The distribution of reflectivities required to implement an arbitrary unitary transformation is skewed towards low values, and this skew becomes stronger the larger the number of modes. …”

Reservoir engineering for maximally efficient quantum engines by Taysa M. Mendonça, Alexandre M. Souza, Rogério J. de Assis, Norton G. de Almeida, Roberto S. Sarthour, Ivan S. Oliveira, Celso J. Villas-Boas

“…This artificial reservoir allowed us to implement a single qubit quantum engine that operates at a single reservoir at effective negative temperature and with maximum efficiency, independent of the unitary transformation performed on the qubit system, as long as it changes the qubit state. …”
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A Numerically Exact Approach to Quantum Impurity Problems in Realistic Lattice Geometries by Andrew Allerdt, Adrian E. Feiguin

“…We review a controlled numerical approach to quantum impurity problems in realistic geometries, consisting of exactly mapping the complete lattice Hamiltonian onto an equivalent one dimensional system through a unitary transformation. The resulting dimensional and entanglement reduction allows one to study the quantum many-body problem on arbitrary d-dimensional lattices using the density matrix renormalization group (DMRG) method. …”
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Time-Rescaling of Dirac Dynamics: Shortcuts to Adiabaticity in Ion Traps and Weyl Semimetals by Agniva Roychowdhury, Sebastian Deffner

“…In this work, we show how time-rescaling can be applied to Dirac dynamics, and we show that all time-dependence can be absorbed into the effective potentials through a judiciously chosen unitary transformation. This is demonstrated for two experimentally relevant scenarios, namely for ion traps and adiabatic creation of Weyl points.…”
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3-Uniform states and orthogonal arrays by Xin-wei Zha, Irfan Ahmed, Yanpeng Zhang

“…We propose a criterion for the k-uniform state via local unitary transformation invariant and find for what N there are 3-uniform states of N-qubits. …”
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Quantum algorithms for Schrieffer-Wolff transformation by Zongkang Zhang, Yongdan Yang, Xiaosi Xu, Ying Li

“…The Schrieffer-Wolff transformation aims to solve degenerate perturbation problems and give an effective Hamiltonian that describes the low-energy dynamics of the exact Hamiltonian in the low-energy subspace of an unperturbed Hamiltonian. This unitary transformation decoupling the low-energy and high-energy subspaces for the transformed Hamiltonian can be realized by quantum circuits. …”
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Spatiotemporal coupled-mode equations for arbitrary pulse transformation by Zhaohui Dong, Xianfeng Chen, Luqi Yuan

“…We further demonstrated a temporal Mach-Zehnder interferometer and universal multiport interferometer, which enables arbitrary unitary transformation for pulses. We showcase a universal approach for transforming pulses among coupled temporal waveguides, which requires only one spatial waveguide under spatiotemporal modulation, and hence provide a flexible, compact, and highly compatible method for optical signal processing in time domain.…”
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Dynamics for two atoms interacting with intensity-dependent two-Mode qantized cavity fields in the ladder configuration by Singh, S., Amrita, S., Ooi, Chong Heng Raymond

“…Exact solutions are obtained for a collective model of two identical two-level atoms interacting with a quantized bimodal field with intensity-dependent coupling terms in a lossless cavity. A unitary transformation method is used to solve the time-dependent problem that also gives the eigensolutions of the interaction Hamiltonian. …”

Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems by Jeong Ryeol Choi

“…Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. …”
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On Schur Forms for Matrices with Simple Eigenvalues by Mihail Mihaylov Konstantinov, Petko Hristov Petkov

“…In this paper, we consider various aspects of the Schur problem for a square complex matrix <i>A</i>, namely the similarity unitary transformation of <i>A</i> into upper triangular form containing the eigenvalues of <i>A</i> on its diagonal. …”
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Realistic Approach of the Relations of Uncertainty of Heisenberg by Paul E. Sterian

“…On the other hand, based on Schwinger's action principle and using the quadridimensional form of the unitary transformation generator function of the quantum operators in the paper, the general form of the evolution equation for these operators is established. …”
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Foundations of statistical mechanics from symmetries of entanglement by Sebastian Deffner, Wojciech H Zurek

“…In particular, the microcanonical equilibrium of a system ${ \mathcal S }$ with Hamiltonian ${H}_{{ \mathcal S }}$ is a fully energetically degenerate quantum state envariant under every unitary transformation. The representation of the canonical equilibrium then follows from simply counting degenerate energy states. …”
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