Semicoherent Symmetric Quantum Processes: Theory and Applications
arXiv:2403.05470 · doi:10.1116/5.0215919
Abstract
Discovering pragmatic and efficient approaches to construct -approximations of quantum operators such as real (imaginary) time-evolution propagators in terms of the basic quantum operations (gates) is challenging. Prior -approximations are invaluable, in that they enable the compilation of classical and quantum algorithm modeling of, e.g., dynamical and thermodynamic quantum properties. In parallel, symmetries are powerful tools concisely describing the fundamental laws of nature; the symmetric underpinnings of physical laws have consistently provided profound insights and substantially increased predictive power. In this work, we consider the interplay between the -approximate processes and the exact symmetries in a semicoherent context -- where measurements occur at each logical clock cycle. We draw inspiration from Pascual Jordan's groundbreaking formulation of nonassociative, but commutative, symmetric algebraic form. Our symmetrized formalism is then applied in various domains such as quantum random walks, real-time evolutions, variational algorithm ansatzes, and efficient entanglement verification. Our work paves the way for a deeper understanding and greater appreciation of how symmetries can be used to control quantum dynamics in settings where coherence is a limited resource.
19 pages, 5 figures, significant revision from v1, comments welcome
References in corpus (29)
- Hamiltonian Simulation by Qubitization
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- Towards Practical Quantum Variational Algorithms
- A Theory of Trotter Error
- Bell-type inequalities to detect true n-body non-separability
- Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory
- The SWAP test and the Hong-Ou-Mandel effect are equivalent
- Quantum stochastic processes and quantum non-Markovian phenomena
- Near-optimal ground state preparation
- Experimental test of Mermin inequalities on a 5-qubit quantum computer
- Quantum algorithm for simulating real time evolution of lattice Hamiltonians
- Hamiltonian Simulation Using Linear Combinations of Unitary Operations
- Rodeo Algorithm for Quantum Computing
- Symmetry-adapted variational quantum eigensolver
- Efficient Fully-Coherent Quantum Signal Processing Algorithms for Real-Time Dynamics Simulation
- Optimised Trotter Decompositions for Classical and Quantum Computing
- Hidden Quantum Markov Models and non-adaptive read-out of many-body states
- Two-Unitary Decomposition Algorithm and Open Quantum System Simulation
- Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation
- Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective
- Projection algorithm for state preparation on quantum computers
- Operational approach to Bell inequalities: applications to qutrits
- Quantum state matching of qubits via measurement-induced nonlinear transformations
- Well-conditioned multiproduct Hamiltonian simulation
- Quantum algorithm for spectral projection by measuring an ancilla iteratively
- Using Random Walks for Iterative Phase Estimation
- Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in JB-Algebras
- Quantum signal processing with continuous variables
- Exploiting Maximally Mixed States for Spectral Estimation by Time Evolution