A randomized compilation of LCHS for non-unitary dynamics, with an observable-driven variant and a symmetry-aware sampler, claims reduced ancilla and circuit depth at the cost of more repetitions.
BELT: Block Encoding of Linear Transformation on Density Matrices
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abstract
Linear maps that are not completely positive play a crucial role in the study of quantum information, yet their non-completely positive nature renders them challenging to realize physically. The core difficulty lies in the fact that when acting such a map $\mathcal{N}$ on a state $\rho$, $\mathcal{N}(\rho)$ may not correspond to a valid density matrix, making it difficult to prepare directly in a physical system. We introduce Block Encoding of Linear Transformation (BELT), a systematic protocol that simulates arbitrary linear maps by embedding the output $\mathcal{N}(\rho)$ into a block of a unitary operator. BELT enables the manipulation and extraction of information about $\mathcal{N}(\rho)$ through coherent quantum evolution. Notably, BELT accommodates maps that fall outside the scope of quantum singular value transformation, such as the transpose map. BELT finds applications in entanglement detection, quantum channel inversion, and simulating pseudo-differential operators, and demonstrates improved sample complexity compared to protocols based on Hermitian-preserving map exponentiation.
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Circuit-Efficient Randomized Quantum Simulation of Non-Unitary Dynamics with Observable-Driven and Symmetry-Aware Designs
A randomized compilation of LCHS for non-unitary dynamics, with an observable-driven variant and a symmetry-aware sampler, claims reduced ancilla and circuit depth at the cost of more repetitions.