Quantum Analogies

Daniela Dragoman, Mircea Dragoman

Yiming Huang, Jiaxing Song, Xiaoxia Cai +1 more

Analog quantum simulators emulate complex many-body dynamics through native continuous-time evolution under hardware-defined interactions. Yet once a platform is specified, its interaction structure is largely fixed by the underlying hardware, restricting the Hamiltonians that can be realized and limiting programmability. Here we introduce universal analog quantum simulation (UAQS), a hybrid framework that systematically expands the range of accessible quantum evolutions within a given analog platform. UAQS employs optimized continuous-time control fields to engineer target dynamics directly, avoiding decomposition into discrete gate sequences. By preserving native analog evolution while extending the set of achievable Hamiltonians, UAQS transforms fixed-interaction analog devices into programmable simulators. Numerical studies on representative architectures, including superconducting circuits and Rydberg-atom arrays, show that UAQS accurately reproduces non-trivial many-body dynamics beyond the intrinsic interaction structure of the hardware. These results establish UAQS as a practical route toward programmable analog quantum simulation.

Masao Nomura

Quantized quantum-analog rotation function (QQRF), which the present author introduced previously as quantized version of quantum-analog rotation function, are discussed in detail. It is shown that the QQRF is describable as a coupled pair of basis operators. The QQRF has various symmetries, and its form is preserved under several kinds of transformations. Emphasis is put on expanding a product of QQRF's as a sum of QQRF's.

Daniela Dragoman, Mircea Dragoman

Manaka Okuyama, Masayuki Ohzeki

We investigate the effect of deterministic analog control errors in the time-dependent Hamiltonian on isolated quantum dynamics. Deterministic analog control errors are formulated as time-dependent operators in the Schrodinger equation. We give an upper bound on the distance between two states in time evolution with and without deterministic analog control errors. As a result, we prove that, if the strength of deterministic analog control errors is less than the inverse of computational time, the final state in quantum dynamics without deterministic analog control errors can be obtained through a constant-order number of measurements in quantum dynamics with deterministic analog control errors.

Miroslav Svítek