State-Based Quantum Simulation: Releasing the Powers of Quantum States and Copies

TL;DR

This paper introduces a novel quantum simulation method using state-based decompositions and auxiliary systems, enabling simulation of nonlinear, open, and time-dependent quantum dynamics beyond traditional gate-based approaches.

Contribution

The authors present a new state-based quantum simulation framework that extends capabilities to simulate nonlinear Hamiltonians, open systems, and adiabatic processes, surpassing conventional gate-based methods.

Findings

Simulates classical nonlinear and delayed differential equations.

Enables nonlinear adiabatic quantum computation and eigenstate preparation.

Supports simulation of open quantum systems and nonlinear Hamiltonians.

Abstract

Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing their Hamiltonian evolution in a series of quantum gates. Here, we introduce a method for quantum simulation in which the Hamiltonian is decomposed in terms of states and the resulting evolution is realized by only controlled-swap gates and measurements applied on a set of auxiliary systems whose quantum states define the system dynamics. These auxiliary systems can be identically prepared in an arbitrary number of copies of known states at any intermediate time. This parametrization of the quantum simulation goes beyond traditional gate-based methods and permits simulation of, e.g., state-dependent (nonlinear) Hamiltonians and open quantum systems. We show how classical nonlinear and time-delayed ordinary differential equations can be simulated with the state-based method, and how a nonlinear variant of shortcut to adiabaticity permits adiabatic quantum computation, preparation of eigenstates, and solution of optimization tasks.