Quantum Computing Without Wavefunctions: Time-Dependent Density Functional Theory for Universal Quantum Computation

TL;DR

This paper extends the theorems of time-dependent density functional theory to universal quantum Hamiltonians, enabling the use of single-qubit expectation values as fundamental variables for quantum computation and simulation.

Contribution

It demonstrates that TDDFT can be applied to universal qubit Hamiltonians, allowing for the approximation of quantum observables via density functionals and enabling simulation with different Hamiltonians.

Findings

Single-qubit expectation values can serve as basic variables in quantum computation.

TDDFT provides an exact method to simulate universal Hamiltonians with alternative interactions.

The approach opens new avenues for practical quantum computation and simulation.

Abstract

We prove that the theorems of TDDFT can be applied to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions.