Quantum arithmetics via computation with minimized external control: The half-adder

The while-you-wait computing paradigm combines elements of digital and analog quantum computation with the aim of minimizing the need of external control. In this architecture the computer is split into logic units, each continuously implementing a single recurring multigate operation via the unmodulated Hamiltonian evolution of a quantum many-body system. Here we use evolutionary algorithms to engineer such many-body dynamics, and develop logic units capable of continuously implementing a quantum half-adder in a time-independent four-qubit network, where qubits are coupled with either Ising or Heisenberg interactions. Our results provide a step for the development of larger modules for full quantum arithmetics.

Figure 1

A half-adder constructed with a xor and and gate.

Figure 2

A quantum half-adder constructed with a Toffoli and cnot gate.

Figure 3

An undirected graph representing a quantum network split into register and ancillae qubits.

Figure 4

The optimization curve for the average gate fidelity using differential evolution.

Figure 5

The optimization curve for the average gate fidelity when the smallest parameters are iteratively forced to zero. At the iteration marked by vertical dotted lines a new interaction, specified in the legend, is removed. A local optimization algorithm is then carried out for a corresponding reduced set of parameters; see discussion in the text.

Figure 6

Complex network transforms into a simplified network with much fewer interactions after iteratively setting small parameters to 0 and minimizing.

Figure 7

The average gate fidelity and fidelity of random states given by the implemented quantum half-adder when varying one parameter, $J_{12}^{ZZ}$, around its optimal value.