Efficient eigenvalue determination for arbitrary Pauli products based on generalized spin-spin interactions

Understand

Effective spin-spin interactions between N+1 qubits enable the determination of the eigenvalue of an arbitrary Pauli product of dimension N with a constant, small number of multi-qubit gates that is independent of N and encodes the eigenvalue in the measurement basis states of an extra ancilla qubit.

• Such interactions are available whenever qubits can be coupled to a shared harmonic oscillator, a situation that can be realized in several physical qubit implementations.
• For example, suitable interactions have already been realized for up to 14 qubits in ion traps.
• It should be possible to implement stabilizer codes for quantum error correction with a constant number of multi-qubit gates, in contrast to typical constructions using a number of two-qubit gates that increases as a function of N.