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

TL;DR

This paper presents a method to efficiently determine the eigenvalues of arbitrary Pauli products using generalized spin-spin interactions, enabling constant-depth quantum measurements independent of the number of qubits.

Contribution

It introduces a novel approach leveraging shared harmonic oscillator couplings to perform eigenvalue measurements with a fixed number of multi-qubit gates, regardless of system size.

Findings

Eigenvalues of arbitrary Pauli products can be measured with constant gates

Implementation demonstrated for up to 14 qubits in ion traps

Potential for efficient quantum error correction stabilizer codes

Abstract

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. The special case of finding the parity of N qubits only requires a small number of operations that is independent of N. This compares favorably to algorithms for computing the parity on conventional machines, which implies a genuine quantum advantage.