Benchmarks of nonclassicality for qubit arrays

Abstract

We present a set of practical benchmarks for N -qubit arrays that economically test the fidelity of achieving multiqubit nonclassicality. The benchmarks are measurable correlators similar to 2-qubit Bell correlators, and are derived from a particular set of geometric structures from the N -qubit Pauli group. These structures prove the Greenberger-Horne-Zeilinger (GHZ) theorem, while the derived correlators witness genuine N -partite entanglement and establish a tight lower bound on the fidelity of particular stabilizer state preparations. The correlators need only M ≤ N +1 distinct measurement settings, as opposed to the 2 2N − 1 settings that would normally be required to tomographically verify their associated stabilizer states. We optimize the measurements of these correlators for a physical array of qubits that can be nearest-neighbor-coupled using a circuit of controlled-Z gates with constant gate depth to form N -qubit linear cluster states. We numerically simulate the provided circuits for a realistic scenario with N = 3, ..., 9 qubits, using ranges of T 1 energy relaxation times, T 2 dephasing times, and controlled-Z gate-fidelities consistent with Google's 9-qubit superconducting chip. The simulations verify the tightness of the fidelity bounds and witness nonclassicality for all nine qubits, while also showing ample room for improvement in chip performance.

Self-testing maximally-dimensional genuinely entangled subspaces within the stabilizer formalism

“…Building on it, we then establish what is the maximal dimension of a genuinely entangled subspace within the stabilizer formalism proving the conjecture posed recently in Ref. [24], and present an exemplary construction of such maximally-dimensional subspaces for any number of qubits. Third, we show that each such subspace can be self-tested from maximal violation of a multipartite Bell inequality constructed with the aid of the approach presented in Refs.…”

“…Let us first find an upper bound on the maximal dimension of the GME stabilizer subspaces (see also [24]). Theorem 3.…”

“…Interestingly, taking advantage of the stabilizer formalism we can construct multipartite Bell inequalities that are maximally violated by any state from the maximally-dimensional subspaces introduced in the preceding section (see also Ref. [24,34] for earlier constructions of Bell inequalities maximally violated by entangled subspaces). Our construction builds on a general approach for constructing CHSH-like Bell inequalities within the stabilizer formalism introduced in Refs.…”

Entanglement certification from theory to experiment

“…Depending on the specific choice of atomic species and electronic energy levels, the qubit transitions can either be driven by spatially addressing the ions with laser light (e.g., the setups used in [245][246][247][248]), or (near-field [249,250], or far-field [251][252][253]) frequency addressed microwave signals. Although the generation of GME is not necessarily the raison d'être for many current multi-qubit devices, the controlled generation and detection of GME is often considered as a means to benchmark their functionality [254][255][256]. Consequently, a first generation of ion trap GME experiments has focused on the generation and detection of specific GME states, resulting in the observation of genuine 6-partite GHZ-type entanglement [257], 8-qubit W-type GME [258], with a record of 14-partite GHZ-type GME [259].…”

Benchmarking Quantum State Transfer on Quantum Devices using Spatio-Temporal Steering

“…Such quantum devices can now be applied to implement some quantum algorithms [49][50][51][52]. In general, benchmarks of quantum devices provide us with a simple method to evaluate the performance of the quantum devices under certain quantum information tasks, e.g., benchmarking the shallow quantum circuits [53], the nonclassicality for qubit arrays [54], quantum chemistry [55],…”