Implementing and Characterizing Precise Multiqubit Measurements

Abstract

There are two general requirements to harness the computational power of quantum mechanics: the ability to manipulate the evolution of an isolated system and the ability to faithfully extract information from it. Quantum error correction and simulation often make a more exacting demand: the ability to perform nondestructive measurements of specific correlations within that system. We realize such measurements by employing a protocol adapted from Nigg and Girvin [Phys. Rev. Lett. 110, 243604 (2013)], enabling real-time selection of arbitrary register-wide Pauli operators. Our implementation consists of a simple circuit quantum electrodynamics module of four highly coherent 3D transmon qubits, collectively coupled to a high-Q superconducting microwave cavity. As a demonstration, we enact all seven nontrivial subset-parity measurements on our three-qubit register. For each, we fully characterize the realized measurement by analyzing the detector (observable operators) via quantum detector tomography and by analyzing the quantum backaction via conditioned process tomography. No single quantity completely encapsulates the performance of a measurement, and standard figures of merit have not yet emerged. Accordingly, we consider several new fidelity measures for both the detector and the complete measurement process. We measure all of these quantities and report high fidelities, indicating that we are measuring the desired quantities precisely and that the measurements are highly nondemolition. We further show that both results are improved significantly by an additional error-heralding measurement. The analyses we present here form a useful basis for the future characterization and validation of quantum measurements, anticipating the demands of emerging quantum technologies.

Three-qubit direct dispersive parity measurement with tunable coupling qubits

“…The Hamiltonian Eq. (15) implies that the evolution of the resonators' annihilation operators is dependent on the Hamming weight of the string of qubits. In particular, we have from Eqs.…”

Towards a heralded eigenstate-preserving measurement of multi-qubit parity in circuit QED

“…In [7,16] this was achieved by utilizing the dispersive interaction of superconducting transmon qubits with the quantized field of a microwave resonator [25,26]. This interaction is characterized by the Hamiltonian term…”

“…In Refs. [7,16] the cavity state is swapped onto that of an ancilla qubit. The ancilla is initialized in its ground state and is dispersively coupled to the cavity field encoding the parity of the remaining qubits according to (4).…”

“…An advantage of this readout via an ancilla qubit is that after the entanglement swapping, the cavity is back in the vacuum state and no further information about the multi-qubit state can leak out from the cavity. However, the decoherence of the ancilla does limit the fidelity of the parity mapping and readout as observed in [16].…”

“…Blumoff * patrick.huembeli@icfo.eu † simon.nigg@unibas.ch et al [16] succesfully measured the parity of an arbitrary subset of three superconducting transmon qubits in an approximately eigenstate-preserving fashion based on the theoretical proposal of Nigg and Girvin [7]. In this approach in a first stage, the parity bit is first mapped onto the phase of a coherent state of a microwave field dispersively coupled to the qubits.…”