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arXiv:1107.4774 · Physical Review Letters

Benchmarking a Quantum Teleportation Protocol in Superconducting Circuits Using Tomography and an Entanglement Witness

Matthias Baur, Arkady Fedorov, L. Steffen, Stefan Filipp, Marcus Palmer Da Silva, Andreas J. Wallraff

Published Jan 24, 2012• 88 citations
arXivHTMLPDF

Abstract

Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to reconstruct the teleported state. Repeating this procedure for a complete set of input states we find an average output state fidelity of 86%.

DOI
10.1103/physrevlett.108.040502

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Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to reconstruct the teleported state. Repeating this procedure for a complete set of input states we find an average output state fidelity of 86%.
Demonstration of quantum entanglement, a key resource in quantum computation arising from a nonclassical correlation of states, requires complete measurement of all states in varying bases. By using simultaneous measurement and state tomography, we demonstrated entanglement between two solid-state qubits. Single qubit operations and capacitive coupling between two super-conducting phase qubits were used to generate a Bell-type state. Full two-qubit tomography yielded a density matrix showing an entangled state with fidelity up to 87%. Our results demonstrate a high degree of unitary control of the system, indicating that larger implementations are within reach.
Abstract Quantum teleportation transfers an unknown qubit state from a sender to a receiver using a shared entangled pair and a classically conditioned correction without moving the physical carrier. On the dynamic-circuit hardware, the complete protocol (which includes mid-circuit measurement and conditional feedforward) now runs on a single circuit. We use this to benchmark three-qubit teleportation on a 156-qubit IBM Heron r2 processor (ibm_fez). A single-qubit RY(θ) input was teleported at six angles along a meridian of the Bloch sphere and reconstructed by state tomography alongside two ablation controls; one without entanglement and the other without feedforward. The full protocol returns a mean fidelity of about 0.945, nearly constant across the angles and above the 2/3 full-Bloch-sphere reference at all six sampled angles. Removing feedforward lowered the fidelity to about 0.51, close to a maximally mixed state. On the other hand, removing entanglement yields (1 + cos²θ)/2 with a mean near 0.75, transferring the population but losing the coherence. Together, these results establish that entanglement and feedforward are both necessary. The calibration-limited fidelity serves as a reference for this class of hardware. A separate run returned a Bell-state fidelity value of 0.957. A branch-resolved analysis confirmed that the four measurement branches are Pauli rotations of the target realigned by feedforward. The reported fidelity depends only on the rotation angle and the device noise.
Accurate and precise detection of multi-qubit entanglement is key for the experimental development of quantum computation. Traditionally, non-classical correlations between entangled qubits are measured by counting coincidences between single-shot readouts of individual qubits. We report entanglement metrology using a single detection channel with direct access to ensemble-averaged correlations between two superconducting qubits. Following validation and calibration of this joint readout, we demonstrate full quantum tomography on both separable and highly-entangled two-qubit states produced on demand. Using a subset of the measurements required for full tomography, we perform entanglement metrology with ~95% accuracy and ~98% precision despite ~10% fidelity of single measurements. For the highly entangled states, measured Clauser-Horne-Shimony-Holt operators reach a maximum value of 2.61+/-0.04 and entanglement witnesses give a lower bound of ~88% on concurrence. In its present form, this detector will be able to resolve future improvements in the production of two-qubit entanglement and is immediately extendable to 3 or 4 qubits.
Abstract A single-shot entangling gate plays a crucial role in quantum information processing due to its high fidelity. This operation gate is fast to create a maximally entangled state and forms a universal gate set for quantum computing. Currently, the preparation and demonstration of multi-qubit entanglement are achieved based on sequences of single- and two-qubit operations, yielding lower fidelity and requiring longer execution time. Here, we demonstrate by numerically simulating the use of quantum process tomography to fully characterize the performance of a single-shot three-qubit entangling gate. This gate is used to create a Greenberger–Horne–Zeilinger entangled state in Sakhouf et al (2021 J. Phys. B: At. Mol. Opt. Phys. 54 175501), directly generated by three transmon-type superconducting qubits which are mediated by a resonator with the assistance of a microwave field. Comparing ideal and simulated quantum process tomography, we characterize the entangling gate performance by calculating the mean fidelity achieving a high value ≻ 0.93 .
Quantum teleportation~\cite{Bennett1993} is of both fundamental interest and great practical importance in quantum information science. To date, quantum teleportation has been implemented in various physical systems~\cite{Pirandola2015}, among which superconducting qubits are of particular practical significance as they emerge as a leading system to realize large-scale quantum computation~\cite{Arute2019,Wu2021}. Nevertheless, the number of superconducting qubits on the same chip is severely limited by the available chip size, the cooling power, and the wiring complexity. Realization of quantum teleportation and remote computation over qubits on distant superconducting chips is a key quantum communication technology to scaling up the system through a distributed quantum computational network~\cite{Gottesman1999,Eisert2000,Jiang2007,Kimble2008,Monroe2014}. However, this goal has not been realized yet in experiments due to the technical challenge of making a quantum interconnect between distant superconducting chips and the inefficient transfer of flying microwave photons over the lossy interconnects~\cite{Kurpiers2018,Axline2018,Campagne2018,Magnard2020}. Here we demonstrate deterministic teleportation of quantum states and entangling gates between distant superconducting chips connected by a 64-meter-long cable bus featuring an ultralow loss of 0.32~dB/km at cryogenic temperatures, where high fidelity remote entanglement is generated via flying microwave photons utilizing time-reversal-symmetry~\cite{Cirac1997,Korotkov2011}. Apart from the fundamental interest of teleporting macroscopic superconducting qubits over a long distance, our work lays a foundation to realization of large-scale superconducting quantum computation through a distributed computational network~\cite{Gottesman1999,Eisert2000,Jiang2007,Kimble2008,Monroe2014}.