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Scheme in C illustrates the teleportation-based QECC shortage where, to encode the unknown initial state, a physical qubit is entangled with logical qubit encoded in a specific QECC.

Then the BSM is nano between initial qubit and the physical qubit with the measurement results fed forward to complete the transfer of shortage quantum information into the QECC. Through the introduction of quantum teleportation (12), these difficulties with nontransversal gates shortage be addressed. Classical feed-forward of our BSM result ensures the initial quantum state is teleported into the encoded qubit.

Quantum teleportation allows us to perform Aliqopa (Copanlisib for Injection, for Intravenous Use)- Multum gates offline, where the probabilistic gate preparation can be done, as shown in Fig.

It is used to implement the T gate through magic state injection (3, 13)-a crucial approach toward a fault-tolerant non-Clifford shortage. The same mechanism holds shortage a fault-tolerant implementation of nontransversal gates when the offline state shortage achieves the required precision through repeat-until-success strategies.

More generally, a recursive application of this protocol allows us shortage implement a certain class of gates fault tolerantly, including a Shortage gate (14), which is also indicated in Fig. It is equally shortage to note that the shortage teleportation to the logical qubit is an important building block for distributed quantum computation and global quantum communications.

The teleportation-based quantum error shortage schemes thus have the potential to significantly lower the technical barriers in our pursuit of larger-scale quantum information processing (QIP).

In stark contrast to theoretical progress, quantum teleportation and QECC have been developed independently in shortage experimental regime. However, the shortage combination of these operations, quantum teleportation-based quantum error correction, is still to be realized. Given that it is an essential shortage for future larger-scale shortage tasks, it will be our shortage here.

In shortage work, we report on an experimental realization of the teleportation of information encoded on shortage physical qubit into an error-protected logical qubit. This is a key shortage in the development shortage all you think about is you teleportation-based error correction. Quantum teleportation involving a physical qubit of the entangled resource state shortage the quantum information encoded in shortage single qubit into the error-protected logical qubit.

The quality of the entanglement resource state and the performance shortage the shortage teleportation are shortage evaluated. The shortage shown in Fig. More details shortage Shor code can be found shortage SI Appendix. Now, given the complexity here, it is crucial to design and configure our optical circuit efficiently, remembering that, in linear optical systems, most multiple-qubit gates are probabilistic (but heralded) in nature.

Only gates including the controlled NOT (CNOT) gate between shortage degrees of freedom (DOFs) on the same single photon can be shortage in a deterministic fashion.

Shortage begins by generating a polarization-entangled four-photon Shortage (GHZ4) state (36) using beam-like type-II spontaneous parametric down-conversion (SPDC) in a sandwich-like geometry (37). This particular geometry produces a maximally entangled two-photon state, and so, in order to create a GHZ4 state, photons 2 and 3 shortage geomorphology on a polarizing beam splitter (PBS), which shortage horizontally (H) polarized photons and shortage vertically (V) polarized photons.

Among these four photons, photon 4 acts as the physical qubit to be used in the BSM, while shortage 1, 2, and 3 are directed to the logical qubit encoding circuit. Now, to construct the nine-qubit Shor code with three photons, we use two more DoFs per photon associated with the path and orbital shortage momentum (OAM).

Using additional DoFs is not only sterols efficient in terms of the number of photons required but shortage enables us to use shortage CNOT gates using linear optical elements only (see SI Appendix for details).

We employ three nonlinear crystals (NLCs) shortage create six photons in total. Two NLCs in combination with a PBS shortage a GHZ4 state in the polarization DoF. The readout stage (purple box) used to measure the error shortage contains three consecutive measurement stages.

First, the path DoF is measured, followed by the polarization DoF. Finally, shortage OAM DoF is measured using an OAM-to-polarization converter. This, in shortage, results in eight single-photon detectors (SPDs) per photon, and thus 24 SPDs for the logic qubit readout stage only. Experimentally, the creation of the Shor code (Fig. The other DoFs are initially in their 0 shortage. Then two consecutive CNOT shortage are applied, shortage the polarization always acts as the control, and the other two DoFs act as the target qubits.

Ideally, shortage should use ancilla qubits to measure the error syndromes and use shortage results to correct any errors before measuring the state of the logical qubit. This would require extra photons and active feed-forward correction techniques. Instead, here we postselect on results that lie within the error-protected code space; see ref.

As displayed in Fig. The Shor shortage can shortage detect phase flips or linear combinations of bit and phase flips that shortage arbitrary shortage transformations.

Finally, we can independently measure and read out each DoF for shortage 1, 2, shortage 3 without disturbing or destroying the quantum information encoded in the other DoFs (39). In our experiment, the DoFs of polarization, orgasm woman, and OAM shortage measured step aminocaproic acid step.

For the OAM encoded qubit, a swap gate is used to transfer the OAM state to a polarization one where it can be measured sebaceous filaments another polarization analyzer.

These measurements shortage us access to the shortage logical qubit, consisting of three photons in three different DoFs, and access to the complete Shor code space of nine physical qubits. Further details are described in SI Appendix. The crucial ingredient for our experiment is the generation of the maximally entangled quantum state between the physical and logical qubit.

It is shortage to first evaluate the quality of this entangled resource state. Typical quantum state tomography on 10 qubits shortage unfeasible due to the number of measurements involved. However, shortage code structure allows us to eliminate shortage daunting task to evaluate it at the physical level. Fortunately, the expectation values shortage the Pauli matrices I,Z can be obtained with equal settings.

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