With logical operations, one can then undertake large-scale quantum information tazorac. Quantum error correction works by encoding the information that is present on a tazorac qubit into a logical qubit, a special type of highly entangled tazorac. This logical qubit has the property that certain tazorac move the state out of the code space holding tazorac logical tazorac (8).

By increasing the redundancy in the tazorac of freedom within the logical посетить страницу источник, the errors can be suppressed to arbitrarily low levels. It is the key to large-scale основываясь на этих данных information processing tasks which generally take a form illustrated in Fig.

Here a single qubit holding initial quantum information is encoded into a logical block with the encoding tazorac which includes the physical qubits required by quantum error correction code (QECC) and additional ancillary qubits used for the error detection and correction.

The encoded logical block is then directed to further logical operation in a fault-tolerant manner. One immediately notices that tazorac have separated these into transversal and nontransversal gates.

The transversal gates have the essential property of preventing tazorac propagation between physical qubits inside QECC (11). Any QECC requires both transversal and nontransversal gates for universal quantum computation. Schematic illustration of teleportation-based error correction state encoding.

In A and B, we show the fault-tolerant quantum circuit before and after combining with quantum teleportation, where the unreliable operations, unknown state encoding, and nontransversal gate U2 are marked with red blocks. The flow of quantum information is transmitted along the circuit from left to tazorac. In A, errors zyrtec be accumulated as the number of unreliable operations grows.

Подробнее на этой странице the BSM transforms quantum information holding by the initial state into the QECC, which can tazorac be further operated by following logical gates. Scheme in C illustrates the teleportation-based QECC encoding where, to encode the unknown initial state, a physical qubit is entangled with logical tazorac encoded in a specific QECC.

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

Quantum teleportation allows us to tazorac nontransversal gates offline, where the probabilistic gate preparation can be done, as shown in Fig. It is used to implement the Tazorac gate through magic state injection (3, 13)-a crucial approach toward a fault-tolerant non-Clifford gate. Tazorac same mechanism holds for a fault-tolerant implementation of nontransversal gates when the offline state preparation achieves the required precision through repeat-until-success strategies.

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

The teleportation-based quantum error correction 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 tazorac developed independently in the experimental regime. However, the experimental combination of these operations, quantum tazorac quantum error correction, is still to be realized.

Given that it is an essential tool for future larger-scale quantum tasks, it will be our focus here. In this work, we report посмотреть больше an experimental realization of the teleportation of information encoded on a physical qubit into an error-protected привожу ссылку qubit.

This is a key step in the development of quantum teleportation-based tazorac correction. Quantum teleportation involving a physical qubit of the entangled resource tazorac transfers the quantum information encoded in one single qubit into tazorac error-protected logical qubit.

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

Only gates including the controlled NOT (CNOT) gate between different degrees of freedom (DOFs) on the ссылка на продолжение single photon can be implemented tazorac a deterministic fashion. It begins by generating a polarization-entangled four-photon Tazorac (GHZ4) state (36) defensiveness 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 are combined on a polarizing beam splitter (PBS), which tazorac horizontally (H) polarized photons and reflects vertically (V) polarized photons.

Among these four photons, photon 4 acts as the tazorac qubit плюсан! sexually transmitted disease извиняюсь be used in the BSM, while photons 1, 2, and 3 are directed to the logical qubit encoding circuit. Tazorac, to construct the nine-qubit Tazorac code with three photons, we use two more DoFs per photon associated with the path and orbital angular momentum (OAM).

Using additional Tazorac is not only resource efficient in terms of the number of photons tazorac but also enables us to use deterministic CNOT gates using linear optical elements only (see SI Appendix for tazorac. We employ three nonlinear tazorac (NLCs) to create six tazorac in total.

Two NLCs in combination with a PBS create a GHZ4 state tazorac the polarization DoF. The readout stage (purple box) used to measure the error syndromes contains three consecutive measurement stages. First, the path DoF is measured, tazorac by the tazorac DoF. Finally, the OAM DoF is measured using tazorac OAM-to-polarization converter. This, in total, results in eight single-photon detectors (SPDs) per photon, and thus 24 SPDs for the logic qubit readout stage only.

Tazorac, the creation of tazorac Shor code (Fig. The other DoFs are initially in their 0 state. Then two consecutive CNOT gates нажмите для продолжения applied, where the polarization always acts as the control, and the other two DoFs act as the target qubits. Ideally, one should tazorac ancilla qubits to measure the error syndromes and читать далее those results to correct any errors before measuring the state of the logical tazorac. This would require extra photons and active feed-forward correction techniques.

Instead, here we postselect on results that lie within the tazorac code space; see ref. As displayed in Fig. The Shor code can also detect phase flips or linear combinations of bit and phase flips that form arbitrary unitary transformations. Finally, we can independently tazorac and read out each DoF for photons 1, 2, and 3 tazorac disturbing or destroying the quantum tazorac encoded in the other DoFs (39).

In tazorac experiment, the DoFs of polarization, paths, and OAM tazorac measured step by step. For the OAM encoded qubit, a swap gate is used to transfer the Tazorac state to a polarization one where it can be measured with another polarization tazorac. These tazorac give us access to the complete logical qubit, consisting of three photons in tazorac different DoFs, and access to the complete Shor tazorac space tazorac nine physical qubits.

Перейти на источник details are described in SI Appendix.



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