![]() For different combinations of the primitives, logical state fidelity measurements are made after applying the gate to different input states, providing bounds on the process fidelity. The two codes were implemented on different but similar devices, and in both instances, all of the quantum error correction primitives, including the determination of corrections via decoding, are implemented during runtime using a classical compute environment that is tightly integrated with the quantum processor. In the second instance, a twenty-qubit trapped-ion quantum computer is used to implement a transversal logical CNOT gate on two ] color codes. ![]() The operation is evaluated with varying degrees of fault tolerance, which are provided by including quantum error correction circuit primitives known as flagging and pieceable fault tolerance. In one instance, a twelve-qubit trapped-ion quantum computer is used to implement a non-transversal logical CNOT gate between two five qubit codes. We compare two different implementations of fault-tolerant entangling gates on logical qubits. Our work demonstrates each key aspect of the ] code and verifies the viability of experimental realization of quantum error correcting codes with superconducting qubits. Finally, we realise the decoding circuit and recover the input state with an overall fidelity of $74.5(6)\%$, in total with 92 gates. We further implement logical Pauli operations with a fidelity of $97.2(2)\%$ within the code space. ![]() Then, the arbitrary single-qubit errors introduced manually are identified by measuring the stabilizers. The encoded states are prepared with an average fidelity of $57.1(3)\%$ while with a high fidelity of $98.6(1)\%$ in the code space. In the experiment, having optimised the encoding circuit, we employ an array of superconducting qubits to realise the ] code for several typical logical states including the magic state, an indispensable resource for realising non-Clifford gates. To address this challenge, we experimentally realise the ] code, the so-called smallest perfect code that permits corrections of generic single-qubit errors. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal quantum error correcting code, with the subsequent verification of all key features including the identification of an arbitrary physical error, the capability for transversal manipulation of the logical state, and state decoding. The time difference is due to the physical operations being fundamentally slower and to the stabilizers being measured one after the other instead of in parallel.Quantum error correction is an essential ingredient for universal quantum computing. They did use a complex cycle involving flag qubits (see fig 7) but it was maybe 3x more complex than a raw surface code cycle not 200000 times more complex. For example, "Realization of real-time fault-tolerant quantum error correction" used an ion trap and achieved a cycle time of around 200 milliseconds. It's basically already demonstrated.įor other types of quantum computers, where there is less parallelism or slower operations, a 1us cycle time would not be a reasonable assumption. So, in superconducting qubits, I think a 1 microsecond cycle time is an extremely reasonable assumption. The surface code cycle basically doubles the unitary part which is an extra 80ns roughly for a total of 1.04 microseconds. If you look at figure 1 of "Exponential suppression of bit or phase flip errors with repetitive error correction", which runs rep codes from distance 3 to distance 11 on a superconducting qubit chip, you can see it shows a fixed duration rep code cycle lasting 960ns (without any reference to the distance). ![]() Adding more of them doesn't slow down the cycle. In a superconducting qubit quantum computer there are separate control lines going to each qubit, so they can all be operated in parallel.
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