![]() ![]() In the past two decades, various constructions of quantum error-correcting codes (QECCs) have been developed, leading to many good code families. In experiment, we implement basic functions of the code by realising logical state preparation, transversal logical operations and state decoding.Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. As a preparatory theoretical step, we recompile the universal encoding circuit that prepares an arbitrary logical state in order to realise it with the fewest possible number of nearest-neighbour two-qubit gates. Here, we focus on the realisation of the five-qubit code with superconducting qubit systems. While proof-of-principle experimental demonstrations of the code have been conducted on NMR systems , whether it could be incorporated in more scalable quantum computing systems and protect errors presented in these systems remain open. Here, we focus on the five-qubit code, the ‘perfect’ code that can protect a logical qubit from an arbitrary single physical error using the smallest number of qubits . It remains an open challenge to realise a fully-functional QECC. Nevertheless, previous experiments are limited to restricted codes for correcting certain types of errors or the preparation of specific logical states. These works have shown the success of realising error-correcting codes with non-destructive stabiliser measurements and their application in extending the system lifetime . In experiment, several small quantum error-correcting codes (QECCs), including the repetition code , the four-qubit error-detecting code , the seven-qubit color code , the bosonic quantum error-correcting code and others , have been realised with different hardware platforms. Providing that the machine is sufficiently large (high qubit count), and that physical errors happen with a probability below a certain threshold, then such errors can be systematically detected and corrected . The logical qubits of an algorithm can be represented using a larger number of flawed physical qubits. The theory of fault tolerance has been developed as the long-term solution to this issue, enabling universal error-free quantum computing with noisy quantum hardware . However, quantum computers are notoriously difficult to control, due to their ubiquitous yet inevitable interaction with their environment, together with imperfect manipulations that constitute the algorithm. ![]() Quantum computers can tackle classically intractable problems and efficiently simulate many-body quantum systems . Quantum error-correcting code, superconducting qubit, five-qubit code, error detection, logical operation INTRODUCTION Our work demonstrates each key aspect of the code and verifies the viability of experimental realisation 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 stabilisers. 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. Quantum error correction is an essential ingredient for universal quantum computing. ![]()
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