Quantum error correction is a crucial step to realize large-scale universal quantum computing, and the condition for realizing quantum error correction is that the error probability of each operation step must below some threshold. This requires that the qubits’ quality and the quantum gates precision can reach a certain level experimentally. We firstly discuss the mechanism of quantum errors: the precision of quantum gates corresponds to unitary operator errors, and the quality of qubits is attributed to decoherence. Then, according to the threshold of the surface code error correction, we proved the minimum of quantum gate fidelity should not be less than 1 − p with the error probability p, and found the natural decoherence time of qubits that can be used for error correction. This provides some kind of theoretical supports for qubits preparation and performing quantum operations experimentally.
Quantum error correction is a crucial step to realize large-scale universal quantum computing, and the condition for realizing quantum error correction is that the error probability of each operation step must below some threshold. This requires that the qubits’ quality and the quantum gates precision can reach a certain level experimentally. We firstly discuss the mechanism of quantum errors: the precision of quantum gates corresponds to unitary operator errors, and the quality of qubits is attributed to decoherence. Then, according to the threshold of the surface code error correction, we proved the minimum of quantum gate fidelity should not be less than 1 − p with the error probability p, and found the natural decoherence time of qubits that can be used for error correction. This provides some kind of theoretical supports for qubits preparation and performing quantum operations experimentally.
Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be the first major step towards fault-tolerant quantum computation. Here we propose an experiment using the smallest surface code that would allow errors to be detected and corrected for both the X and Z basis of a qubit. This requires 17 physical qubits initially prepared in a product state, on which 16 two-qubit entangling gates are applied before a final measurement of all qubits. Using a realistic error model, it is found that this set-up could successfully demonstrate error correction with two qubit gate fidelities greater that 91% and mesurement fidelities greater than 96%. Fidelities of greater than 99%, however, are required to demonstrate a more convincing route to scalability.
The field of quantum computation currently lacks a formal proof of experimental feasibility. Qubits are fragile and sophisticated quantum error correction is required to achieve reliable quantum computation. The surface code is a promising quantum error correction code, requiring only a physically reasonable 2D lattice of qubits with nearest neighbor interactions. However, existing proofs that reliable quantum computation is possible using this code assume the ability to measure four-body operators and, despite making this difficult to realize assumption, require that the error rate of these operator measurements is less than 10(-9), an unphysically low target. High error rates have been proved tolerable only when assuming tunable interactions of strength and error rate independent of distance, which is also unphysical. In this work, given a 2D lattice of qubits with only nearest neighbor two-qubit gates, and single-qubit measurement, initialization, and unitary gates, all of which have error rate p, we prove that arbitrarily reliable quantum computation is possible provided p < 7.4 × 10(-4), a target that many experiments have already achieved. This closes a long-standing open problem, formally proving the experimental feasibility of quantum computation under physically reasonable assumptions.
A quantum error correction (QEC) code uses Nc quantum bits to construct one ``logical'' quantum bit of better quality than the original ``physical'' ones. QEC theory predicts that the failure probability pL of logical qubits decreases exponentially with Nc provided the failure probability p of the physical qubit is below a certain threshold p<pth. In particular, QEC theorems imply that the logical qubits can be made arbitrarily precise by simply increasing Nc. In this article, we search for physical mechanisms that lie outside of the hypothesis of QEC theorems and set a limit ${\ensuremath{\eta}}_{\mathrm{L}}$ to the precision of the logical qubits (irrespectively of Nc). ${\ensuremath{\eta}}_{\mathrm{L}}$ directly controls the maximum number of operations $\ensuremath{\propto}1/{\ensuremath{\eta}}_{\mathrm{L}}^{2}$ that can be performed before the logical quantum state gets randomized, hence the depth of the quantum circuits that can be considered. We identify a type of error---silent stabilizer failure---as a mechanism responsible for finite ${\ensuremath{\eta}}_{\mathrm{L}}$ and discuss its possible causes. Using the example of the topological surface code, we show that a single local event can provoke the failure of the logical qubit, irrespectively of Nc.
Abstract Fault-tolerant quantum computing requires many qubits with long lifetimes and accurate quantum gate operations. However, external noise limits the computing time and hampers accurate quantum gate operations. Quantum error correction (QEC) codes may extend such limits, but imperfect gate operations during QEC cause errors, which could cancel out QEC. We used density matrix simulations to examine the performance of QEC codes with five qubits. In current quantum devices, less than ten qubits are needed to conduct sufficient gate operations within their lifetime so that it is feasible to implement QEC codes. We analyzed the maximum tolerable error rate and error correction effect of individual QEC codes according to the qubit arrangement and gate accuracy. Assuming a 0.1% gate error probability, a logical ∣ 1 〉 state encoded by a five-qubit QEC code is expected to have a 0.25 higher fidelity than its physical counterpart.
By using a superconducting processor, Google Quantum AI group demonstrated that a logic qubit realized by surface code of quantum error correction performs better when the number of physical qubits increases. Two surface codes to encode logic qubits for scaling are realized experimentally, with multiple cycles of quantum error correcting assisted by ancillary qubits. This result can be considered as an important step toward fault-tolerant quantum computers. In this review paper, we introduce briefly the mechanism of quantum error correction. As an example, Shor’s nine-qubit error correction code is explained. Then, the new experiments of Google quantum AI group are introduced to show their significance in scaling. The advances in other quantum error correction experiments are also reviewed. Finally, the development of quantum computers is discussed.
Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be a major step towards fault-tolerant quantum computation. Here we propose a surface code based experiment that is the smallest, both in terms of code size and circuit depth, that would allow errors to be detected and corrected for both the X and Z bases of a qubit. This requires 17 physical qubits initially prepared in a product state, on which 16 two-qubit entangling gates are applied before a final measurement of all qubits. A platform agnostic error model is applied to give some idea of the noise levels required for success. It is found that a true demonstration of quantum error correction will require fidelities for the preparation and measurement of qubits and the entangling gates to be above 99.