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Register a new userPractical quantum error correction with the XZZX code and Kerr-cat qubits
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The development of robust architectures capable of large-scale fault-tolerant quantum computation should consider both their quantum error-correcting codes, and the underlying physical qubits upon which they are built, in tandem. Following this design principle we demonstrate remarkable error correction performance by concatenating the XZZX surface code with Kerr-cat qubits. We contrast several variants of fault-tolerant systems undergoing different circuit noise models that reflect the physics of Kerr-cat qubits. Our simulations show that our system is scalable below a threshold gate infidelity of $p_mathrm{CX} sim 6.5%$ within a physically reasonable parameter regime, where $p_mathrm{CX}$ is the infidelity of the noisiest gate of our system; the controlled-not gate. This threshold can be reached in a superconducting circuit architecture with a Kerr-nonlinearity of $10$MHz, a $sim 6.25$ photon cat qubit, single-photon lifetime of $gtrsim 64mu$s, and thermal photon population $lesssim 8%$. Such parameters are routinely achieved in superconducting circuits.
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A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum electrodynamics (cQED) architecture. There, the low energy states of a nonlinear electronic oscillator are isolated and addressed as a qubit. These qubits are capacitively coupled to the modes of a microwave-frequency transmission line resonator which serves as a quantum communication bus. Microwave electrical pulses are applied to the resonator to manipulate or measure the qubit state. State control is calibrated using diagnostic sequences that expose systematic errors. Hybridization of the resonator with the qubit gives it a nonlinear response when driven strongly, useful for amplifying the measurement signal to enhance accuracy. Qubits coupled to the same bus may coherently interact with one another via the exchange of virtual photons. A two-qubit conditional phase gate mediated by this interaction can deterministically entangle its targets, and is used to generate two-qubit Bell states and three-qubit GHZ states. These three-qubit states are of particular interest because they redundantly encode quantum information. They are the basis of the quantum repetition code prototypical of more sophisticated schemes required for quantum computation. Using a three-qubit Toffoli gate, this code is demonstrated to autonomously correct either bit- or phase-flip errors. Despite observing the expected behavior, the overall fidelity is low because of decoherence. A superior implementation of cQED replaces the transmission-line resonator with a three-dimensional box mode, increasing lifetimes by an order of magnitude. In-situ qubit frequency control is enabled with control lines, which are used to fully characterize and control the system Hamiltonian.
Biased-noise qubits are a promising candidate for realizing hardware efficient fault-tolerant quantum computing. One promising biased-noise qubit is the Kerr cat qubit, which has recently been demonstrated experimentally. Despite various unique advantages of Kerr cat qubits, we explain how the noise bias of Kerr cat qubits is severely limited by heating-induced leakage in their current implementations. Then, we show that by adding frequency-selective single-photon loss to Kerr cat qubits we can counteract the leakage and thus recover much of their noise bias. We refer to such Kerr cat qubits combined with frequency-selective single-photon loss as colored Kerr cat qubits as they are protected by a colored dissipation. In particular, we show how a suitably engineered lossy environment can suppress the leakage and bit-flip errors of a Kerr cat qubit while not introducing any additional phase-flip errors. Since our scheme only requires single-photon loss, it can be readily implemented by using passive and linear elements. Moreover, our frequency-selectivity technique can be generally applied to energy-gap protected qubits whose computational basis states are given by near degenerate ground states of a Hamiltonian with a non-zero energy gap between the ground and excited state manifolds.
Experimental realization of stabilizer-based quantum error correction (QEC) codes that would yield superior logical qubit performance is one of the formidable task for state-of-the-art quantum processors. A major obstacle towards realizing this goal is the large footprint of QEC codes, even those with a small distance. We propose a circuit based on the minimal distance-3 QEC code, which requires only 5 data qubits and 5 ancilla qubits, connected in a ring with iSWAP gates implemented between neighboring qubits. Using a density-matrix simulation, we show that, thanks to its smaller footprint, the proposed code has a lower logical error rate than Surface-17 for similar physical error rates. We also estimate the performance of a neural network-based error decoder, which can be trained to accommodate the error statistics of a specific quantum processor by training on experimental data.
Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction procedures that use only two ancilla qubits. The procedures are based on adding flags to catch the faults that can lead to correlated errors on the data. They work for various distance-three codes. In particular, our scheme allows one to test the [[5,1,3]] code, the smallest error-correcting code, using only seven qubits total. Our techniques also apply to the [[7,1,3]] and [[15,7,3]] Hamming codes, thus allowing to protect seven encoded qubits on a device with only 17 physical qubits.
Performing large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. The challenge is to design practical quantum error-correcting codes that perform well against realistic noise using modest resources. Here we show that a variant of the surface code -- the XZZX code -- offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favourable sub-threshold resource scaling that can be obtained by specialising a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation.
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