I construct a quantum error correction code (QECC) in higher spin systems using the idea of multiplicative group character. Each $N$ state quantum particle is encoded as five $N$ state quantum registers. By doing so, this code can correct any quantum error arising from any one of the five quantum registers. This code generalizes the well-known five qubit perfect code in spin-1/2 systems and is shown to be optimal for higher spin systems. I also report a simple algorithm for encoding. The importance of multiplicative group character in constructing QECCs will be addressed.
State preparation and measurement (SPAM) errors limit the performance of near-term quantum computers and their potential for practical application. SPAM errors are partly correctable after a calibration step that requires, for a complete implementation on a register of $n$ qubits, $2^n$ additional measurements. Here we introduce an approximate but efficient method for multiqubit SPAM error characterization and mitigation requiring the classical processing of $2^n \! \times 2^n$ matrices, but only $O(4^k n^2)$ measurements, where $k=O(1)$ is the number of qubits in a correlation volume. We demo…
Hybrid Quantum Error Correction and Mitigation by Purification
New York University Shanghai（纽约大学上海分校）；NYU-ECNU Institute of Physics at NYU Shanghai（纽约大学上海纽约大学-华东师范大学物理研究所）；Department of Physics, New York University（纽约大学物理系）；Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, New York University Abu Dhabi（阿布扎比纽约大学研究学院量子与拓扑系统中心）；New York University（纽约大学）
Five-wave-packet quantum error correction based on continuous-variable cluster entanglement
量子纠错在量子通信和量子计算中保护量子态不受噪声和退相干的影响，使人们能够进行故障洪流量子信息处理。实验证明了一种针对单一随机错误的五波包码量子纠错方案，其理论模型是由S. L. Braunstein和T. A.沃克利用连续变量团簇纠缠态的五个子模作为五个编码通道。特别地，在我们的编码方案中，输入态的信息只分布在五个通道中的三个通道上，因此在剩下的两个通道中出现的任何错误都不会影响输出态，即输出量子态不受这两个通道中的错误的影响。对真空态和压缩态的单通道随机误差进行了修正，得到的输出态的量子效率超过了相应的经典极限。
In quantum error correction, it is an important assumption that errors on different qubits are independent. In our previous work [Phys. Rev. A {\bf 92}, 052320 (2015)], the generality of the concatenated five-qubit code has been investgated when noises of the principal system and the auxiliary environment are assumed to be the same. In the error correction with concatenated code, tiny differences (in fidelity or independent errors) between initial quantum channels may introduce different effective channels in the next level, and therefore, it is necessary to study a meaningful question: Does f…
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, t…
Quantum error correction will be essential for realizing the full potential of large-scale quantum information processing devices. Fundamental to its experimental realization is the repetitive detection of errors via projective measurements of quantum correlations among qubits, and correction using conditional feedback. Performing these tasks repeatedly requires a system in which measurement and feedback decision times are short compared to qubit coherence times, where the measurement reproduces faithfully the desired projection, and for which the measurement process has no detrimental effect …
Quantum error correction requires the detection of errors by reliable measurements of suitable multi-qubit correlation operators. Here, we experimentally demonstrate a fault-tolerant weight-4 parity check measurement scheme. An additional 'flag' qubit serves to detect errors occurring throughout the parity measurement, which would otherwise proliferate into uncorrectable weight-2 errors on the qubit register. We achieve a flag-conditioned parity measurement single-shot fidelity of 93.2(2)\%. Deliberately injecting bit and phase-flip errors, we show that the fault-tolerant protocol is capable o…
The accumulation of quantum phase in response to a signal is the central mechanism of quantum sensing, as such, loss of phase information presents a fundamental limitation. For this reason approaches to extend quantum coherence in the presence of noise are actively being explored. Here we experimentally protect a room-temperature hybrid spin register against environmental decoherence by performing repeated quantum error correction whilst maintaining sensitivity to signal fields. We use a long-lived nuclear spin to correct multiple phase errors on a sensitive electron spin in diamond and realiz…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spi…
Solid state quantum emitters with spin registers are promising platforms for quantum communication, yet few emit in the narrow telecom band necessary for low-loss fiber networks. Here we create and isolate near-surface single vanadium dopants in silicon carbide (SiC) with stable and narrow emission in the O-band (1278-1388 nm), with brightness allowing cavity-free detection in a wafer-scale CMOS-compatible material. In vanadium ensembles, we characterize the complex d1 orbital physics in all five available sites in 4H-SiC and 6H-SiC. The optical transitions are sensitive to mass shifts from lo…
