اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRobustness of operator quantum error correction with respect to initialization errors
105
0
0.0
(
0
)
تأليف
Ognyan Oreshkov
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In the theory of operator quantum error correction (OQEC), the notion of correctability is defined under the assumption that states are perfectly initialized inside a particular subspace, a factor of which (a subsystem) contains the protected information. If the initial state of the system does not belong entirely to the subspace in question, the restriction of the state to the otherwise correctable subsystem may not remain invariant after the application of noise and error correction. It is known that in the case of decoherence-free subspaces and subsystems (DFSs) the condition for perfect unitary evolution inside the code imposes more restrictive conditions on the noise process if one allows imperfect initialization. It was believed that these conditions are necessary if DFSs are to be able to protect imperfectly encoded states from subsequent errors. By a similar argument, general OQEC codes would also require more restrictive error-correction conditions for the case of imperfect initialization. In this study, we examine this requirement by looking at the errors on the encoded state. In order to quantitatively analyze the errors in an OQEC code, we introduce a measure of the fidelity between the encoded information in two states for the case of subsystem encoding. A major part of the paper concerns the definition of the measure and the derivation of its properties. In contrast to what was previously believed, we obtain that more restrictive conditions are not necessary neither for DFSs nor for general OQEC codes. This is because the effective noise that can arise inside the code as a result of imperfect initialization is such that it can only increase the fidelity of an imperfectly encoded state with a perfectly encoded one.
قيم البحث
اقرأ أيضاً
We study the performance of quantum error correction codes(QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the most promi
sing surface code, we find that the detection-induced coherent error will result in undetected error terms, which will accumulate and evolve into logical errors. However, we show that this kind of errors will be alleviated by increasing the code size, akin to eliminating other types of errors discussed previously. We also find that with detection-induced coherent errors, the exact surface code becomes an approximate QECC.
We study the conditions under which a subsystem code is correctable in the presence of noise that results from continuous dynamics. We consider the case of Markovian dynamics as well as the general case of Hamiltonian dynamics of the system and the e
nvironment, and derive necessary and sufficient conditions on the Lindbladian and system-environment Hamiltonian, respectively. For the case when the encoded information is correctable during an entire time interval, the conditions we obtain can be thought of as generalizations of the previously derived conditions for decoherence-free subsystems to the case where the subsystem is time dependent. As a special case, we consider conditions for unitary correctability. In the case of Hamiltonian evolution, the conditions for unitary correctability concern only the effect of the Hamiltonian on the system, whereas the conditions for general correctability concern the entire system-environment Hamiltonian. We also derive conditions on the Hamiltonian which depend on the initial state of the environment, as well as conditions for correctability at only a particular moment of time. We discuss possible implications of our results for approximate quantum error correction.
Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can become excited,
creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code for quantum error correction. We investigate the accumulation and dynamics of leakage during error correction. Using this protocol, we find lower rates of logical errors and an improved scaling and stability of error suppression with increasing qubit number. This demonstration provides a key step on the path towards scalable quantum computing.
Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near
$10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local and that performance is maintained over many rounds of error correction, two major outstanding experimental challenges. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than $100times$ when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing.
To implement fault-tolerant quantum computation with continuous variables, the Gottesman--Kitaev--Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to real
ize large scale quantum computation with the GKP qubit [Phys. Rev. X. {bf 8}, 021054 (2018)], harnessing the virtue of analog information in the GKP qubits. In the present work, to reduce the number of qubits required for large scale quantum computation, we propose the tracking quantum error correction, where the logical-qubit level quantum error correction is partially substituted by the single-qubit level quantum error correction. In the proposed method, the analog quantum error correction is utilized to make the performances of the single-qubit level quantum error correction almost identical to those of the logical-qubit level quantum error correction in a practical noise level. The numerical results show that the proposed tracking quantum error correction reduces the number of qubits during a quantum error correction process by the reduction rate $left{{2(n-1)times4^{l-1}-n+1}right}/({2n times 4^{l-1}})$ for $n$-cycles of the quantum error correction process using the Knills $C_{4}/C_{6}$ code with the concatenation level $l$. Hence, the proposed tracking quantum error correction has great advantage in reducing the required number of physical qubits, and will open a new way to bring up advantage of the GKP qubits in practical quantum computation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
