Performance of topological quantum error correction in the presence of correlated noise

Abstract

We investigate the efficacy of topological quantum error-correction in correlated noise model which permits collective coupling of all the codeword qubits to the same non-Markovian environment. In this noise model, the probability distribution over set of phase-flipped qubits, decays sub-exponentially in the size of the set and carries non-trivial likelihood of the occurring large numbers of qubits errors. We find that in the presence of noise correlation, one cannot guarantee arbitrary high computational accuracy simply by incrementing the codeword size while retaining constant noise level per qubit operation. However, if instead, per-operation qubit error probability in an n-qubits long codeword is reduced O(\sqrt{n}) times below the accuracy threshold, arbitrarily accurate quantum computation becomes feasible with acceptable scaling of the codeword size. Our results suggest that progressively reducing noise level in qubits and gates is as important as continuously integrating more qubits to realize scalable and reliable quantum computer.

Reconfiguring quantum error-correcting codes for real-life errors

“…The generality of proposed commute-back method empowers it to subsume variety of realistic noise models that can commute with code-space projection operator P. One interesting case is that of spatially and temporally correlated noise given in [29]. Their noise operator (see figures 3 and 4 in [29]) has the same form as that of ε used in this study, except for the unitary noise component.…”

“…The generality of proposed commute-back method empowers it to subsume variety of realistic noise models that can commute with code-space projection operator P. One interesting case is that of spatially and temporally correlated noise given in [29]. Their noise operator (see figures 3 and 4 in [29]) has the same form as that of ε used in this study, except for the unitary noise component. The mapping is very simple; the control unitary gate of ε become controlled rotations about z-axis where (small) rotation angle approximates the strength of correlated noise (please find detailed discussion on correlation strength parameter L 0 in section-4 of [29]).…”

“…Their noise operator (see figures 3 and 4 in [29]) has the same form as that of ε used in this study, except for the unitary noise component. The mapping is very simple; the control unitary gate of ε become controlled rotations about z-axis where (small) rotation angle approximates the strength of correlated noise (please find detailed discussion on correlation strength parameter L 0 in section-4 of [29]). Another example of commuting noise is the depolarizing operation, its admissibility considerably broadens applicability of the method.…”

Decoherence in quantum cavities: Environmental erasure of carpet-type structures

“…Decoherence is ubiquitous in a myriad of systems and applications [9], e.g., quantum dots [10][11][12], quantum game theory [13,14], quantum walks [15,16], quantum information [17][18][19][20], two-level systems [21][22][23], cavities [24][25][26], ion trapping [27] or the spin-boson model [9,28]. Similarly different models have been proposed to study and quantify its effects on the coherence of quantum systems as well as to control them [29][30][31][32][33][34][35][36][37][38][39]. Furthermore, a number of experiments has also been conduced in recent year to test some of such models at a fundamental level [40][41][42][43].…”

Quantum Circuit Engineering for Correcting Coherent Noise

“…In state-of-art quantum processors, two-qubit gates are at least order of magnitude noisier than their single-qubit counterparts and limit the fidelity of quantum circuit [1][2][3][4]. Higher operational inaccuracy is not the only bottleneck of state fidelity, action of CNOT gates sequence adds to several context-dependent noise sources including crosstalk [5], coherent/systematic errors [6,7], correlated errors [8] and non-markovian bath [9,10]. These are some examples of unforeseen errors [11] mostly unfolding during the execution of quantum circuit.…”