We analytically characterize how the location and the local or correlated structure of stochastic Pauli errors affect a three-qubit coherent quantum-teleportation circuit. Independent local channels and a fully correlated two-qubit channel are inserted separately in six configurations. Propagating each Pauli-error realization through the Clifford circuit yields the effective channel on Bob's qubit and analytical expressions for the average and state-resolved fidelities. Under a common ordered-pair probability convention, the six configurations form three pairs that induce equivalent reduced channels on Bob. Within each pair, corresponding Pauli-error realizations have the same probabilities and produce the same effective Pauli operator on Bob's output state. The equivalence therefore holds for every input state within the stochastic Pauli models considered here, rather than only for the average fidelity. Correlated Z errors do not affect the output for the first pair; local X and Z errors exhibit complementary qubit sensitivity for the second; and correlated same-axis Pauli errors cancel for the third. These results classify the error response of the selected circuit configurations and show that it depends jointly on the error statistics, Pauli axis, and position within the protocol.
We analytically characterize how the location and the local or correlated structure of stochastic Pauli errors affect a three-qubit coherent quantum-teleportation circuit. Independent local channels and a fully correlated two-qubit channel are inserted separately in six configurations. Propagating each Pauli-error realization through the Clifford circuit yields the effective channel on Bob's qubit and analytical expressions for the average and state-resolved fidelities. Under a common ordered-pair probability convention, the six configurations form three pairs that induce equivalent reduced channels on Bob. Within each pair, corresponding Pauli-error realizations have the same probabilities and produce the same effective Pauli operator on Bob's output state. The equivalence therefore holds for every input state within the stochastic Pauli models considered here, rather than only for the average fidelity. Correlated Z errors do not affect the output for the first pair; local X and Z errors exhibit complementary qubit sensitivity for the second; and correlated same-axis Pauli errors cancel for the third. These results classify the error response of the selected circuit configurations and show that it depends jointly on the error statistics, Pauli axis, and position within the protocol.
Abstract The purpose of this paper is to further investigate the correlated and memory effects in 3D-Pauli-like noisy channels for controlled teleportation of an arbitrary unknown single-qutrit state. We first construct a three-qutrit maximally entangled state in a three-dimensional (3D) Hilbert space and subsequently propose a 3D controlled quantum teleportation (CQT) scheme for an arbitrary unknown single-qutrit state using the constructed three-qutrit maximally entangled state as the quantum channel. In this ideal case, through a few simple 3D unitary operations, the two communicating parties can perfectly accomplish the teleportation task under the supervision of the controller. Subsequently, we examine the performance of this CQT scheme under two successive uses of a 3D-Pauli-like noisy channel with memory, where the noise errors are categorized into four types: trit-flip, t-phase-flip, trit-phase-flip, and t-depolarizing. For each noise type, an analytical expression of the average fidelity is derived as a function of both the noise and memory parameters. Specifically, we find that, regardless of the noise strength, memory enhances the average fidelity for trit-flip and t-depolarizing noises, whereas for t-phase-flip and trit-phase-flip noises, memory reduces the average fidelity once the noise intensity exceeds a certain threshold. This indicates that in the first two noisy channels, memory can improve the communication efficiency of CQT, while in the latter two, excessive noise causes memory to diminish the teleportation performance.
Quantum noise is a central challenge in quantum computing across many applications. Extensive work has examined how qubits couple to their environment, leading to decoherence and irreversible relaxation. This work studies a continuous coherent noise model for quantum circuits and compares it with a discrete Pauli model. The focus is on small, coherent gate errors that accumulate across circuit depth. These errors are modeled as random rotations on the Bloch sphere using a von Mises-Fisher distribution. In the small-angle limit, the model reduces to an isotropic Gaussian distribution. We test the model on quantum error-correction circuits based on the [[5,1,3]] and [[7,1,3]] codes. A variant of Grover's search circuit with different qubit counts is also examined. To enable fair comparison, we introduce a model-independent matching scheme. Pauli and continuous noise channels are aligned using the binary entropy at readout. This isolates the effect of noise structure at fixed uncertainty. An approximate analytical method for the propagation of coherent errors is also developed. The method tracks error distributions both on Clifford and non-Clifford circuits without full Monte Carlo sampling. It reduces simulation cost while preserving accuracy for circuit-level error estimates. The approximation is validated against brute-force simulations, identifying its regime of validity with Clifford and non-Clifford circuits under error correction. Our results show that continuous coherent noise and Pauli noise lead to comparable logical-error trends in the stabilizer-code circuits studied here. This behavior is consistent with syndrome extraction projecting a general single-qubit error onto Pauli-error subspaces before recovery. They also show where simplified propagation models work well and where their accuracy is reduced.
Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip, and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.
Characterizing noise in quantum circuits is fundamentally limited by gauge degrees of freedom; certain parameters, such as the individual contributions of state preparation and measurement (SPAM) errors, are in principle unlearnable from any experiment within the gate set. Here, we show that the physical structure of realistic noise processes imposes approximate symmetry constraints on the Pauli fidelities of gate noise channels. These symmetries relate the fidelity of a Pauli P and its gate-conjugate UgPUg†, and can be used to fix the gauge using only knowledge of the error type and not its magnitude. Using Lindbladian perturbation theory, we analyze a broad class of Clifford gates, including ZZπ/2, CZ, CNOT, iSWAP, and SWAP, and demonstrate that coherent errors do not induce first-order asymmetry, while only a restricted set of predominantly off-diagonal dissipative errors can break the symmetry at first order, for which we derive simple selection rules. Notably, common single-qubit noise sources such as T1-relaxation and T2φ-pure-dephasing can only cause asymmetry at second order. Leveraging these symmetries to fix the gauge enables systematic identification of SPAM errors, simplifying error characterization and mitigation. We validate our results numerically and experimentally on IBM Kingston.
We investigate noise propagation in encrypted quantum cloning by formulating the protocol in terms of effective recovery channels. For local single-qubit completely positive trace-preserving noise, a Pauli-basis expansion of the Kraus operators reveals a strong dependence on the location of the physical channel. Noise on an auxiliary signal qubit leaves the reduced recovered state unchanged, whereas noise on an auxiliary key qubit induces a Pauli-diagonal effective channel on the recovered qubit. For the core qubits, the error propagation additionally depends on the parity of the number of entangled pairs. In particular, for noise on the core key qubit with odd parity, distinct physical Pauli sectors merge into the same effective sector, converting isotropic depolarizing noise into an anisotropic recovery channel. We also relate Werner-type resource imperfections to local depolarizing noise and distinguish distributed product depolarization from genuine global depolarization. The results demonstrate that the effective recovery noise is governed not only by noise strength, but also by its physical location and by the structure of the encryption-decryption protocol.
Randomized compiling (RC) is an established tool to tailor arbitrary quantum noise channels into Pauli errors. The effect of both spatial and temporal noise correlations in randomly compiled circuits, however, is not fully understood. Here, we show that for a broad class of correlated Gaussian noise, RC reduces both the strength and temporal range of correlations. For Clifford circuits, we derive a simple analytical expression for the circuit fidelity of randomly compiled circuits. Surprisingly, we show that this fidelity is always increased by the presence of correlations, suggesting that correlations are a resource in randomly compiled circuits. To leading order in system-bath coupling, we also show that RC suppresses the quantum component of bath correlations, implying that one can safely treat weak noise as being classical. Finally, through extensive numerical simulations, we show that our results remain valid for many relevant non-Clifford circuits. These results clarify how RC mitigates memory effects and enhances circuit robustness.