It is by now well established that noise itself can be useful for performing quantum information processing tasks. We present results which show how one can effectively reduce the error rate associated with a noisy quantum channel by counteracting its detrimental effects with another form of noise. In particular, we consider the effect of adding on top of a purely Markovian (Lindblad) dynamics, a more general form of dissipation, which we refer to as generalized-Markovian noise. This noise has an associated memory kernel and the resulting dynamics are described by an integrodifferential equation. The overall dynamics are characterized by decay rates which depend not only on the original dissipative time scales but also on the new integral kernel. We find that one can engineer this kernel such that the overall rate of decay is lowered by the addition of this noise term. We illustrate this technique for the case where the bare noise is described by a dephasing Pauli channel. We analytically solve this model and show that one can effectively double (or even triple) the length of the channel, while achieving the same fidelity, entanglement, and error threshold. We numerically verify this scheme can also be used to protect against thermal Markovian noise (at nonzero temperature), which models spontaneous emission and excitation processes. A physical interpretation of this scheme is discussed, whereby the added generalized-Markovian noise causes the system to become periodically decoupled from the background Markovian noise.
It is by now well established that noise itself can be useful for performing quantum information processing tasks. We present results which show how one can effectively reduce the error rate associated with a noisy quantum channel by counteracting its detrimental effects with another form of noise. In particular, we consider the effect of adding on top of a purely Markovian (Lindblad) dynamics, a more general form of dissipation, which we refer to as generalized-Markovian noise. This noise has an associated memory kernel and the resulting dynamics are described by an integrodifferential equation. The overall dynamics are characterized by decay rates which depend not only on the original dissipative time scales but also on the new integral kernel. We find that one can engineer this kernel such that the overall rate of decay is lowered by the addition of this noise term. We illustrate this technique for the case where the bare noise is described by a dephasing Pauli channel. We analytically solve this model and show that one can effectively double (or even triple) the length of the channel, while achieving the same fidelity, entanglement, and error threshold. We numerically verify this scheme can also be used to protect against thermal Markovian noise (at nonzero temperature), which models spontaneous emission and excitation processes. A physical interpretation of this scheme is discussed, whereby the added generalized-Markovian noise causes the system to become periodically decoupled from the background Markovian noise.
Non-Markovian noise, arising from environmental memory effects, is the most general and challenging form of noise in quantum computing, and is typically difficult to characterize and suppress. Here, we analyze and experimentally demonstrate a non-Markovian noise suppression scheme inspired by quantum purification protocols. We theoretically prove that, even without noise calibration and assumptions on specific noise models, the scheme can exponentially reduce non-Markovian error rates with respect to the ancillary system size. We implement the protocol using nuclear spins, demonstrating that non-Markovian noise can be suppressed for both unitary operations and non-unitary channels. The observed fidelities and process tomography show close agreement with theoretical predictions, confirming the practicality and effectiveness of the scheme.
Noise forms a central obstacle to effective quantum information processing. Recent experimental advances have enabled the tailoring of noise properties through Pauli twirling, transforming arbitrary noise channels into Pauli channels. This underpins theoretical descriptions of fault-tolerant quantum computation and forms an essential tool in noise characterization and error mitigation. Pauli-Lindblad channels have been introduced to aptly parameterize quasi-local Pauli errors across a quantum register, excluding negative Pauli-Lindblad parameters relying on the Markovianity of the underlying noise processes. We point out that caution is required when parameterizing channels as Pauli-Lindblad channels with nonnegative parameters. For this, we study the effects of Pauli twirling on Markovianity. We use the notion of Markovianity of a channel (rather than that of an entire semigroup) and prove a general Pauli channel is non-Markovian if and only if at least one of its Pauli-Lindblad parameters is negative. Using this, we show that Markovian quantum channels often become non-Markovian after Pauli twirling. The Pauli-twirling induced non-Markovianity necessitates the use of negative Pauli-Lindblad parameters for a correct noise description in experimentally realistic scenarios. An important example is the implementation of the X-gate under standard Markovian noise. As such, our results have direct implications for quantum error mitigation protocols that rely on accurate noise characterization.
Non-Markovian noise, arising from environmental memory effects, is the most general and challenging form of noise in quantum computing, and is typically difficult to characterize and suppress. Here, we analyze and experimentally demonstrate a non-Markovian noise suppression scheme inspired by quantum purification protocols. We theoretically prove that, even without noise calibration and assumptions on specific noise models, the scheme can exponentially reduce non-Markovian error rates with respect to the ancillary system size. We implement the protocol using nuclear spins, demonstrating that non-Markovian noise can be suppressed for both unitary operations and nonunitary channels. The observed fidelities and process tomography show close agreement with theoretical predictions, confirming the practicality and effectiveness of the scheme.
A major problem in exploiting microscopic systems for developing a new technology based on the principles of quantum information is the influence of noise, which tends to work against the quantum features of such systems. It thus becomes crucial to understand how noise affects the evolution of quantum circuits: several techniques have been proposed, among which stochastic differential equations (SDEs) can represent a very convenient tool. We show how SDEs naturally map any Markovian noise into a linear operator, which we call a noise gate, acting on the wave function describing the state of the circuit, and we discuss some examples. We show that these gates can be manipulated like any standard quantum gate, thus simplifying in certain circumstances the task of computing the overall effect of the noise at each stage of the protocol. This approach yields equivalent results to those derived from the Lindblad equation; yet, as we show, it represents a handy and fast tool for performing computations, and, moreover, it allows for fast numerical simulations and generalizations to non-Markovian noise. In detail we review the depolarizing channel and the generalized amplitude damping channel in terms of this noise gate formalism and show how these techniques can be applied to any quantum circuit.
The ubiquitous effects of the environment on quantum-mechanical systems generally cause temporally correlated fluctuations. This particularly holds for systems of interest for quantum computation where such effects lead to correlated errors. The Markovian approximation neglects these correlations and thus fails to accurately describe open-system dynamics where these correlations become relevant. In driven open systems, yet another approximation is persistently used, often unknowingly, in which one describes the decay effects independently from the time-dependent controlling fields acting on the system, thereby ignoring further temporally correlated effects. To overcome these shortcomings, we develop a quantum master equation for driven systems weakly coupled to quantum environments that avoids the aforementioned field-independent approximation, as well as the Markovian approximation. Our method makes it possible to track all occurring decay channels and their time-dependent generalized rates which we illustrate in the example of a generally driven two-level system. We also demonstrate that correlated and field-dependent dissipative effects can lead to an increase in the performance of single-qubit gate operations.
An essential action in quantum information processing is the manipulation (control) of a single qubit, ideally a closed two-level system. However, in realistic applications, quantum processes are often under the influence of the external environment, e.g., presenting some degree of dissipation and decoherence. In this paper we address the emerging difficulties in the (tracking) quantum control of a two-level system under the influence of both Markovian and non-Markovian noise. We employ a same framework to treat both situations, a Lindblad-type equation, but considering that for the former (latter) case, the decay rate $\mathrm{\ensuremath{\Gamma}}$ is time independent (dependent). We discuss the conditions leading to a breakdown of the quantum control and eventual ways to overcome the problem, like employing a fast control scheme or controlling the off-diagonal terms of the system density matrix. Surprisingly, for Markovian noise such breakdown time decreases with $\mathrm{\ensuremath{\Gamma}}$ not as an exponential but as a power law. This indicates that the quantum control should be possible for a coupling between the system and the environment stronger than previously expected. Moreover, we find that for non-Markovian noise, the breakdown time is longer when there is backflow, i.e., $\mathrm{\ensuremath{\Gamma}}(t)$ can be negative. The present theoretical results point to certain favorable scenarios to operate qubits even in a noisy medium.