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.
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.
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.
Non-Markovian noise, arising from memory effects in the environment, poses substantial challenges to conventional quantum noise suppression protocols, including quantum error correction and mitigation. We introduce a channel representation for arbitrary non-Markovian quantum dynamics, termed the Choi channel, which translates the complex dynamics of non-Markovian noise into the familiar picture of noise channels. It therefore provides a systematic way to design non-Markovian noise suppression protocols: one can apply existing channel-level error-suppression techniques in the Choi-channel picture and then translate them back to the circuit picture. The performance of the resulting non-Markovian protocols, including their noise-suppression effects and complexity, can often be inherited directly from the corresponding Choi-channel protocols without requiring a separate analysis. With this framework, we devise new protocols using Pauli twirling, probabilistic error cancellation, and virtual channel purification. Pauli twirling reduces non-Markovian noise to noise with only classical temporal correlations; probabilistic error cancellation can fully cancel non-Markovian noise; and virtual channel purification can suppress non-Markovian noise without detailed knowledge of its specific form. Through these examples, the Choi channel serves as a foundational bridge for systematically converting existing channel-level techniques into non-Markovian noise suppression protocols.
As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate-set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one- and two-qubit gates can be compressed by 10× and 100× , respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two-qubit interleaved randomized benchmarking fidelities of 99.8% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large arrays of quantum devices with non-Markovian noise. Published by the American Physical Society 2024
In non-Markovian systems, the current state of the system depends on the full or partial history of its past evolution. Owing to these time correlations, non-Markovian noise violates common assumptions in gate characterization protocols such as randomized benchmarking and gate-set tomography. Here, we perform a case study of the effects of a quantum non-Markovian bath on qubit randomized benchmarking experiments. We consider a model consisting of qubits coupled to a multimode bosonic bath. We apply unitary operations on the qubits, interspersed with brief interactions with the environment governed by a Hamiltonian. Allowing for non-Markovianity in the interactions leads to clear differences in the randomized benchmarking decay curves in this model, which we analyze in detail. The Markovian model’s decay is exponential as expected, whereas the model with non-Markovian interactions displays a much slower, almost polynomial, decay. We develop efficient numerical methods for this problem that we use to support our theoretical results. These results inform efforts on incorporating quantum non-Markovian noise in the characterization and benchmarking of quantum devices.
Simulating open quantum systems on digital quantum computers typically relies on the use of auxiliary qubits, resulting in overheads of noisy multi-qubit gates, that severely limit execution on near-term hardware. In this work, we explore the simulation of non-Markovian dynamics as well as memory channels leveraging the method of trajectory mixing, valid for mixed unitary channels. This allows to drastically reduce circuit depth, trading entangling gates for a statistical mixture of independent, pure state trajectories. Using a realistic noise model calibrated to modern quantum processors, we show the benefits of this approach, yielding higher state fidelity and better preservation of quantum correlations. This shows the possibility of simulating long-time non-Markovian evolutions with low noise and limited resources.
Abstract In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress well into the complex multi-qubit regime, attention is turning to understanding the appearance and mitigation of correlated — or non-Markovian — noise, which poses a serious challenge to the progression of quantum technology. This error type has previously remained elusive to characterisation techniques. Here, we develop a framework for characterising non-Markovian dynamics in quantum systems and experimentally test it on multi-qubit superconducting quantum devices. Where noisy processes cannot be accounted for using standard Markovian techniques, our reconstruction predicts the behaviour of the devices with an infidelity of 10 −3 . Our results show this characterisation technique leads to superior quantum control and extension of coherence time by effective decoupling from the non-Markovian environment. This framework, validated by our results, is applicable to any controlled quantum device and offers a significant step towards optimal device operation and noise reduction.