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arXiv:1603.03761 · Physical Review Letters

Estimating the Coherence of Noise in Quantum Control of a Solid-State Qubit

Guanru Feng, Joel J. Wallman, Brandon Buonacorsi, Franklin H. Cho, Daniel K. Park, Tao Xin, Dawei Lu, Jonathan Baugh, Raymond Laflamme

Published Dec 20, 2016• 44 citations
arXivHTMLPDF

Abstract

To exploit a given physical system for quantum information processing, it is critical to understand the different types of noise affecting quantum control. Distinguishing coherent and incoherent errors is extremely useful as they can be reduced in different ways. Coherent errors are generally easier to reduce at the hardware level, e.g., by improving calibration, whereas some sources of incoherent errors, e.g., T_{2}^{*} processes, can be reduced by engineering robust pulses. In this work, we illustrate how purity benchmarking and randomized benchmarking can be used together to distinguish between coherent and incoherent errors and to quantify the reduction in both of them due to using optimal control pulses and accounting for the transfer function in an electron spin resonance system. We also prove that purity benchmarking provides bounds on the optimal fidelity and diamond norm that can be achieved by correcting the coherent errors through improving calibration.

DOI
10.1103/physrevlett.117.260501

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To exploit a given physical system for quantum information processing, it is critical to understand the different types of noise affecting quantum control. Distinguishing coherent and incoherent errors is extremely useful as they can be reduced in different ways. Coherent errors are generally easier to reduce at the hardware level, e.g., by improving calibration, whereas some sources of incoherent errors, e.g., T_{2}^{*} processes, can be reduced by engineering robust pulses. In this work, we illustrate how purity benchmarking and randomized benchmarking can be used together to distinguish between coherent and incoherent errors and to quantify the reduction in both of them due to using optimal control pulses and accounting for the transfer function in an electron spin resonance system. We also prove that purity benchmarking provides bounds on the optimal fidelity and diamond norm that can be achieved by correcting the coherent errors through improving calibration.
Noise mechanisms in quantum systems can be broadly characterized as either coherent (i.e., unitary) or incoherent. For a given fixed average error rate, coherent noise mechanisms will generally lead to a larger worst-case error than incoherent noise. We show that the coherence of a noise source can be quantified by the unitarity , which we relate to the average change in purity averaged over input pure states. We then show that the unitarity can be efficiently estimated using a protocol based on randomized benchmarking that is efficient and robust to state-preparation and measurement errors. We also show that the unitarity provides a lower bound on the optimal achievable gate infidelity under a given noisy process.
In this study, we employ purity benchmarking (PB) to explore the dynamics of gate noise in a superconducting qubit system. Over 1110 h of observations on an Xmon qubit, we simultaneously measure the coherence noise budget across two different operational frequencies. We find that incoherent errors, which predominate in overall error rates, exhibit minimal frequency dependence, suggesting that they are primarily due to wideband, diffusive incoherent error sources. In contrast, coherent errors, although less prevalent, show significant sensitivity to operational frequency variations and telegraphic noise. We hypothesize that this sensitivity is due to interactions with a single strongly coupled environmental defect—modeled as a two-level system—which influences qubit control parameters and causes coherent calibration errors. Our results also demonstrate that PB offers improved sensitivity, capturing additional dynamics that conventional relaxation time measurements cannot detect, thus presenting a more comprehensive method for capturing dynamic interactions within quantum systems. The intricate nature of these coherence dynamics underscores the need for further research.
Complex quantum systems and their various applications are susceptible to noise of coherent and incoherent nature. Characterization of noise and its sources is an open, key challenge in quantum technology applications, especially in terms of distinguishing between inherent incoherent noise and systematic coherent errors. In this paper, we study a scheme of repeated sequential measurements that enables the characterization of incoherent errors by reducing the effects of coherent errors. We demonstrate this approach using a coherently controlled nitrogen vacancy in diamond, coupled to both a natural nuclear spin bath (non-Markovian) and to experimentally controlled relaxation through an optical pumping process (nearly Markovian). Our results show mitigation of coherent errors both for Markovian and non-Markovian incoherent noise profiles. We apply this scheme to the estimation of the dephasing time (T2*) due to incoherent noise. We observe an improved robustness against coherent errors in the estimation of dephasing time (T2*) compared to the standard (Ramsey) measurement.
Quantum information processing has been the subject of countless discoveries since the early 1990's. It is believed to be the way of the future for computation: using quantum systems permits one to perform computation exponentially faster than on a regular classical computer. Unfortunately, quantum systems that not isolated do not behave well. They tend to lose their quantum nature due to the presence of the environment. If key information is known about the noise present in the system, methods such as quantum error correction have been developed in order to reduce the errors introduced by the environment during a given quantum computation. In order to harness the quantum world and implement the theoretical ideas of quantum information processing and quantum error correction, it is imperative to understand and quantify the noise present in the quantum processor and benchmark the quality of the control over the qubits. Usual techniques to estimate the noise or the control are based on quantum process tomography (QPT), which, unfortunately, demands an exponential amount of resources. \n \nThis thesis presents work towards the characterization of noisy processes in an efficient manner. The protocols are developed from a purely abstract setting with no system-dependent variables. To circumvent the exponential nature of quantum process tomography, three different efficient protocols are proposed and experimentally verified. The first protocol uses the idea of quantum error correction to extract relevant parameters about a given noise model, namely the correlation between the dephasing of two qubits. Following that is a protocol using randomization and symmetrization to extract the probability that a given number of qubits are simultaneously corrupted in a quantum memory, regardless of the specifics of the error and which qubits are affected. Finally, a last protocol, still using randomization ideas, is developed to estimate the average fidelity per computational gates for single and multi qubit systems. \n \nEven though liquid state NMR is argued to be unsuitable for scalable quantum information processing, it remains the best test-bed system to experimentally implement, verify and develop protocols aimed at increasing the control over general quantum information processors. For this reason, all the protocols described in this thesis have been implemented in liquid state NMR, which then led to further development of control and analysis techniques.
Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (2008 Phys. Rev. A 77 012307). We report an error per randomized π/2 pulse of 1.3±0.1 × 10 −4 with a single-qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one- and two-qubit gates of 4.7±0.3 × 10 −3 for a three-qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.
Characterization of quantum devices generates insights into their sources of disturbances. State-of-the-art characterization protocols often focus on incoherent noise and eliminate coherent errors when using Pauli or Clifford twirling techniques. This approach biases the structure of the effective noise and adds a circuit and sampling overhead. We motivate the extension of an incoherent local Pauli noise model to coherent errors and present a practical characterization protocol for an arbitrary gate layer. Notably, the coherent noise estimation is robust to Pauli noise. We demonstrate our protocol on a superconducting hardware platform and identify the leading coherent errors. To verify the characterized noise structure, we mitigate its coherent and incoherent components using a gate-level coherent noise mitigation scheme in conjunction with probabilistic error cancelation. The proposed characterization procedure opens up possibilities for device calibration, hardware development, and improvement of error mitigation and correction techniques.