Researchers at the Karlsruhe Institute of Technology have identified that non-Poissonian quantum jump traces reveal the presence of long-lived two-level systems that hinder the performance of superconducting qubits. The team demonstrates that the standard model for qubit energy loss, the Born-Markov approximation, fails when these systems couple to qubits and retain memory of past states.
By fitting the Solomon equations to measured quantum jumps, the researchers disentangle qubit coupling to both a thermal bath and these problematic, long-lived TLSs. This work provides a method to identify these TLSs, revealing distinct peaks associated with systems that outlive the qubit itself.
TLS Polarization Reveals Breakdown of Markov Approximation
Measurements of qubit decay have revealed that long-lived two-level systems (TLSs) within superconducting circuits exhibit a surprising ability to retain memory of past qubit states, challenging the standard Born-Markov approximation used to model energy loss. This polarization allows the TLS to effectively “remember” the qubit’s previous state, introducing non-Markovian dynamics into the system. The team’s analysis of quantum jumps, discrete shifts in qubit state, demonstrated that these jumps are not random, as predicted by the Markov approximation, but exhibit correlations extending beyond the qubit’s lifetime.
Specifically, the correlation function of quantum jumps, when analyzed using the Solomon equations, showed results consistent with measured data. This contrasts sharply with the expected anti-bunching behavior of a system adhering to the Markov model, where jumps should be exponentially uncorrelated. The presence of these correlations indicates that the TLS is influencing the timing of subsequent qubit jumps, a clear sign of memory effects.
Further investigation involved sweeping the qubit frequency to identify distinct peaks, each corresponding to a TLS that persists longer than the qubit itself. This spectroscopic technique allows researchers to understand the microscopic origins of these problematic TLSs, revealing that some respond to electric fields by increasing frequency, others decrease, some remain constant, and still others jump in time. “The fluxonium qubit spectrum is insensitive to charge bias, therefore we only expect changes in the environment that is electric field susceptible,” the researchers noted, highlighting the role of electric field sensitivity in identifying these long-lived defects.
This ability to differentiate between short-lived and long-lived TLS species represents an advancement in characterizing qubit environments. The implications of these findings extend to error correction algorithms, where time correlations in error syndromes can arise due to a single TLS repeatedly flagging the same error.
The team’s work highlights that qubit lifetime (T1) alone is an insufficient metric for assessing qubit performance, as it fails to capture the memory effects induced by these long-lived TLSs. By disentangling the coupling of the qubit to both the thermal bath and these persistent TLSs, the research provides a method for identifying and potentially mitigating the impact of these defects on superconducting quantum processors, an important step toward achieving fault tolerance.
Solomon Equations Disentangle TLS and Thermal Bath Coupling
Non-Poissonian patterns in qubit behavior is a direct indicator of long-lived two-level systems (TLSs), according to new work disentangling qubit energy loss mechanisms. These unusual quantum jump traces distinguish persistent TLSs from the expected behavior of a standard Markovian thermal bath, offering a new diagnostic for a major obstacle to stable quantum computation. The research reveals that when the rate at which a TLS dissipates energy into a thermal bath is comparable to the coupling rate between the qubit and the TLS, the TLS becomes polarizable, effectively retaining a memory of the qubit’s past states.
This challenges the Born-Markov approximation, which assumes a memoryless environment, and explains observed deviations from expected qubit decay patterns. The team demonstrated that these temporal correlations differ from spatial correlations caused by ionizing radiation impacting multiple qubits on a chip simultaneously.
The existence of this memory effect is associated with TLSs that last significantly longer than the qubit itself, by orders of magnitude. Dynamics of the coupled qubit-TLS system are described by the Solomon equations, which account for the joint evolution of excitation probabilities for both the qubit and the TLS. These equations incorporate a thermal population term, , representing the thermal energy present in both systems.
Fitting the Solomon equations to measured qubit relaxation, conditioned on its previous state, allows isolation of the contributions from the Markovian bath and individual, long-lived TLSs. Sweeping the qubit frequency revealed distinct resonant features in the qubit-TLS coupling rates, directly identifying these long-lived TLSs across frequency spans of tens of megahertz within a few minutes. “When > , this energy exchange can repeat several times before the qubit excitation is ultimately released into the bath,” the researchers write.
Non-Poissonian Quantum Jumps Signal Memory Effects
Non-Poissonian quantum jump traces reveal a surprising persistence in qubit environments, indicating that energy isn’t always lost to a “memoryless” thermal bath as previously assumed. Analysis of these unusual patterns in qubit behavior demonstrates that long-lived two-level systems (TLSs) retain information about the qubit’s prior states, violating the core principle of the Born-Markov approximation.
The research details how these TLSs, unlike those expected in standard models, exhibit a coupling rate to the thermal bath that is comparable to, or even slower than, their interaction with the qubit itself. The team’s findings are quantified through the correlation function, a measure of the probability of observing quantum jumps at specific time intervals.
Simulations based on the Solomon equations, and confirmed by measured data, show that a single long-lived TLS induces “bunching” of quantum jumps, emission probabilities exceeding their steady-state value, over timescales significantly longer than the qubit’s intrinsic energy relaxation time, . The observed bunching is a direct signature of the TLS’s ability to temporarily store and re-emit energy, effectively creating a memory effect within the qubit’s environment.
Measurements also reveal that this non-exponential qubit decay and hyperpolarization of the qubit environment point to the existence of this memory effect in qubit dissipation. The presence of these correlated errors has immediate practical consequences for quantum error correction algorithms, potentially causing syndrome qubits to repeatedly flag the same error. “Although we observe the expected antibunching at short τ, for τ exceeding the qubit relaxation time we instead find bunching,” the study reports, highlighting the deviation from expected behavior.
The research identifies a short-lived TLS, labeled D, within the Markovian background, indicating its relaxation rate is comparable to its interaction with the qubit. However, the focus remains on the longer-lived TLSs, which persist for timescales orders of magnitude greater than the qubit’s intrinsic energy relaxation.
These extended timescales exclude the influence of the qubit’s higher energy levels, potentially induced by the readout process, further solidifying the role of the long-lived TLSs in creating the observed memory effects. The team’s work suggests that as superconducting qubit technology advances and error correction becomes integral to quantum devices, mitigating these long-lived environmental memory effects will be a critical necessity.
Qubit Frequency Sweeps Uncover TLS Spectrum
Sweeping the frequency of a superconducting qubit reveals distinct peaks linked to two-level systems (TLSs) that persist longer than the qubit’s own lifetime, providing a new method for understanding the microscopic origins of these problematic defects. This technique bypasses the need for qubit manipulation, continuously monitoring the qubit through quantum jumps and eliminating the delays inherent in resetting the system between measurements.
Researchers used quantum jump correlation spectroscopy, varying qubit frequency and electric field bias to uncover a spectrum of electric field-sensitive TLS memories superimposed on a largely uniform Markovian environment. This approach differs from previous pump-probe experiments by its continuous nature, and the analysis of quantum jumps provides a unique signature for distinguishing long-lived TLSs from the standard, rapidly decaying background.
The team found that when a TLS is coupled to a thermal bath at a rate comparable to its coupling to the qubit, it becomes effectively storing and re-emitting energy. This behavior manifests as an increase in the TLS population immediately before a qubit jump down event, followed by a decay back to its thermal state, a phenomenon verified through simulations using Equation 3. To further investigate, the researchers performed spectroscopy by repeating quantum jump traces while varying the qubit frequency, revealing a spectrum of TLSs.
This correlation spectroscopy reveals peaks associated with long-lived TLSs, tracking their frequency as it changes with applied electric field. Some TLSs exhibit a frequency that increases with field, labeled E, while others decrease at varying rates, labeled B, C, and F. Still others maintain a constant frequency, labeled A, D, and G, or experience jumps in frequency over time, labeled D and G.
Correlated Quantum Jumps Quantify Long-Lived TLSs
Researchers achieved this differentiation by analyzing the temporal correlations within these quantum jumps, revealing a “memory” effect previously unaccounted for in qubit dissipation models. This approach allows for the isolation of contributions from each environment, revealing that the existence of memory within the qubit environment is directly linked to TLSs exceeding qubit lifetimes by orders of magnitude. Measurements confirm that the qubit-TLS decay rate exhibits distinct peaks susceptible to electric field bias, while the Markovian environment remains largely featureless.
Insets within the study show qubit dynamics performed under varying electric fields, demonstrating a clear contrast between a predominantly Markovian environment and a resonant long-lived TLS. The researchers labeled these long-lived TLSs A through H, each exhibiting unique characteristics. A defining feature of a quantum two-level system, they note, is its inability to emit another photon immediately after one, a principle reflected in the observed antibunching of quantum jumps.
However, the presence of even a single long-lived TLS introduces bunching of quantum jumps, a phenomenon quantified using the correlation function. This function, where P(↓,t|↓,t−τ) denotes the conditional probability of a jump down at time t given a jump down at time t-τ, and P(↓) is the unconditional decay probability, reveals the degree of correlation between jumps.
The researchers report, highlighting the impact of TLSs on qubit behavior. This ability to quantify and disentangle the coupling to long-lived TLSs represents an advancement in understanding and addressing a key obstacle to achieving fault tolerance in superconducting quantum computing.
👉 More information
🗞 Probing the memory of a superconducting qubit environment
✍️ Nicolas Gosling et al.
🧠 DOI: http://link.aps.org/doi/10.1103/j1r2-5ph7
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