arXiv subjects

Moein Malekakhlagh

Publications and source records attributed to Moein Malekakhlagh.

At least 19 recordsLinked to original sources

arXiv2026

Large-scale Lindblad learning from time-series data

Learned open-quantum-system models have broad applications in device characterization, device calibration, realistic noise model construction, and bounding observable estimates in quantum simulation. To this end, we develop a highly scalable Lindblad learning protocol assuming an effective time-independent Lindblad generator with local interactions. For a given operation that can be applied repeatedly on a quantum computer, the protocol learns the Lindbladian by forming a linear system of equations for the model parameters in terms of a set of observable values and their gradients. The required gradient information is obtained by fitting time-series data with sums of exponentially damped sinusoids and differentiating those curves. We develop a robust curve-fitting procedure that finds a parsimonious representation of the data up to shot noise. We demonstrate the approach by learning the Lindbladian for a full layer of gates on a 156-qubit superconducting quantum processor, providing the first learning experiment of this kind. We study the effects of state-preparation and measurement errors and limitations on the operations that can be learned. For improved performance under readout errors, we propose an optional fine-tuning strategy that improves the fit between the time-evolved model and the measured data.

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arXiv2026

Symmetries of Pauli Noise from Lindbladian Dynamics

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 $U_g P U_g ^{\dagger}$, 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 $ZZ_{π/2}$, 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 $T_1$-relaxation and $T_{2ϕ}$-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.

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arXiv2026

Single snapshot non-Markovianity of Pauli channels

Pauli channels are widely used to describe errors in quantum computers, particularly when noise is shaped via Pauli twirling. A common assumption is that such channels admit a Markovian generator, namely a Pauli-Lindblad model with non-negative rates, but the validity of this assumption has not been systematically examined. Here, using CP-indivisibility as our criterion for non-Markovianity, we study multi-qubit Pauli channels from a single snapshot of the dynamics. We find that while the generator always has the same structure as the standard Pauli-Lindblad model, the rates may be negative or complex. We show that random Pauli channels are almost always non-Markovian, with the probability of encountering a negative rate converging doubly exponentially to unity with the number of qubits. For physically motivated noise models shaped by Pauli twirling, including single-qubit over-rotations and two-qubit amplitude damping errors, we find that negative rates are generic, even when the underlying physical noise is Markovian. We generalize probabilistic error amplification and cancellation to non-Markovian generators, and quantify the sampling overhead introduced by negative and complex rates. Experiments on superconducting qubits confirm that allowing negative rates in the learned noise model yields more accurate predictions than restricting to non-negative rates.

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arXiv2026

Distilled remote entanglement between superconducting qubits across optical channels

A promising quantum computing architecture comprises modules of superconducting quantum processors linked via optical channels using quantum transducers. As quantum transducer hardware improves, a need has arisen to understand the quantitative relationship between transducer-device characteristics and the strength of the resulting remote entanglement. Using Monte Carlo simulations that incorporate 2-to-1 and 3-to-1 entanglement distillation methods, our model maps transducer device performance up to system-level channel performance, thereby allowing the performance of remote entanglement approaches to be compared and optimized. We find the extreme photon loss (EPL) distillation protocol to be particularly high performing. Moreover, even without distillation, present-day transducers with added noise of photons are at the threshold of enabling remote Bell pairs with fidelities exceeding 50%. If the next generation of transducers can improve by 3 orders of magnitude in added noise, efficiency, and repetition rates, then they would allow for remote two-qubit gates achieving 99.7% fidelities at MHz rates. These results set practical targets for transducers to be ready for deployment into modular quantum computing systems.

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arXiv2025

Randomized benchmarking of a high-fidelity remote CNOT gate over a meter-scale microwave interconnect

High-fidelity, meter-scale microwave interconnects between superconducting quantum processor modules are a key technology for extending system size beyond constraints imposed by device manufacturing equipment, yield, and signal delivery. Although tomographic experiments have been used in previous demonstrations for benchmarking remote state transfer between modules, they do not reliably separate State Preparation and Measurement (SPAM) error from the error per state transfer. Recent developments based on randomized benchmarking provide a compatible theory for separating these two errors. In this work, we present a module-to-module interconnect based on Tunable-Coupling Qubits (TCQs) and benchmark, in a SPAM-error-tolerant manner enabled by a frame-tracking technique, a remote state transfer fidelity of 0.988 across a 60cm-long coplanar waveguide (CPW). The state transfer is implemented via a superadiabatic transitionless driving method, which suppresses intermediate excitation in the internal modes of the CPW. We further propose and construct a remote CNOT gate between modules, composed of local CZ gates in each module and remote state transfers, and report a gate fidelity of 0.933 using the randomized benchmarking method. The remote CNOT construction and benchmarking we present provide a way to fully characterize the module-to-module link operation and standardize reporting fidelity, analogous to randomized benchmarking protocols for other quantum gates.

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arXiv2025

Efficient Lindblad synthesis for noise model construction

Effective noise models are essential for analyzing and understanding the dynamics of quantum systems, particularly in applications like quantum error mitigation and correction. However, even when noise processes are well-characterized in isolation, the effective noise channels impacting target quantum operations can differ significantly, as different gates experience noise in distinct ways. Here, we present a noise model construction method that builds an effective model from a Lindbladian description of the physical noise processes acting simultaneously to the desired gate operation. It employs the Magnus expansion and Dyson series, and can be utilized for both low-order symbolic and high-order numerical approximations of the noise channel of a multi-qubit quantum gate. We envision multiple use cases of our noise construction method such as (i) computing the corresponding noise channel from a learned Lindbladian, and (ii) generating the noise channel starting with physically motivated Lindbladians for a given hardware architecture. In doing so, we close the gap between physical Lindbladians and operational level noise model parameters. We demonstrate a strong agreement between our symbolic noise construction and full numerical Lindblad simulations for various two-qubit gates, in isolation and in three- and four-qubit scenarios, for a variety of physically motivated noise sources. Our symbolic construction provides a useful breakdown of how noise model parameters depend on the underlying physical noise parameters, which gives qualitative insight into the structure of errors. For instance, our theory provides insight into the interplay of Lindblad noise with the intended gate operations, and can predict how local Lindblad noise can effectively spread into multi-qubit error.

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arXiv2024

Suppressing Correlated Noise in Quantum Computers via Context-Aware Compiling

Coherent errors, and especially those that occur in correlation among a set of qubits, are detrimental for large-scale quantum computing. Correlations in noise can occur as a result of spatial and temporal configurations of instructions executing on the quantum processor. In this paper, we perform a detailed experimental characterization of many of these error sources, and theoretically connect them to the physics of superconducting qubits and gate operations. Equipped with this knowledge, we devise compiler strategies to suppress these errors using dynamical decoupling or error compensation into the rest of the circuit. Importantly, these strategies are successful when the context at each layer of computation is taken into account: how qubits are connected, what crosstalk terms exist on the device, and what gates or idle periods occur in that layer. Our context-aware compiler thus suppresses some dominant sources of error, making further error mitigation or error correction substantially less expensive. For example, our experiments show an increase of 18.5\% in layer fidelity for a candidate 10-qubit circuit layer compared to context-unaware suppression. Owing to the exponential nature of error mitigation, these improvements due to error suppression translate to several orders of magnitude reduction of sampling overhead for a circuit consisting of a moderate number of layers.

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arXiv2024

Entanglement-enhanced learning of quantum processes at scale

Learning unknown processes affecting a quantum system reveals underlying physical mechanisms and enables suppression, mitigation, and correction of unwanted effects. Describing a general quantum process requires an exponentially large number of parameters. Measuring these parameters, when they are encoded in incompatible observables, is constrained by the uncertainty principle and requires exponentially many measurements. However, for Pauli channels, having access to an ideal quantum memory and entangling operations allows encoding parameters in commuting observables, thereby exponentially reducing measurement complexity. In practice, though, quantum memory and entangling operations are always noisy and introduce errors, making the advantage of using noisy quantum memory unclear. To address these challenges we introduce error-mitigated entanglement-enhanced learning and show, both theoretically and experimentally, that even with noise, there is a separation in efficiency between learning Pauli channels with and without entanglement with noisy quantum memory. We demonstrate our protocol's efficacy in examples including hypothesis testing with up to 64 qubits and learning inherent noise processes in a layer of parallel gates using up to 16 qubits on a superconducting quantum processor. Our protocol provides accurate and practical information about the process, with an overhead factor of $1.33 \pm 0.05$ per qubit, much smaller than the fundamental lower bound of 2 without entanglement with quantum memory. Our study demonstrates that entanglement with auxiliary noisy quantum memory combined with error mitigation considerably enhances the learning of quantum processes.

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arXiv2024

Enhanced Quantum State Transfer and Bell State Generation over Long-Range Multimode Interconnects via Superadiabatic Transitionless Driving

Achieving high-fidelity direct two-qubit gates over meter-scale long quantum interconnects is challenging in part due to the multimode nature of such systems. One alternative scheme is to combine local operations with remote quantum state transfer or remote entanglement. Here, we study quantum state transfer and entanglement generation for two distant qubits, equipped with tunable interactions, over a common multimode interconnect. We employ the SuperAdiabatic Transitionless Driving (SATD) solutions for adiabatic passage and demonstrate various favorable improvements over the standard protocol. In particular, by suppressing leakage to a select (resonant) interconnect mode, SATD breaks the speed-limit relation imposed by the qubit-interconnect interaction $g$, where instead the operation time is limited by leakage to the adjacent modes, i.e. free spectral range $Δ_c$ of the interconnect, allowing for fast operations even with weak $g$. Furthermore, we identify a multimode error mechanism for Bell state generation using such adiabatic protocols, in which the even/odd modal dependence of qubit-interconnect interaction breaks down the dark state symmetry, leading to detrimental adiabatic overlap with the odd modes growing as $(g/Δ_c)^2$. Therefore, adopting a weak coupling, imposed by a multimode interconnect, SATD provides a significant improvement in terms of operation speed and consequently sensitivity to incoherent error.

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arXiv2023

Three-qubit Parity Gate via Simultaneous Cross Resonance Drives

Native multi-qubit parity gates have various potential quantum computing applications, such as entanglement creation, logical state encoding and parity measurement in quantum error correction. Here, using simultaneous cross-resonance drives on two control qubits with a common target, we demonstrate an efficient implementation of a three-qubit parity gate. We have developed a calibration procedure based on the one for the echoed cross-resonance gate. We confirm that our use of simultaneous drives leads to higher interleaved randomized benchmarking fidelities than a naive implementation with two consecutive CNOT gates. We also demonstrate that our simultaneous parity gates can significantly improve the parity measurement error probability for the heavy-hexagon code on an IBM Quantum processor using seven superconducting qubits with all-microwave control.

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arXiv2023

Algorithms for perturbative analysis and simulation of quantum dynamics

We develop general purpose algorithms for computing and utilizing both the Dyson series and Magnus expansion, with the goal of facilitating numerical perturbative studies of quantum dynamics. To enable broad applications to models with multiple parameters, we phrase our algorithms in terms of multivariable sensitivity analysis, for either the solution or the time-averaged generator of the evolution over a fixed time-interval. These tools simultaneously compute a collection of terms up to arbitrary order, and are general in the sense that the model can depend on the parameters in an arbitrary time-dependent way. We implement the algorithms in the open source software package \qiskitdynamics{}, utilizing the JAX array library to enable just-in-time compilation, automatic differentiation, and GPU execution of all computations. Using a model of a single transmon, we demonstrate how to use these tools to approximate fidelity in a region of model parameter space, as well as construct perturbative robust control objectives. We also derive and implement Dyson and Magnus-based variations of the recently introduced Dysolve algorithm [Shillito et al., Physical Review Research, 3(3):033266] for simulating linear matrix differential equations. We show how the pre-computation step can be phrased as a multivariable expansion computation problem with fewer terms than in the original method. When simulating a two-transmon entangling gate on a GPU, we find the Dyson and Magnus-based solvers provide a speedup over traditional ODE solvers, ranging from roughly $2\times$ to $4\times$ for a solution and $10\times$ to $60\times$ for a gradient, depending on solution accuracy.

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arXiv2023

Floquet Analysis of Frequency Collisions

Implementation of high-fidelity gate operations on integrated-qubit systems is of vital importance for fault-tolerant quantum computation. Qubit frequency allocation is an essential part of improving control fidelity. A metric for qubit frequency allocation, frequency collision, has been proposed on simple systems of only a few qubits driven by a mono-modal microwave drive. However, frequency allocation for quantum processors for more advanced purposes, such as quantum error correction, needs further investigation. In this study, we propose a Floquet analysis of frequency collisions. The key to our proposed method is a reinterpretation of frequency collisions as an unintended degeneracy of Floquet states, which allows a collision analysis on more complex systems with many qubits driven by multi-modal microwave drives. Although the Floquet state is defined in an infinite-dimensional Hilbert space, we develop algorithms, based on operation perturbation theory, to truncate the Hilbert space down to the optimal computational complexity. In particular, we show that the computational complexity of the collision analysis for a sparse qubit lattice is linear with the number of qubits. Finally, we demonstrate our proposed method on Cross-Resonance based experimental protocols. We first study the Cross-Resonance gate in an isolated three-qubit system, where the effectiveness of our method is verified by comparing it with previous studies. We next consider the more complex problem of syndrome extraction in the heavy-hexagon code. Our proposed method advances our understanding of quantum control for quantum processors and contributes to their improved design and control.

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arXiv2022

Time-dependent Schrieffer-Wolff-Lindblad Perturbation Theory: measurement-induced dephasing and second-order Stark shift in dispersive readout

We develop a time-dependent Schrieffer-Wolff-Lindblad perturbation theory to study effective interactions for driven open quantum systems. The starting point of our analysis is a given Lindblad equation, based on which we obtain an effective (averaged) map that describes the renormalization of both the Hamiltonian and collapse operators due to the drive. As a case study, we apply this method to the dispersive readout of a transmon qubit and derive an effective disperive map that describes measurement-induced dephasing and Stark shift for the transmon. The effective map we derive is completely positive and trace-preserving under adiabatic resonator response. To benchmark our method, we demonstrate good agreement with a numerical computation of the effective rates via the Lindbladian spectrum. Our results are also in agreement with, and extend upon, an earlier derivation of such effects by Gambetta et al. (Phys. Rev. A 74, 042318 (2006)) using the positive P-representation for the resonator field.

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arXiv2021

Optimization of the resonator-induced phase gate for superconducting qubits

The resonator-induced phase gate is a two-qubit operation in which driving a bus resonator induces a state-dependent phase shift on the qubits equivalent to an effective $ZZ$ interaction. In principle, the dispersive nature of the gate offers flexibility for qubit parameters. However, the drive can cause resonator and qubit leakage, the physics of which cannot be fully captured using either the existing Jaynes-Cummings or Kerr models. In this paper, we adopt an ab-initio model based on Josephson nonlinearity for transmon qubits. The ab-initio analysis agrees well with the Kerr model in terms of capturing the effective $ZZ$ interaction in the weak-drive dispersive regime. In addition, however, it reveals numerous leakage transitions involving high-excitation qubit states. We analyze the physics behind such novel leakage channels, demonstrate the connection with specific qubits-resonator frequency collisions, and lay out a plan towards device parameter optimization. We show this type of leakage can be substantially suppressed using very weakly anharmonic transmons. In particular, weaker qubit anharmonicity mitigates both collision density and leakage amplitude, while larger qubit frequency moves the collisions to occur only at large anharmonicity not relevant to experiment. Our work is broadly applicable to the physics of weakly anharmonic transmon qubits coupled to linear resonators. In particular, our analysis confirms and generalizes the measurement-induced state transitions noted in Sank et al. (Phys. Rev. Lett. 117, 190503) and lays the groundwork for both strong-drive resonator-induced phase gate implementation and strong-drive dispersive qubit measurement.

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arXiv2021

Mitigating off-resonant error in the cross-resonance gate

Off-resonant error for a driven quantum system refers to interactions due to the input drives having non-zero spectral overlap with unwanted system transitions. For the cross-resonance gate, this includes leakage as well as off-diagonal computational interactions that lead to bit-flip error on the control qubit. In this work, we quantify off-resonant error, with more focus on the less studied off-diagonal control interactions, for a direct CNOT gate implementation. Our results are based on numerical simulation of the dynamics, while we demonstrate the connection to time-dependent Schrieffer-Wolff and Magnus perturbation theories. We present two methods for suppressing such error terms. First, pulse parameters need to be optimized so that off-resonant transition frequencies coincide with the local minima due to the pulse spectrum sidebands. Second, we show the advantage of a $Y$-DRAG pulse on the control qubit in mitigating off-resonant error. Depending on qubit-qubit detuning, the proposed methods can improve the average off-resonant error from approximately $10^{-3}$ closer to the $10^{-4}$ level for a direct CNOT calibration.

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arXiv2020

First-principles analysis of cross-resonance gate operation

We present a comprehensive theoretical study of the cross-resonance gate operation covering estimates for gate parameters and gate error as well as analyzing spectator qubits and multi-qubit frequency collisions. We start by revisiting the derivation of effective Hamiltonian models following Magesan et al. (arXiv:1804.04073). Transmon qubits are commonly modeled as a weakly anharmonic Kerr oscillator. Kerr theory only accounts for qubit frequency renormalization, while adopting number states as the eigenstates of the bare qubit Hamiltonian. Starting from the Josephson nonlinearity and by accounting for the eigenstates renormalization, due to counter-rotating terms, we derive a new starting model for the cross-resonance gate with modified qubit-qubit interaction and drive matrix elements. Employing time-dependent Schrieffer-Wolff perturbation theory, we derive an effective Hamiltonian for the cross-resonance gate with estimates for the gate parameters calculated up to the fourth order in drive amplitude. The new model with renormalized eigenstates lead to 10-15 percent relative correction of the effective gate parameters compared to Kerr theory. We find that gate operation is strongly dependent on the ratio of qubit-qubit detuning and anharmonicity. In particular, we characterize five distinct regions of operation, and propose candidate parameter choices for achieving high gate speed and low coherent gate error when the cross-resonance tone is equipped with an echo pulse sequence. Furthermore, we generalize our method to include a third spectator qubit and characterize possible detrimental multi-qubit frequency collisions.

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arXiv2019

Lifetime renormalization of weakly anharmonic superconducting qubits: I. Role of number non-conserving terms

The dynamics of a weakly anharmonic superconducting qubit in a complex electromagnetic environment is generally well-described by an effective multimode Kerr Hamiltonian at sufficiently weak excitation. This Hamiltonian can be embedded in a master equation with losses determined by the details of the electromagnetic environment. Recent experiments indicate, however, that when a superconducting circuit is driven with microwave signals the observed relaxation rates appear to be substantially different from expectations based on the electromagnetic environment of the qubit alone. This issue is a limiting factor in the optimization of superconducting qubit readout schemes. We claim here that an effective master equation with drive-power dependent parameters is an efficient approach to model such quantum dynamics. In this sequence of papers, we derive effective master equations, whose parameters exhibit nonlinear dependence on the excitation level of the circuit as well as the electromagnetic environment of the qubit. We show that the number non-conserving terms in the qubit nonlinearity generally lead to a renormalization of dissipative parameters of the effective master equation, while the number conserving terms give rise to a renormalization of the system frequencies. Here, in Part I, we consider the excitation-relaxation dynamics of a transmon qubit that is prepared in a certain initial state, but is not driven otherwise. A unitary transformation technique is introduced to study the renormalization of i) qubit relaxation due to coupling to a generic bath and ii) Purcell decay. Analytic expressions are provided for the dependence of the nonlinear dissipative terms on the details of the electromagnetic environment of the qubit. The perturbation technique based on unitary transformations developed here is generalized to the continuously driven case in Part II.

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arXiv2019

Lifetime renormalization of driven weakly anharmonic superconducting qubits: II. The readout problem

Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the maximum measurement strength and thus the achievable readout speed and fidelity. We address this problem here and provide a plausible mechanism for drive-power dependence of relaxation rates. To this end we introduce a two-parameter perturbative expansion in qubit anharmonicity and the drive amplitude through a unitary transformation technique introduced in Part I. This approach naturally reveals number non-conserving terms in the Josephson potential as a fundamental mechanism through which applied microwave drives can activate additional relaxation mechanisms. We present our results in terms of an effective master equation with renormalized state- and drive-dependent transition frequency and relaxation rates. Comparison of numerical results from this effective master equation to those obtained from a Lindblad master equation which only includes number-conserving terms (i.e. Kerr interactions) shows that number non-conserving terms can lead to significant drive-power dependence of the relaxation rates. The systematic expansion technique introduced here is of general applicability to obtaining effective master equations for driven-dissipative quantum systems that contain weakly non-linear degrees of freedom.

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