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Kade Head-Marsden

Publications and source records attributed to Kade Head-Marsden.

At least 19 recordsLinked to original sources

Designing robust molecular spins for quantum technologies with theoretical chemistry

Molecular spins represent a versatile platform for quantum information science, with the potential to offer chemically tunable, addressable qubits. However, achieving this requires understanding and mitigating quantum decoherence. This Chapter provides a theoretical overview of current state-of-the-art chemical theory connecting ab initio electronic structure with open quantum system dynamics to guide the rational design of long-lived molecular qubits. Beginning at the electronic level, multi-reference and relativistic electronic structure methods to parameterize effective spin Hamiltonians are discussed, with a primary focus on accurately capturing $g$-tensors, zero-field splitting, and hyperfine interactions. These parameters feed into models of spin-phonon and spin-spin coupling to quantify $T_1$ and $T_2$ relaxation across various environmental regimes. This Chapter evaluates a hierarchy of dynamical methods, ranging from factorization to matrix product state approaches, balancing computational cost against accuracy and generalizability. Ultimately, mapping these theoretical models to molecular architecture can establish design principles, such as isotopic substitution and spatial spin delocalization, to understand and extend coherence lifetimes.

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Understanding the effects of competing spin-pair dephasing pathways in molecular spins

Molecular spins offer promise in emerging quantum technologies such as quantum sensing and computing. At low temperatures, nuclear spin-spin interactions affect electron spin coherence lifetimes through pure dephasing. Nuclear-spin noise can originate from spin pairs within a molecule itself, pairs in a surrounding environment system, or pairs in which one spin is on the molecule and the other in the environment. Improving coherence times requires detailed knowledge of the dominant sources of dephasing. Here, we analyze the decoherence behavior of two molecular qubit candidates with various ligands and in different nuclear-spin containing solvents. We apply an electronic-structure enhanced, non-Markovian perturbative theoretical method to connect experimentally comparable dephasing times to individual spin pairs. This analysis allows the development of a computational workflow to strategically improve coherence lifetimes in spin systems where decoherence is dominated by spin-spin dephasing.

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Subspace Selected Variational Quantum Configuration Interaction with a Partial Walsh Series

Estimating the ground-state energy of a quantum system is one of the most promising applications for quantum algorithms. Here we propose a variational quantum eigensolver (VQE) \emph{Ansatz} for finding ground state configuration interaction (CI) wavefunctions. We map CI for fermions to a quantum circuit using a subspace superposition, then apply diagonal Walsh operators to encode the wavefunction. The algorithm can be used to solve both full CI and selected CI wavefunctions, resuling in exact and near-exact solutions for electronic ground states. Both the subspace selection and wavefunction \emph{Ansatz} can be applied to any Hamiltonian that can be written in a qubit basis. The algorithm bypasses costly classical matrix diagonalizations, which is advantageous for large-scale applications. We demonstrate results for several molecules using quantum simulators and hardware.

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A perturbative non-Markovian treatment to low-temperature spin decoherence

Molecular spins are promising candidates for quantum information science, leveraging coherent electronic spin states for quantum sensing and computation. However, the practical application of these systems is hindered by electronic spin decoherence, driven by interactions with nuclear spins in the molecule and the surrounding environment at low temperatures. Predicting dephasing dynamics remains a formidable challenge due to the complexity of the spin bath. In this work, we develop a non-Markovian time-convolutionless master equation to treat an electronic spin coupled to a nuclear-spin bath. By relating ab initio electronic structure parameters directly to the decoherence dynamics, we provide a framework that accounts for pure dephasing in the low-temperature limit. We apply this method to a series of molecular qubit candidates and demonstrate good agreement with experimental relaxation trends. This approach offers a computationally efficient path for the prediction of low-temperature decoherence trends in molecular spin systems.

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Preserving fermionic statistics for single-particle approximations in microscopic quantum master equations

Microscopic master equations have gained traction for the dissipative treatment of molecular spin and solid-state systems for quantum technologies. Single particle approximations are often invoked to treat these systems, which can lead to unphysical evolution when combined with master equation approaches. We present a mathematical constraint on the system-environment parameters to ensure that microscopically-derived Markovian master equations preserve fermionic, $N$-representable statistics when applied to reduced systems. We demonstrate these constraints for the recently derived unified master equation and universal Lindblad equation, along with the Redfield master equation for cases when positivity issues are not present. For operators that break the constraint, we explore the addition of Pauli factors to recover $N$-representability. This work promotes feasible applications of novel microscopic master equations for realistic chemical systems.

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Quantum Simulation of Two-Level $PT$-Symmetric Systems Using Hermitian Hamiltonians

Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the quantum dynamics of $PT$-symmetric systems on unitary-gate-based quantum computers by leveraging Hermitian equivalents through similarity transformations. We introduce two algorithms for simulating $PT$-symmetric systems near exceptional points where eigenvalues and eigenstates coalesce. The first is a hybrid classical-quantum algorithm and the second reduces the classical component by using an ancilla qubit. We then use perturbation theory to extend this method to consider the dynamics of two weakly interacting $PT$-symmetric systems. Demonstrations on a quantum device and noisy simulators validate the algorithm on current quantum devices, offering potential for scalable simulations of $PT$-symmetric systems and pseudo-Hermitian operators in quantum computation.

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Information back-flow in quantum non-Markovian dynamics and its connection to teleportation

A quantum process is called non-Markovian when memory effects take place during its evolution. Quantum non-Markovianity is a phenomenon typically associated with the information back-flow from the environment to the principal system, however it has been shown that such an effect is not necessary. In this work, we establish a connection between quantum non-Markovianity and the protocol of quantum teleportation in both discrete and continuous-variable systems. We also show how information flows during a teleportation protocol between the principal system and the environment in a bidirectional way leading up to a state revival.

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Orbital Entanglement and The Double $d$-Shell Effect in Binary Transition Metal Molecules

Accurate modeling of transition metal-containing compounds is of great interest due to their wide-ranging and significant applications. These systems present several challenges from an electronic structure perspective, including significant multi-reference character and many chemically-relevant orbitals. A further complication arises from the so-called double $d$-shell effect, which is known to cause a myriad of issues in the treatment of first-row transition metals with both single- and multi-reference methods. While this effect has been well documented for several decades, a comprehensive understanding of its consequences and underlying causes is still evolving. Here, we characterize the second $d$-shell effect by analyzing the information entropy of correlated wavefunctions in a periodic series of $3d$ and $4d$ transition metal molecular hydrides and oxides. These quantum information techniques provide unique insight into the nuanced electronic structure of these species, and are powerful tools for study of weak and strong correlation in the transition metal $d$ manifold.

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Stabilizing steady-state properties of open quantum systems with parameter engineering

Realistic quantum systems are affected by environmental loss, which is often seen as detrimental for applications in quantum technologies. Alternatively, weak coupling to an environment can aid in stabilizing highly entangled and mixed states, but determining optimal system-environment parameters can be challenging. Here, we describe a technique to optimize parameters for generating desired non-equilibrium steady states (NESSs) in driven-dissipative quantum systems governed by the Lindblad equation. We apply this approach to predict highly-entangled and mixed NESSs in Ising, Kitaev, and Dicke models in several quantum phases.

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Low temperature decoherence dynamics in molecular spin systems using the Lindblad master equation

Understanding the spin dynamics in low-temperature settings is crucial to designing and optimizing molecular spin systems for use in emerging quantum technologies. At low temperatures, irreversible loss occurs due to ensemble dynamics facilitated by electronic-nuclear spin interactions. We develop a combined open quantum systems and electronic structure theory capable of predicting trends in relaxation rates in molecular spin ensembles. We use the Gorini-Kossakowski-Sudarshan-Lindblad master equation and explicitly include electronic structure information in the decoherence channels. We apply this theory to several molecular systems pertinent to contemporary quantum technologies. Our theory provides a framework to describe irreversible relaxation effects in molecular spin systems with applications in quantum information science, quantum sensing, molecular spintronics, and other spin systems dominated by spin-spin relaxation.

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Quantum Algorithms and Applications for Open Quantum Systems

Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction of static and dynamic molecular properties. In recent years, quantum algorithms have been leveraged for the computation of open quantum systems as the predicted quantum advantage of quantum devices over classical ones may allow previously inaccessible applications. Accomplishing this goal will require input and expertise from different research perspectives, as well as the training of a diverse quantum workforce, making a compilation of current quantum methods for treating open quantum systems both useful and timely. In this Review, we first provide a succinct summary of the fundamental theory of open quantum systems and then delve into a discussion on recent quantum algorithms. We conclude with a discussion of pertinent applications, demonstrating the applicability of this field to realistic chemical, biological, and material systems.

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Singular value decomposition quantum algorithm for quantum biology

There has been a recent interest in quantum algorithms for the modelling and prediction of non-unitary quantum dynamics using current quantum computers. The field of quantum biology is one area where these algorithms could prove to be useful, as biological systems are generally intractable to treat in their complete form, but amenable to an open quantum systems approach. Here we present the application of a recently developed singular value decomposition algorithm to two well-studied benchmark systems in quantum biology: excitonic energy transport through the Fenna-Matthews-Olson complex and the radical pair mechanism for avian navigation. We demonstrate that the singular value decomposition algorithm is capable of capturing accurate short- and long-time dynamics for these systems through implementation on a quantum simulator, and conclude that this algorithm has the potential to be an effective tool for the future study of systems relevant to quantum biology.

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Quantum Simulation of Open Quantum Systems Using Density-Matrix Purification

Electronic structure and transport in realistically-sized systems often require an open quantum system (OQS) treatment, where the system is defined in the context of an environment. As OQS evolution is non-unitary, implementation on quantum computers -- limited to unitary operations -- is challenging. We present a general framework for OQSs where the system's $d \times d$ density matrix is recast as a $d^{2}$ wavefunction which can be evolved by unitary transformations. This theory has two significant advantages over conventional approaches: (i) the wavefunction requires only an $n$-qubit, compared to $2n$-qubit, bath for an $n$-qubit system and (ii) the purification includes dynamics of any pure-state universe. We demonstrate this method on a two-level system in a zero temperature amplitude damping channel and a two-site quantum Ising model. Quantum simulation and experimental-device results agree with classical calculations, showing promise in simulating non-unitary operations on NISQ quantum devices.

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A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex

Using quantum algorithms to simulate complex physical processes and correlations in quantum matter has been a major direction of quantum computing research, towards the promise of a quantum advantage over classical approaches. In this work we develop a generalized quantum algorithm to simulate any dynamical process represented by either the operator sum representation or the Lindblad master equation. We then demonstrate the quantum algorithm by simulating the dynamics of the Fenna-Matthews-Olson (FMO) complex on the IBM QASM quantum simulator. This work represents a first demonstration of a quantum algorithm for open quantum dynamics with a moderately sophisticated dynamical process involving a realistic biological structure. We discuss the complexity of the quantum algorithm relative to the classical method for the same purpose, presenting a decisive query complexity advantage of the quantum approach based on the unique property of quantum measurement.

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Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators

Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based algorithm to simulate non-unitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal non-unitary operator, which we show can be implemented by a diagonal unitary operator in a 1-qubit dilated space. While dilation techniques increase the number of qubits in the calculation, and thus the gate complexity, our algorithm limits the operations required in the dilated space to a diagonal unitary operator, which has known circuit decompositions. We use this algorithm to prepare random sub-normalized two-level states on a quantum device with high fidelity. Furthermore, we present the accurate non-unitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude damping channel computed on a quantum device. The algorithm presented will be most useful for implementing general non-unitary operations when the SVD can be readily computed, which is the case with most operators in the noisy intermediate-scale quantum computing era.

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Capturing Non-Markovian Dynamics on Near-Term Quantum Computers

With the rapid progress in quantum hardware, there has been an increased interest in new quantum algorithms to describe complex many-body systems searching for the still-elusive goal of 'useful quantum advantage'. Surprisingly, quantum algorithms for the treatment of open quantum systems (OQSs) have remained under-explored, in part due to the inherent challenges of mapping non-unitary evolution into the framework of unitary gates. Evolving an open system unitarily necessitates dilation into a new effective system to incorporate critical environmental degrees of freedom. In this context, we present and validate a new quantum algorithm to treat non-Markovian dynamics in OQSs built on the Ensemble of Lindblad's Trajectories approach, invoking the Sz.-Nagy dilation theorem. Here we demonstrate our algorithm on the Jaynes-Cummings model in the strong coupling and detuned regimes, relevant in quantum optics and driven quantum systems studies. This algorithm, a key step towards generalized modeling of non-Markovian dynamics on a noisy-quantum device, captures a broad class of dynamics and opens up a new direction in OQS problems.

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Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators

Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a non-unitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here we present a general algorithm for implementing the action of any non-unitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. The results are in agreement with classical calculations, showing promise in simulating non-unitary operations on intermediate-term and future quantum devices.

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Unboxing Quantum Black Box Models: Learning Non-Markovian Dynamics

Characterizing the memory properties of the environment has become critical for the high-fidelity control of qubits and other advanced quantum systems. However, current non-Markovian tomography techniques are either limited to discrete superoperators, or they employ machine learning methods, neither of which provide physical insight into the dynamics of the quantum system. To circumvent this limitation, we design learning architectures that explicitly encode physical constraints like the properties of completely-positive trace-preserving maps in a differential form. This method preserves the versatility of the machine learning approach without sacrificing the efficiency and fidelity of traditional parameter estimation methods. Our approach provides the physical interpretability that machine learning and opaque superoperators lack. Moreover, it is aware of the underlying continuous dynamics typically disregarded by superoperator-based tomography. This paradigm paves the way to noise-aware optimal quantum control and opens a path to exploiting the bath as a control and error mitigation resource.

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