Long-time error-mitigating simulation of open quantum systems on near term quantum computers
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Rost, Brian↗
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Open quantum system violates generalized Pauli constraints on quantum device
Abstract The Pauli exclusion principle governs the fundamental structure and function of fermionic systems from molecules to materials. Nonetheless, when such a fermionic system is in a pure state, it is subject to additional restrictions known as the generalized Pauli constraints (GPCs). Here we verify experimentally the violation of the GPCs for an open quantum system using data from a superconducting-qubit quantum computer. We prepare states of systems with three-to-seven qubits directly on the quantum device and measure the one-fermion reduced density matrix (1-RDM) from which we can test the GPCs. We find that the GPCs of the 1-RDM are sufficiently sensitive to detect the openness of the 3-to-7 qubit systems in the presence of a single-qubit environment. Results confirm experimentally that the openness of a many-fermion quantum system can be decoded from only a knowledge of the 1-RDM with potential applications from quantum computing and sensing to noise-assisted energy transfer.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Efficient Simulation of Open Quantum Systems on NISQ Trapped‐Ion Hardware
Abstract Simulating open quantum systems, which interact with external environments, presents significant challenges on noisy intermediate‐scale quantum (NISQ) devices due to limited qubit resources and noise. In this study, an efficient framework is proposed for simulating open quantum systems on NISQ hardware by leveraging a time‐perturbative Kraus operator representation of the system's dynamics. This approach avoids the computationally expensive Trotterization method and exploits the Lindblad master equation to represent time evolution in a compact form, particularly for systems satisfying specific commutation relations. The efficiency of this method is demonstrated by simulating quantum channels, such as the continuous‐time Pauli channel and damped harmonic oscillators, on NISQ trapped‐ion hardware, including IonQ Harmony and Quantinuum H1‐1. Additionally, hardware‐agnostic error mitigation techniques are introduced, including Pauli channel fitting and quantum depolarizing channel inversion, to enhance the fidelity of quantum simulations. These results show strong agreement between the simulations on real quantum hardware and exact solutions, highlighting the potential of Kraus‐based methods for scalable and accurate simulation of open quantum systems on NISQ devices. This framework opens pathways for simulating more complex systems under realistic conditions in the near term.
Burdine, Colin [Department of Electrical and Compu↗
Decoherence and dissipation for a quantum system coupled to a local environment
Decoherence and dissipation in quantum systems has been studied extensively in the context of Quantum Brownian Motion. Effective decoherence in coarse grained quantum systems has been a central issue in recent efforts by Zurek and by Hartle and Gell-Mann to address the Quantum Measurement Problem. Although these models can yield very general classical phenomenology, they are incapable of reproducing relevant characteristics expected of a local environment on a quantum system, such as the characteristic dependence of decoherence on environment spatial correlations. I discuss the characteristics of Quantum Brownian Motion in a local environment by examining aspects of first principle calculations and by the construction of phenomenological models. Effective quantum Langevin equations and master equations are presented in a variety of representations. Comparisons are made with standard results such as the Caldeira-Leggett master equation.
Gallis, Michael R.↗
Fidelity Comparison of Time-Bin and Fock State Encoding in Hybrid Quantum Systems Under Channel and Transduction Effects
Future quantum networks are expected to integrate a heterogeneous combination of quantum systems, owing to the diverse advantages offered by different physical platforms in terms of scalability, coherence times, and interfacing capabilities. Within the context of this emerging quantum communication paradigm, this paper presents an analytical comparison of two photonic encoding schemes—time-bin and Fock state (single rail)—in hybrid quantum systems where flying qubits are entangled with stationary matter qubits. We evaluate their resilience against fiber channel and quantum transduction effects by calculating the fidelity of the final states relative to their ideal forms. Employing the characteristic function approach, we derive analytical fidelity expressions and investigate their dependence on parameters such as transmissivity, noise levels, fiber length, and source generation success probability. Additionally, we simulate the scenario with a dedicated QuTiP software implementation to verify the validity of the theoretical models. Our findings reveal that due to its inherent single-mode structure, the Fock state encoding consistently outperforms time-bin encoding in fidelity, as this structure significantly minimizes susceptibility to losses compared to the two-mode nature of the time-bin scheme. This analysis offers valuable insights for future hybrid quantum communication and information processing applications.
Fiorini, Francesco [Pisa U.]↗
Operator Growth in Open Quantum Systems
The spreading of quantum information in closed systems, often termed scrambling, is a hallmark of many-body quantum dynamics. In open systems, scrambling competes with noise, errors, and decoherence. Here, in this work, we provide a universal framework that describes the scrambling of quantum information in open systems: we predict that the effect of open-system dynamics is fundamentally controlled by operator size distributions and independent of the microscopic error mechanism. This framework allows us to demonstrate that open quantum systems exhibit universal classes of information dynamics that fundamentally differ from their unitary counterparts. Implications for the Loschmidt echo, nuclear magnetic resonance experiments, and the classical simulability of open quantum dynamics will be discussed.
Physics↗
A Quantum Algorithm to Simulate Open Quantum Systems
Given the advent of quantum algorithms for a wide array of problems in linear algebra and machine learning, it is important to develop general methods for the simulation of arbitrary (ie non-unitary) operators on quantum hardware. In this talk, we present a novel quantum algorithm based on the quantum singular value transformation (QSVT) to apply an arbitrary operator K to some input state and subsequently estimate the expectation value of some observable. Our construction then immediately yields a route to estimating observables of states undergoing open quantum dynamics, whose effect is captured by a set of non-unitary Kraus operators. Our algorithm succeeds deterministically given the Sz-Nagy dilation, and we provide details on the algorithm's query and gate complexity, numerical verification, and comparisons with prior methods.
Quantum computing↗
Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
Electron transport in realistic physical and chemical systems often involves the nontrivial 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 nonunitary 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 nonunitary 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. Furthermore, the results are in agreement with classical calculations, showing promise in simulating nonunitary operations on intermediate-term and future quantum devices.
74 ATOMIC AND MOLECULAR PHYSICS↗
Performance Analysis of an Optimization Algorithm for Metamaterial Design on the Integrated High-Performance Computing and Quantum Systems
Optimizing metamaterials with complex geometries is a big challenge. Although an active learning algorithm, combining machine learning (ML), quantum computing, and optical simulation, has emerged as an efficient optimization tool, it still faces difficulties in optimizing complex structures that have potentially high performance. In this work, we comprehensively analyze the performance of an optimization algorithm for metamaterial design on the integrated HPC and quantum systems. We demonstrate significant time advantages through message-passing interface (MPI) parallelization on the high-performance computing (HPC) system showing approximately 54% faster ML tasks and 67 times faster optical simulation against serial workloads. Furthermore, we analyze the performance of a quantum algorithm designed for optimization, which runs with various quantum simulators on a local computer or HPC-quantum system. Results showcase ~24 times speedup when executing the optimization algorithm on the HPC-quantum hybrid system. This study paves a way to optimize complex metamaterials using the integrated HPC-quantum system.
Kim, Seongmin↗
Self-testing of a single quantum system from theory to experiment
Abstract Self-testing allows one to characterise quantum systems under minimal assumptions. However, existing schemes rely on quantum nonlocality and cannot be applied to systems that are not entangled. Here, we introduce a robust method that achieves self-testing of individual systems by taking advantage of contextuality. The scheme is based on the simplest contextuality witness for the simplest contextual quantum system—the Klyachko-Can-Binicioğlu-Shumovsky inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements as a function of the value of the witness under a pragmatic assumption on the measurements. We apply the method in an experiment on a single trapped 40 Ca + using randomly chosen measurements and perfect detection efficiency. Using the observed statistics, we obtain an experimental demonstration of self-testing of a single quantum system.
Physics↗
Simulating large one-dimensional neutral-atom quantum systems
While abstract models of quantum computation assume a closed system of two-level states, practical quantum devices inevitably couple to the environment in some way, creating sources of noise. Understanding the tolerance to noise of specific quantum algorithms run on specific devices is important for determining the feasibility of quantum computing in the current noisy intermediate-scale quantum era. Of particular interest is understanding the noise sensitivity of these devices as more qubits are added to the system. Classical simulations are a useful tool to understand the effects of this noise, but direct classical simulations of open quantum systems are burdened by an exponentially growing cost in the number of qubits and a large local Hilbert space dimension. For onedimensional, shallow circuits, using tensor networks can replace this exponential cost with a linear one and simulate far wider systems than what would normally be available. In this paper, we describe a tensor network simulation of a neutral atom quantum system under the presence of noise, while introducing a purity-preserving truncation technique that compromises between the simplicity of the matrix product state and the positivity of the matrix product density operator. We apply this simulation to a near-optimized iteration of the quantum approximate optimization algorithm on a transverse field Ising model in order to investigate the influence of large system sizes on the performance of the algorithm. We find that while circuits with a large number of qubits fail more often under noise that depletes the qubit population, their outputs on a successful measurement are just as robust under Rydberg atom dissipation or qubit dephasing as smaller systems. However, such circuits might not perform as well under coherent multiqubit errors such as Rydberg atom crosstalk. We also find that the optimized parameters are especially robust to noise, suggesting that a noisier quantum system can be used to find the optimal parameters before switching to a cleaner system for measurements of observables.
Allen, James↗
Distributed Quantum Learning with co-Management in a Multi-tenant Quantum System
The rapid advancement of quantum computing has pushed classical designs into the quantum domain, breaking physical boundaries for computing-intensive and data-hungry applications with the hope that some systems may provide a quantum speedup. For example, variational quantum algorithms have been proposed for quantum neural networks to train deep learning models on qubits, achieving promising results. Existing quantum learning architectures and systems rely on single, monolithic quantum machines with abundant and stable resources, such as qubits. However, fabricating a large, monolithic quantum device is considerably more challenging than producing an array of smaller devices. In this paper, we investigate a distributed quantum system that combines multiple quantum machines into a unified system. We propose DQuLearn, which divides a quantum learning task into multiple subtasks. Each subtask can be executed distributively on individual quantum machines, with the results looping back to classical machines for subsequent training iterations. Additionally, our system supports multiple concurrent clients and dynamically manages their circuits according to the runtime status of quantum workers. Through extensive experiments, we demonstrate that DQuLearn achieves similar accuracies with significant runtime reduction, by up to 68.7% and an increase per-second circuit processing speed, by up to 3.99 times, in a 4-worker multi-tenant setting.
quantum computing↗
Scrambling and operator entanglement in local non-Hermitian quantum systems
The breakdown of Lieb-Robinson bounds in local, non-Hermitian quantum systems opens up the possibility for a rich landscape of quantum many-body phenomenology. We elucidate this by studying information scrambling and quantum chaos in non-Hermitian variants of paradigmatic local quantum spin-chain models. We utilize a mixture of exact diagonalization and tensor network techniques for our numerical results and focus on three dynamical quantities: (i) out-of-time-ordered correlators (OTOCs), (ii) operator entanglement of the dynamics, and (iii) entanglement growth following a quench from product initial states. We show that while OTOCs fail to capture information scrambling in a simple, local, non-Hermitian transverse-field Ising model, the closely related operator entanglement is a robust measure of dynamical properties of interest. Moreover, we show that the short-time growth of operator entanglement can generically detect entanglement phase transitions in these systems while its long-time average is shown to be a reliable indicator of quantum chaos and entanglement phases. This allows us to extend operator entanglement-based diagnostics from previous works on closed and open quantum systems, to the new arena of monitored quantum dynamics. Finally, we remark on the efficacy of these dynamical quantities in detecting integrability/chaos in the presence of continuous monitoring.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Signatures of Open and Noisy Quantum Systems in Single-Qubit Quantum Annealing
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Thermodynamic limits to the conversion of blackbody radiation by quantum systems
Using general thermodynamic arguments, we analyze the conversion of the energy contained in the radiation from a blackbody to useful work by a quantum system. We show that the energy available for conversion is bounded above by the change in free energy in the incident and reradiated fields and that this free energy change depends upon the temperature of the receiving device. Universal efficiency curves giving the ultimate thermodynamic conversion efficiency of the quantum system are presented in terms of the blackbody temperature and the temperature and threshold energy of the quantum system. Application of these results is made to a variety of systems including biological photosynthetic, photovoltaic, and photoelectrochemical systems.
Buoncristiani, A. M.↗
Learning thermodynamic master equations for open quantum systems
The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks. However, the majority of mathematical models describing open quantum systems are linear, and the natural nonlinearities in learnable models have not been incorporated using physical principles. We present a data-driven model for open quantum systems that includes learnable, thermodynamically consistent terms. The trained model is interpretable, as it directly estimates the system Hamiltonian and linear components of coupling to the environment. We validate the model on synthetic two and three-level data, as well as experimental two-level data collected from a quantum device at Lawrence Livermore National Laboratory.
Mathematics and Computing↗
Microscopic Derivation of Transition-state Theory for Complex Quantum Systems
The decay of quantum complex systems through a potential barrier is often described with transition-state theory, also known as RRKM theory in chemistry. Here we derive the basic formula for transition-state theory based on a generic Hamiltonian as might be constructed in a configuration-interaction basis. Two reservoirs of random Hamiltonians from Gaussian orthogonal ensembles are coupled to intermediate states representing the transition states at a barrier. Under the condition that the decay of the reservoirs to open channels is large, an analytic formula for reaction rates is derived. Here, the transition states act as independent Breit–Wigner resonances which contribute additively to the total transition probability, as is well known for electronic conductance through resonant tunneling states. It is also found that the transition probability is independent of the decay properties of the states in the second reservoir over a wide range of decay widths.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Optimal control of large quantum systems: assessing memory and runtime performance of GRAPE
Abstract Gradient Ascent Pulse Engineering (GRAPE) is a popular technique in quantum optimal control, and can be combined with automatic differentiation (AD) to facilitate on-the-fly evaluation of cost-function gradients. We illustrate that the convenience of AD comes at a significant memory cost due to the cumulative storage of a large number of states and propagators. For quantum systems of increasing Hilbert space size, this imposes a significant bottleneck. We revisit the strategy of hard-coding gradients in a scheme that fully avoids propagator storage and significantly reduces memory requirements. Separately, we present improvements to numerical state propagation to enhance runtime performance. We benchmark runtime and memory usage and compare this approach to AD-based implementations, with a focus on pushing towards larger Hilbert space sizes. The results confirm that the AD-free approach facilitates the application of optimal control for large quantum systems which would otherwise be difficult to tackle.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗