Quantum systems are typically controlled by classical devices that necessarily dissipate energy to the surrounding environment. By the fluctuation-dissipation theorem, this implies noise in the control field produced. We investigate the relationship between the resulting errors and the entropy produced by the macroscopic controller, working in the context of a concrete minimal model. In the most experimentally relevant regime of fast control and high fidelity, we find a tradeoff between dissipation and control errors. These findings are exemplified by perturbative calculations of the gate fidelity for simple gate implementations and of the fidelity of state transfer via shortcuts to adiabaticity in the Landau-Zener model. Our results quantitatively demonstrate that suppressing errors in quantum control typically comes at the cost of macroscopic dissipation, which is needed to tame fluctuations in the classical controller.
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The paper asks how dissipation in a macroscopic classical controller relates to errors in the quantum operation it drives. It models a magnetic-field controller as a resistive–inductive circuit with Johnson–Nyquist noise. The resulting control fluctuations have correlation $C(t,s)=(\gamma/\tau_c)e^{-|t-s|/\tau_c}$, while the controller’s entropy production is $\Sigma/k_B=\gamma^{-1}\int_0^\tau g(t)^2dt$, neglecting a positive transient contribution.
Errors are calculated through second-order, noise-averaged state and gate fidelities, expressed as integrals of the noise correlation against ideal-evolution operator correlations. For commuting control dynamics, the susceptibility is $\chi=2\gamma K[\tau+\tau_c(e^{-\tau/\tau_c}-1)]$, independent of pulse shape. Combining this with the pulse-area cost bound gives $\chi\Sigma/k_B\geq K\theta^2F(\tau/\tau_c)$, where $\theta=\int g\,dt$ and $F(x)=2[1+(e^{-x}-1)/x]$. Shorter operations therefore reduce error while increasing dissipation. Examples cover single-qubit gates and an effective CNOT generator.
For counterdiabatic Landau–Zener state transfer, analytical propagators and numerical evaluation with independent noisy control channels show the same tradeoff at short durations. Fitted error–cost exponents range approximately from $-1.92$ to $-1.15$. At long durations, both error and dissipation increase. A general state-fidelity product bound is also derived, but depends on the protocol and initial state and can vanish.
The analysis assumes perfectly prescribed mean voltage, stationary controller noise, and perturbatively small fluctuations, using $\tau^2\gamma/\tau_c\ll1$ as its validity condition. It excludes other noise sources; realistic multi-qubit dissipation prefactors require hardware-specific controller models.
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Error found: The gate-fidelity kernel omits its trace-subtraction term, making the stated CNOT susceptibility incorrect: its leading infidelity is 25% below the reported value and does not equal that of the listed single-qubit gates at fixed duration.
The abstract's characterization of fast control as the most experimentally relevant regime is not supported by a quantitative connection between the controller model and experimental operating parameters.
Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.
Quantum systems are typically controlled by classical devices that necessarily dissipate energy to the surrounding environment. By the fluctuation-dissipation theorem, this implies noise in the control field produced. We investigate the relationship between the resulting errors and the entropy produced by the macroscopic controller, working in the context of a concrete minimal model. In the most experimentally relevant regime of fast control and high fidelity, we find a tradeoff between dissipation and control errors. These findings are exemplified by perturbative calculations of the gate fidelity for simple gate implementations and of the fidelity of state transfer via shortcuts to adiabaticity in the Landau-Zener model. Our results quantitatively demonstrate that suppressing errors in quantum control typically comes at the cost of macroscopic dissipation, which is needed to tame fluctuations in the classical controller.
The paper asks how dissipation in a macroscopic classical controller relates to errors in the quantum operation it drives. It models a magnetic-field controller as a resistive–inductive circuit with Johnson–Nyquist noise. The resulting control fluctuations have correlation C(t,s)=(γ/τc)e−∣t−s∣/τc, while the controller’s entropy production is Σ/kB=γ−1∫0τg(t)2dt, neglecting a positive transient contribution.
Errors are calculated through second-order, noise-averaged state and gate fidelities, expressed as integrals of the noise correlation against ideal-evolution operator correlations. For commuting control dynamics, the susceptibility is χ=2γK[τ+τc(e−τ/τc−1)], independent of pulse shape. Combining this with the pulse-area cost bound gives χΣ/kB≥Kθ2F(τ/τc), where θ=∫gdt and F(x)=2[1+(e−x−1)/x]. Shorter operations therefore reduce error while increasing dissipation. Examples cover single-qubit gates and an effective CNOT generator.
For counterdiabatic Landau–Zener state transfer, analytical propagators and numerical evaluation with independent noisy control channels show the same tradeoff at short durations. Fitted error–cost exponents range approximately from −1.92 to −1.15. At long durations, both error and dissipation increase. A general state-fidelity product bound is also derived, but depends on the protocol and initial state and can vanish.
The analysis assumes perfectly prescribed mean voltage, stationary controller noise, and perturbatively small fluctuations, using τ2γ/τc≪1 as its validity condition. It excludes other noise sources; realistic multi-qubit dissipation prefactors require hardware-specific controller models.
Protocols for nonadiabatic quantum control often require the use of classical time-varying fields. Assessing the thermodynamic cost of such protocols, however, is far from trivial. Here, we study the irreversible entropy produced by the classical apparatus generating the control fields, thus providing a direct link between the cost of a control protocol and dissipation. We focus, in particular, on the case of time-dependent magnetic fields and shortcuts to adiabaticity. Our results are showcased with two experimentally realizable case studies: the Landau-Zener model of a spin-21 particle in a magnetic field and an ion confined in a Penning trap.
Motivated by the need for precise, energy-efficient, and experimentally realistic quantum control protocols, we investigate the thermodynamic cost of performing quantum step-equilibration processes under the influence of classical stochastic control fields. Whereas purely deterministic protocols exhibit dissipation that scales inversely with the number of steps, we show that weak Gaussian noise in the control variables induces dissipative contributions that grow linearly with the number of steps. Consequently, we derive the finite optimal number of steps and minimal achievable average dissipated work and its variance using the quantum thermodynamic length. These results are demonstrated using two paradigmatic examples: a Landau-Zener sweep of a qubit strongly coupled to a thermal bath and the erasure of a transverse-field Ising model.
Quantum systems are inherently sensitive to environmental noise and imperfections in external control fields, which pose a significant challenge for the practical implementation of quantum technologies. These noise sources degrade the fidelity of quantum gates, making their mitigation a key requirement for realizing reliable quantum computing. In this study, we apply Optimal Control Theory (OCT) within a thermodynamically consistent Markovian framework to design high-fidelity quantum gates in the presence of thermal relaxation. Such a description is essential for realistic modeling and optimization of noisy quantum gates in near-term quantum technologies, where strong control fields and thermal environments act simultaneously. Our approach combines OCT with a control-dependent dissipative generator derived from the non-adiabatic master equation framework based on time-dependent invariants of the free evolution. As a result, the driving fields modify both the unitary and dissipative parts of the evolution. We implement the scheme for one- and two-qubit gates embedded in larger Hilbert spaces and compare direct-control and ancilla-assisted architectures. Using logical-subspace-resolved diagnostics, we quantify how the optimized dynamics redistributes the dissipative action between logical and ancillary sectors in the model systems studied here. In particular, we show that ancilla-assisted control can reduce the effective thermal-noise burden on the logical subspace in the relevant parameter regime, while direct control remains the most effective route when available. High-precision propagation of the full open-system dynamics reveals substantial fidelity improvements, in some cases by orders of magnitude, while clarifying the limits of mitigation at large relaxation rates and temperatures.
Present-day quantum processors are open systems in which dissipation and decoherence degrade the information carried by a quantum state as it propagates through a circuit. We study this degradation in dissipative random quantum circuits, modeling each two-qubit gate as a diluted unitary that interpolates between the intended unitary operation and a random dissipative quantum channel. Using the fidelity between the ideal and noisy output states as a diagnostic, we show that sufficiently random unitary gates or dissipative Kraus operators lead to a universal decay of the average fidelity. This decay is determined only by the dissipation strength, system size, and circuit depth, while microscopic details of the gates and noise, including the Kraus rank, appear only in subleading corrections to higher moments. We derive a closed-form expression for the average fidelity in terms of three physically meaningful error parameters, dissipation strength, coherent two-qubit gate-error strength, and connectivity-error probability. Finally, we identify the cases when dissipative effects can be reproduced by an unitary-noise model and when dissipation-induced decoherence remains distinguishable from coherent noise at the level of the average fidelity.
Quantum information processing holds immense promise, but its practical implementation is fundamentally challenged by dissipation, the irreversible loss of information and energy to the environment. The conventional approach treats dissipation as an obstacle to overcome, typically through resource-intensive quantum error correction. Such schemes impose overheads of orders of magnitude in terms of both qubits and operations. This creates significant space, control and time costs, making near-term practical implementation highly challenging. This thesis adopts a different viewpoint, harnessing dissipation for quantum algorithms. We explore the design, application, and conceptual advantages of dissipative quantum algorithms. We establish the foundational tools for this approach by demonstrating how to engineer a universal set of nonunitary operations using intrinsic, controllable dissipation. We present a hardware-efficient method, experimentally realized in a trapped-ion system, for implementing any two-qubit Markovian quantum channel without requiring ancilla qubits or measurements. This provides a practical and versatile toolbox for constructing dissipative algorithms on near-term quantum devices. Building on this, we apply these tools to an inherently dissipative task: the preparation of thermal states. We introduce a variational quantum-classical algorithm that integrates engineered nonunitary operations with unitary gates. By leveraging weak symmetries of the target Hamiltonian, we design efficient ansätze that significantly improve the fidelity of state preparation. Finally, we address one of the most significant barriers to scaling variational quantum algorithms: the prevalence of barren plateaus, where optimization gradients vanish exponentially with system size. We prove that dissipative algorithms, by incorporating periodic qubit resets, can mitigate both noise-induced and unitary barren plateaus. This mechanism allows for a class of scalable computations that are intractable for purely unitary approaches in the presence of noise. Together, these results demonstrate that dissipation is not just a source of error, but a powerful resource. By systematically developing the necessary operations, applying them to relevant problems, and identifying fundamental scalability advantages, this work showcases dissipative quantum computing as a compelling avenue in quantum information processing.
Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, postfacto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.