Accurate quantum computing relies on the precision of quantum gates. However, quantum gates in practice are generally affected by dissipative environments, which can significantly reduce their fidelity. In this paper, we elucidate the fundamental relations between the average fidelity of generic quantum gates and the dissipation that occurs during the computing processes. Considering scenarios in which a quantum gate is subject to Markovian environments, we rigorously derive fidelity-dissipation relations that hold for arbitrary operational times. Intriguingly, when the quantum gate undergoes thermal relaxation, the result can be used as a valuable tool for estimating dissipation through experimentally measurable fidelity, without requiring detailed knowledge of the dissipative structure. For the case of arbitrary environments, we uncover a trade-off relation between the average fidelity and energy dissipation, implying that these quantities cannot be large simultaneously. Our results unveil the computational limitations imposed by thermodynamics, shedding light on the profound connection between thermodynamics and quantum computing. Published by the American Physical Society 2024
Accurate quantum computing relies on the precision of quantum gates. However, quantum gates in practice are generally affected by dissipative environments, which can significantly reduce their fidelity. In this paper, we elucidate the fundamental relations between the average fidelity of generic quantum gates and the dissipation that occurs during the computing processes. Considering scenarios in which a quantum gate is subject to Markovian environments, we rigorously derive fidelity-dissipation relations that hold for arbitrary operational times. Intriguingly, when the quantum gate undergoes thermal relaxation, the result can be used as a valuable tool for estimating dissipation through experimentally measurable fidelity, without requiring detailed knowledge of the dissipative structure. For the case of arbitrary environments, we uncover a trade-off relation between the average fidelity and energy dissipation, implying that these quantities cannot be large simultaneously. Our results unveil the computational limitations imposed by thermodynamics, shedding light on the profound connection between thermodynamics and quantum computing. Published by the American Physical Society 2024
The fidelity of quantum operations is often limited by incoherent errors, which typically can be modeled by fundamental Markovian noise processes such as amplitude damping and dephasing. In Phys. Rev. Lett. 129, 150504 (2022), we presented an analytical result for the average gate fidelity of a general multiqubit operation in terms of the dissipative rates and the corresponding Lindblad jump operators, provided that the operation remains in the computational subspace throughout the time evolution. Here we generalize this expression for the average gate fidelity to include the cases where the system state temporarily leaves the computational subspace during the gate. Such gate mechanisms are integral to several quantum-computing platforms, and our formula is applicable to all of them; as examples, we employ it for the two-qubit controlled-Z gate in both superconducting qubits and neutral atoms. We also obtain the average gate fidelity for simultaneous operations applied in multiqubit systems. These results are useful for understanding the error budgets of quantum gates while scaling up quantum computers.
As quantum-computing platforms are susceptible to noise, the fidelity of quantum operations is limited by decoherence. Understanding this limitation is crucial for building utility-scale quantum processors. In previous works [Phys. Rev. Lett. 129, 150504 (2022); Quantum 9, 1684 (2025)], we presented analytical formulae for the average gate fidelity of multi-qubit operations under static Markovian noise processes, including operations that temporarily leave the computational subspace. However, some quantum-computing architectures dynamically modulate qubit or coupler frequencies to implement two-qubit gates, e.g., baseband flux gates; such modulation can lead to dissipation rates varying in time. In this Letter, we therefore generalize the fidelity-reduction formulae to encompass time-dependent dissipation. Applying our generalized formula, we obtain a fidelity bound for adiabatic operations and demonstrate that flux-dependent noise sensitivity, combined with qubit-coupler hybridization, significantly reduces the fidelity of adiabatic controlled-Z (CZ) gates in superconducting quantum computers. Our work thus provides essential theoretical tools for evaluating error budgets and optimizing the design of quantum operations in tunable quantum-computing architectures, and may also find applications in quantum-sensing and quantum-communication protocols that are affected by time-dependent dissipation.
While the accuracy of qubit operations has been greatly improved in the last decade, further development is demanded to achieve the ultimate goal: a fault-tolerant quantum computer that can solve real-world problems more efficiently than classical computers. With growing fidelities even subtle effects of environmental noise such as qubit–reservoir correlations and non-Markovian dynamics turn into the focus for both circuit design and control. To guide progress, we disclose, in a numerically rigorous manner, a comprehensive picture of the single-qubit dynamics in presence of a broad class of noise sources and for entire sequences of gate operations. Thermal reservoirs ranging from Ohmic to deep 1 / f ɛ -like sub-Ohmic behavior are considered to imitate realistic scenarios for superconducting qubits. Apart from dynamical features, fidelities of the qubit performance over entire sequences are analyzed as a figure of merit. The relevance of retarded feedback and long-range qubit–reservoir correlations is demonstrated on a quantitative level, thus, providing a deeper understanding of the limitations of performances for current devices and guiding the design of future ones. Published by the American Physical Society 2024
The implementation of quantum gates with fidelities that exceed the threshold for reliable quantum computing requires robust gates whose performance is not limited by the precision of the available control fields. The performance of these gates also should not be affected by the noisy environment of the quantum register. Here we use randomized benchmarking of quantum gate operations to compare the performance of different families of gates that compensate errors in the control field amplitudes and decouple the system from the environmental noise. We obtain average fidelities of up to 99.8%, which exceeds the threshold value for some quantum error correction schemes as well as the expected limit from the dephasing induced by the environment.
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.
Autonomous quantum thermal machines have recently been proposed as physics-based computing substrates where logical inputs and outputs are encoded in temperature gradients. While such ``thermodynamic neurons'' exhibit a clear trade-off between computational fidelity and heat dissipation, the fundamental information-theoretic limits of temperature-encoded computation remain uncharacterized. Here, we derive rigorous bounds linking average error probability, channel capacity, and entropy production for finite-capacity thermal reservoirs operating far from equilibrium. We prove that the minimal dissipation required to achieve a target average error probability ⟨ξ⟩ diverges as ⟨ξ⟩ approaches a fundamental minimum error floor $\epsMin$ imposed by finite-reservoir thermal fluctuations. We further establish a thermodynamic channel capacity that saturates at high dissipation, and quantify the minimal dissipation required for cascaded networks to maintain target fidelity. We demonstrate that the required dissipation grows linearly O(L) with network depth for shallow networks, but diverges as the network depth L approaches a fundamental maximum limit $L_{\max} = \epsNet/\epsMin$ imposed by the minimum error floor. Furthermore, under strong noise amplification conditions, the required dissipation can grow up to O(L3). Our framework bridges stochastic thermodynamics, finite-time information theory, and autonomous computation, providing rigorous design principles for energy-efficient analog thermodynamic hardware.