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Dissipative controller as a hidden source of errors in quantum gates

This paper demonstrates that in quantum control, the macroscopic dissipation required by classical controllers to suppress noise-induced errors creates a fundamental tradeoff where achieving high-fidelity, fast quantum gates inevitably comes at the cost of increased energy dissipation.

Original authors: Serhat C. Kadıoğlu, Saulo V. Moreira, Mark T. Mitchison, Anthony Kiely

Published 2026-10-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Serhat C. Kadıoğlu, Saulo V. Moreira, Mark T. Mitchison, Anthony Kiely

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The quest to build a quantum computer is a race to master the strange, fragile rules of the microscopic world. In this realm, particles can exist in multiple states at once, a property that promises to solve problems far beyond the reach of today's supercomputers. To harness this power, scientists must manipulate these particles with extreme precision, using external devices like lasers or magnetic coils to perform logical operations known as quantum gates. Think of these gates as the switches that turn information on or off, but instead of simple on-off states, they must guide delicate quantum states along a specific path without letting them stumble. The challenge is that these quantum systems are incredibly sensitive; even the tiniest disturbance can ruin the calculation. For years, researchers have focused on making these controls faster and more accurate, often treating the control devices themselves as perfect, silent tools that simply do what they are told.

However, a new study suggests that this view of the controller is incomplete. The researchers, working from institutions in Turkey, Ireland, and the United Kingdom, argue that the very devices used to steer quantum particles are not silent. Because these control machines are macroscopic objects made of ordinary matter, they are subject to the laws of thermodynamics. To function, they must dissipate energy into their surroundings, much like a car engine heats up as it runs. This dissipation is not just a side effect; it is inextricably linked to the noise that plagues the system. The team set out to understand the relationship between the energy a controller wastes as heat and the errors it introduces into the quantum operation. They found that the noise generated by the controller's own heat is a hidden source of mistakes, creating a fundamental trade-off: to make a quantum gate more accurate, one must often pay a higher price in energy dissipation.

The researchers built a model to explore this connection, treating the control device as a simple electrical circuit. In their simulation, a current flows through a coil to generate the magnetic field needed to manipulate a quantum bit. Because the circuit has electrical resistance, it naturally produces heat, and this heat causes the current to jitter with tiny, random fluctuations. These fluctuations act as a noisy background signal that interferes with the precise instructions the quantum system is trying to follow. The team calculated how much "entropy," or disorder, the controller produces as it runs, and how much this disorder degrades the quality of the quantum gate. They discovered that the two are locked in a tight relationship. The more the controller dissipates energy to suppress its own internal jitter and maintain a steady signal, the fewer errors appear in the quantum gate. Conversely, if the controller tries to operate with less energy dissipation, the noise grows, and the gate becomes less reliable.

This trade-off was tested in two specific scenarios to see how it plays out in practice. First, the team looked at simple quantum gates, which are the basic building blocks of quantum logic. They simulated different ways of turning these gates on and off, varying the speed of the operation. They found that for fast operations, which are desirable for efficiency, there is a clear cost. To achieve high fidelity, or accuracy, in a short amount of time, the controller must dissipate a significant amount of energy to keep the noise down. If the controller tries to save energy, the gate fails more often. The second scenario involved a more complex process called a "shortcut to adiabaticity," a technique used to move a quantum system from one state to another very quickly. Here, the researchers again saw that the fastest, most accurate transfers required the controller to work harder and generate more entropy. In slower operations, the relationship was less strict, but fast control is generally preferred in quantum computing to avoid other sources of error, making this energy-error trade-off a critical factor for future designs.

The study does not claim to have solved the problem of quantum noise, nor does it suggest that we can simply eliminate this cost. Instead, it provides a quantitative map of the terrain, showing exactly how much dissipation is needed to tame the fluctuations of a classical controller. The authors used computer simulations to model these interactions, confirming that the errors are not just random bad luck but a direct consequence of the thermodynamics of the control hardware. Their work implies that as we push quantum computers toward higher speeds and greater complexity, we cannot ignore the heat generated by the machines that run them. The path to better quantum computers may require not just smarter algorithms, but also a deeper understanding of how the classical world's need to dissipate energy shapes the quantum world's ability to compute. By acknowledging that the controller is a source of noise, engineers can better design systems that balance the need for speed with the unavoidable cost of keeping the noise at bay.

Technical Summary: Dissipative Controller as a Hidden Source of Errors in Quantum Gates

Problem Statement
Quantum technologies, particularly quantum computing, rely on high-fidelity control of fragile quantum systems. While extensive research has addressed the energetic costs of quantum control and potential energy-error trade-offs, previous works have largely focused on the quantum system itself. This paper addresses a critical gap: the errors introduced by the classical control apparatus. To function as a classical controller, an external device (e.g., a laser, electrode, or magnetic field generator) must be a dissipative system undergoing rapid decoherence to prevent entanglement with its quantum target. According to the fluctuation-dissipation theorem, this necessary dissipation generates thermal noise (fluctuations) in the control field. The central problem investigated is the quantitative relationship between the macroscopic entropy production (dissipation) of the controller and the microscopic infidelity (errors) it induces in the quantum system.

Methodology
The authors employ a hybrid theoretical framework combining macroscopic classical thermodynamics with microscopic quantum dynamics:

Macroscopic Controller Model: The control apparatus is modeled as a classical $RL$ circuit (specifically a Helmholtz coil generating a magnetic field). The dynamics are described by a Langevin equation incorporating Johnson-Nyquist noise. The entropy production ( $\Sigma$ ) is quantified via irreversible entropy generation (Joule heating) in the circuit, proportional to the time integral of the squared control field.
Microscopic Quantum Response: The quantum system is treated as a qubit or multi-qubit system subject to a time-dependent Hamiltonian. The control field fluctuations ( $\delta g$ ) are modeled as a classical stochastic perturbation.
Perturbative Analysis: The authors derive a second-order perturbative correction to the noise-averaged fidelity. They define a "fidelity susceptibility" ( $\chi \approx 1 - \langle F \rangle$ ) which depends on the correlation function of the control field noise and the system's response kernel.
Protocols: The study analyzes two specific scenarios:
- Commuting Dynamics: Simple quantum gates where the control operator commutes with the static Hamiltonian ( $[H_S, W] = 0$ ).
- Shortcuts to Adiabaticity (STA): State transfer in the Landau-Zener (LZ) model, utilizing counterdiabatic driving to achieve fast, high-fidelity transitions.

Key Contributions and Results

Derivation of Error-Dissipation Bounds: The paper establishes analytical inequalities linking the entropy production $\Sigma$ and the fidelity susceptibility $\chi$ . Specifically, for commuting dynamics, the product $\chi \Sigma$ is shown to be bounded from below, demonstrating that suppressing errors generally requires increased dissipation.
Gate Fidelity Trade-offs: In the regime of fast control (short protocol duration $\tau$ ), the authors find a clear trade-off: reducing gate infidelity requires increasing the dissipation in the controller. This is demonstrated for single-qubit gates ( $S, T, H$ ) and the CNOT gate. The results show that while different gates have different energetic costs based on their rotation angles, they share a universal dependence of infidelity on the protocol duration relative to the noise correlation time.
Landau-Zener State Transfer: In the context of the Landau-Zener model with STA, the analysis reveals two distinct regimes:
- Fast Control ( $\tau \ll \tau_c$ ): A power-law trade-off exists where decreasing infidelity ( $\chi_S$ ) requires increasing total entropy production ( $\Sigma_{total}$ ). The product $\chi_S \Sigma_{total}$ follows a specific scaling behavior.
- Slow Control ( $\tau \gg \tau_c$ ): The trade-off disappears; both infidelity and energetic cost increase simultaneously. This is attributed to the dominance of the control field's entropy production over time, where the detrimental effect of noise accumulates.
Role of Noise Correlation: The validity of the perturbative approach is constrained by the condition $\tau^2 \gamma / \tau_c \ll 1$ , where $\gamma$ is the noise strength and $\tau_c$ is the correlation time. The trade-off is most pronounced in the fast-driving limit where the controller operates near the boundary of perturbative validity.

Significance and Claims
The paper claims to quantitatively demonstrate that suppressing errors in quantum control typically comes at the cost of macroscopic dissipation. This dissipation is necessary to "tame" the fluctuations in the classical controller. The authors argue that this represents a fundamental macroscopic contribution to the thermodynamic cost of quantum control, distinct from the internal energetics of the quantum system.

The work provides a concrete setting to understand the interplay between the entropy production of a classical controller and the fidelity of the quantum operation it drives. By focusing on the "hidden" source of errors arising from the controller's own thermodynamics, the study suggests that achieving high-fidelity, fast quantum gates is inherently linked to managing the thermodynamic cost of the classical hardware. The authors note that their minimal model likely provides a lower bound on entropy production, implying that more complex controllers would incur even higher costs for the same fidelity.

Limitations and Scope
The authors explicitly state that their analysis is limited to:

Classical controllers modeled as dissipative $RL$ circuits (odd under time reversal).
Perturbative regimes where noise is small compared to the control field intensity.
Specific protocols (commuting gates and Landau-Zener STA).
They do not claim to solve the problem for all quantum control scenarios or provide experimental proposals for new hardware, but rather offer a theoretical framework to quantify existing trade-offs.

Technical Summary: Dissipative Controller as a Hidden Source of Errors in Quantum Gates

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