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Dissipation as a resource in quantum algorithms

Elias Zapusek

Published Jan 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.3929/ethz-c-000796956

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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.
Dissipation engineering has attracted growing interest as an approach to controlling open quantum systems through engineered system-environment interactions. Standard variational quantum circuits are usually built from unitary operations and therefore explore only a restricted family of states. To go beyond this limitation, we introduce a variational dissipative framework in which ancilla-assisted engineered dissipation is incorporated into parameterized quantum algorithms. In this framework, system-only variational layers are combined with trainable dissipative modules, so that the circuit can prepare a broader class of mixed states through ancilla-assisted nonunitary transformations. Within this framework, the same ancilla-assisted dissipative block is used in two representative settings with different objectives. For ground-state search, it is integrated into a dissipative variational quantum eigensolver to improve the convergence toward low-energy states. For state recovery, it is trained as a recovery channel to suppress preparation noise and enhance fidelity with the target state. In both cases, the block is realized through parameterized system-ancilla couplings followed by ancilla reset and trace-out. Our results show that engineered dissipation can be incorporated into variational quantum circuits as a reusable trainable primitive rather than treated only as a source of noise. In this sense, the proposed framework identifies ancilla-assisted dissipative channels as a concrete variational resource that can support both optimization and recovery tasks within a unified design.
In recent years, variational quantum algorithms have gained significant attention due to their adaptability and efficiency on near-term quantum hardware. They have shown potential in a variety of tasks, including linear algebra, search problems, Gibbs, and ground state preparation. Nevertheless, the presence of noise in current day quantum hardware severely limits their performance. In this work, we introduce dissipative variational quantum algorithms (D-VQAs) by incorporating dissipative operations, such as qubit RESET and stochastic gates, as an intrinsic part of a variational quantum circuit. We argue that such dissipative variational algorithms possess some natural resilience to dissipative noise. We demonstrate how such algorithms can prepare Gibbs states over a wide range of quantum many-body Hamiltonians and temperatures, while significantly reducing errors due to both coherent and noncoherent noise. An additional advantage of our approach is that no ancilla qubits are need. Our results highlight the potential of D-VQAs to enhance the robustness and accuracy of variational quantum computations on noisy intermediate-scale quantum (NISQ) devices.
Abstract Variational quantum algorithms represent a powerful approach for solving optimization problems on noisy quantum computers, with a broad spectrum of potential applications ranging from chemistry to machine learning. However, their performances in practical implementations crucially depend on the effectiveness of quantum circuit training, which can be severely limited by phenomena such as barren plateaus. While, in general, dissipation is detrimental for quantum algorithms, and noise itself can actually induce barren plateaus, here we describe how the inclusion of properly engineered Markovian losses after each unitary quantum circuit layer allows for the trainability of quantum models. We identify the required form of the dissipation processes and establish that their optimization is efficient. We benchmark the generality of our proposal in both a synthetic and a practical quantum chemistry example, demonstrating its effectiveness and potential impact across different domains.
Quantum computers hold the potential of solving problems that are intractable using classical means. Yet, to date no quantum computer has actually solved a problem of general interest that could not have been solved otherwise. Bridging this gap from promised theoretical usefulness to practical relevance is an interdisciplinary challenge, requiring experimental progress, solutions of classical software challenges as well as advances in quantum algorithm design. It is these final two points in which this thesis aims to contribute. One of the most promising quantum computing architectures is based on trapping ions in surface-electrode ion-traps. In order to productively operate such trapped-ion quantum computers, we develop and benchmark a compiler that optimizes ion shuttling sequences in order to efficiently map abstract quantum circuits onto a physical trapped-ion chip. This is a necessary component of the infrastructure of a quantum computing setup, however it is alone not sufficient to execute arbitrary quantum algorithms. In particular, a very promising class of quantum algorithms are so-called hybrid quantum-classical algorithms which leverage the computational resources of both quantum and classical computers. To effectively implement such algorithms, a suitable software setup is necessary to allow for tight interplay between the two types of computers without wasting precious coherence time. To solve this challenge, we propose, implement and benchmark our setup for Interpreted Quantum-Classical Computations (IQCCs), demonstrating its feasibility for trapped-ion quantum computers. For the second part of this thesis we focus on the development of quantum algorithms that make use of this setup. As a first application, we investigate quantum simulations of gauge theories. Such theories are prevalent throughout modern physics and are characterized by local constraints that the dynamics are subject to. Errors in noisy simulations of such theories results in these constraints being violated and the simulations becoming unphysical. We show that this problem can be remedied by measuring gauge operators, decoding possible errors on a classical computer and actively correcting them, which reduces simulation errors. Additionally we interpret the scheme as a sympathetic cooling setup, which allows thermal control of the simulation. We finally turn to the task of preparing ground states of frustration-free Hamiltonians in quantum computers. Studying ground states of various systems is of paramount importance for solving optimization problems and understanding phenomena such as magnetism, superconductivity and superfluidity. We frame the ground-state preparation problem as an error correction problem, wherein energy is measured locally, measurements are decoded and corrections are applied to reduce the energy. In physically relevant examples we show up to exponentially improved runtimes over previous, similar algorithms and give a general run-time bound in terms of the Hamiltonian gap.
Variational quantum algorithms (VQAs) offer a promising route toward simulating many-body quantum systems on noisy intermediate-scale quantum (NISQ) hardware. However, their scalability is severely limited by noise-induced barren plateaus (NIBPs), where hardware noise causes the gradients of the cost function to vanish exponentially with circuit depth, rendering optimization impossible. In this work, we demonstrate that introducing nonunitary elements into the variational ansatz can mitigate NIBPs in open-quantum systems. Using an analytically tractable infinite-range dissipative Ising model, we show that a nonunitary ansatz restores finite gradients in the presence of depolarizing noise, enabling convergence to the correct symmetry-broken steady state. We also develop a Floquet-type variational ansatz in which each layer repeats the same parameters, reducing the deep variational circuit to an effective quantum channel whose fixed points can be analyzed directly. We then extend these ideas to a realistic quantum-chemistry system by simulating electron transport through Oligophenylethynylene-sulfurmethyl (OPE-SMe) using Hamiltonians and jump operators of the model derived from first-principles polarizable QM/MM calculations. Our results show that nonunitary variational ansätze provide a scalable and physically grounded route for simulating open-system steady states on NISQ hardware, offering a pathway to overcoming one of the limitations of current quantum hardware.
Abstract Irreversible logic is at odds with unitary quantum evolution. Emulating such operations by classical measurements can result in disturbances and high resource demands. To overcome these limitations, we propose protocols that harness dissipation to realize the nonunitary evolution required for irreversible gate operations. Using additional excited states subject to decay, we engineer effective decay processes that perform the desired gate operations on the smallest stable Hilbert space. These operate deterministically and in an autonomous fashion, without the need for measurements. We exemplify our approach considering several classical logic operations, such as the OR, NOR, and XOR gates. Towards experimental realization, we discuss a possible implementation in quantum dots. Our study shows that irreversible logic operations can be efficiently performed on realistic quantum systems and that dissipation engineering is an essential tool for obtaining nonunitary evolutions. The proposed operations expand the quantum engineers’ toolbox and have promising applications in NISQ algorithms and quantum machine learning.