Elias Zapusek’s scientific contributions

There is an ongoing effort to find quantum speedups for learning problems. Recently [Y. Liu et al., Nat. Phys. 17, 1013 (2021)] proved an exponential speedup for quantum support vector machines by leveraging the speedup of Shor's algorithm. We expand upon this result and identify a speedup utilizing Grover's algorithm in the kernel of a support vector machine. To show the practicality of the kernel structure we apply it to a problem related to pattern matching, providing a practical yet provable advantage. Moreover, we show that combining quantum computation in a preprocessing step with classical methods for classification further improves classifier performance.

We introduce a novel reservoir engineering approach for stabilizing multi-component Schr\"odinger's cat manifolds. The fundamental principle of the method lies in the destructive interference at crossings of gain and loss Hamiltonian terms in the coupling of an oscillator to a zero-temperature auxiliary system, which are nonlinear with respect to the oscillator's energy. The nature of these gain and loss terms is found to determine the rotational symmetry, energy distributions, and degeneracy of the resulting stabilized manifolds. Considering these systems as bosonic error-correction codes, we analyze their properties with respect to a variety of errors, including both autonomous and passive error correction, where we find that our formalism gives straightforward insights into the nature of the correction. We give example implementations using the anharmonic laser-ion coupling of a trapped ion outside the Lamb-Dicke regime as well as nonlinear superconducting circuits. Beyond the dissipative stabilization of standard cat manifolds and novel rotation symmetric codes, we demonstrate that our formalism allows for the stabilization of bosonic codes linked to cat states through unitary transformations, such as quadrature-squeezed cats. Our work establishes a design approach for creating and utilizing codes using nonlinearity, providing access to novel quantum states and processes across a range of physical systems.

We demonstrate a novel experimental tool set that enables irreversible multiqubit operations on a quantum platform. To exemplify our approach, we realize two elementary nonunitary operations: the or and nor gates. The electronic states of two trapped Ca40+ ions encode the logical information, and a cotrapped Sr88+ ion provides the irreversibility of the gate by a dissipation channel through sideband cooling. We measure 87% and 81% success rates for the or and nor gates, respectively. The presented methods are a stepping stone toward other nonunitary operations such as in quantum error correction and quantum machine learning.

We demonstrate a novel experimental toolset that enables irreversible multi-qubit operations on a quantum platform. To exemplify our approach, we realize two elementary nonunitary operations: the OR and NOR gates. The electronic states of two trapped $^{40}$Ca$^{+}$ ions encode the logical information, and a co-trapped $^{88}$Sr$^{+}$ ion provides the irreversibility of the gate by a dissipation channel through sideband cooling. We measure $87\%$ and $81\%$ success rates for the OR and NOR gates, respectively. The presented methods are a stepping stone towards other nonunitary operations such as in quantum error correction and quantum machine learning.

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.

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.