Oleksandr Kyriienko

University of Exeter | UoE · Department of Physics and Astronomy

We can learn from analyzing quantum convolutional neural networks (QCNNs) that: 1) working with quantum data can be perceived as embedding physical system parameters through a hidden feature map; 2) their high performance for quantum phase recognition can be attributed to generation of a very suitable basis set during the ground state embedding, wh...

A quantum algorithm is proposed for sampling from a solution of stochastic differential equations (SDEs). Using differentiable quantum circuits (DQCs) with a feature map encoding of latent variables, the quantile function is represented for an underlying probability distribution and samples extracted as DQC expectation values. Using quantile mechan...

We propose a physics-informed quantum algorithm to solve nonlinear and multidimensional differential equations (DEs) in a quantum latent space. We suggest a strategy for building quantum models as state overlaps, where exponentially large sets of independent basis functions are used for implicitly representing solutions. By measuring the overlaps b...

We develop a paradigm for building quantum models in the orthonormal space of Chebyshev polynomials. We show how to encode data into quantum states with amplitudes being Chebyshev polynomials with degree growing exponentially in the system size. Similar to the quantum Fourier transform which maps computational basis space into the phase (Fourier) b...

Nonlinear interactions between excitons strongly coupled to light are key for accessing quantum many-body phenomena in polariton systems. Atomically-thin two-dimensional semiconductors provide an attractive platform for strong light-matter coupling owing to many controllable excitonic degrees of freedom. Among these, the recently emerged exciton hy...

We propose several approaches for solving regression problems and differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are represented using automatic differentiation of quantum circuits. While previously quantum...

We consider a nonlinearly coupled electromechanical system, and develop a quantitative theory for two-phonon cooling. In the presence of two-phonon cooling, the mechanical Hilbert space is effectively reduced to its ground and first excited states, allowing for quantum operations at the level of individual phonons and preparing nonclassical mechani...

We develop a microscopic theory for a nonlinear phase space filling (NPSF) in strongly coupled two-dimensional polaritonic lattices. Ubiquitous in polaritonic experiments, the theoretical description of NPSF, remains limited to perturbative treatment and homogeneous samples. In this study, we go beyond the existing theoretical description and disco...

Quantum Generative Modelling (QGM) relies on preparing quantum states and generating samples from these states as hidden - or known - probability distributions. As distributions from some classes of quantum states (circuits) are inherently hard to sample classically, QGM represents an excellent testbed for quantum supremacy experiments. Furthermore...

We show that the regime of strong-light matter coupling with remarkable magnetic properties can be realized in systems based on monolayers of chromium triiodide (CrI3). This two-dimensional material combines the presence of ferromagnetic ordering with the possibility of forming strongly-bound excitonic complexes even at room temperature. Using micr...

Photonic platforms are an excellent setting for quantum technologies as weak photon–environment coupling ensures long coherence times. The second key ingredient for quantum photonics is interactions between photons, which can be provided by optical nonlinearities in the form of cross-phase modulation. This approach underpins many proposed applicati...

We develop quantum protocols for anomaly detection and apply them to the task of credit card fraud detection (FD). First, we establish classical benchmarks based on supervised and unsupervised machine learning methods, where average precision is chosen as a robust metric for detecting anomalous data. We focus on kernel-based approaches for ease of...

We develop a theoretical description of Coulomb interactions between trions (charged excitons) that define a nonlinear optical response in doped two-dimensional semiconductors. First, we formulate a microscopic theory of trion-trion interactions based on composite nature of these particles, and account for all possible exchange processes. Next, we...

We theoretically investigate the nonlinearity of trion-polaritons in a two-dimensional material that arises from Coulomb interaction between quasiparticles. To evaluate the interaction constant, we solve a three-body Wannier equation precisely by expanding trion wavefunctions into a Gaussian basis. Using these wavefunctions, we calculate the trion-...

Nonlinear interactions between excitons strongly coupled to light are key for accessing quantum many-body phenomena in polariton systems. Atomically-thin two-dimensional semiconductors provide an attractive platform for strong light-matter coupling owing to many controllable excitonic degrees of freedom. Among these, the recently emerged exciton hy...

We study a doped transition metal dichalcogenide (TMDC) monolayer in an optical microcavity. Using the microscopic theory, we simulate spectra of quasiparticles emerging due to the interaction of material excitations and a high-finesse optical mode, providing a comprehensive analysis of optical spectra as a function of Fermi energy and predicting s...

We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are represented using automatic differentiation of quantum circuits. While previously quantum kernel methods primaril...

We propose an approach for learning probability distributions as differentiable quantum circuits (DQC) that enable efficient quantum generative modelling (QGM) and synthetic data generation. Contrary to existing QGM approaches, we perform training of a DQC-based model, where data is encoded in a latent space with a phase feature map, followed by a...

Polaritonic lattices offer a unique testbed for studying nonlinear driven-dissipative physics. They show qualitative changes of their steady state as a function of system parameters, which resemble non-equilibrium phase transitions. Unlike their equilibrium counterparts, these transitions cannot be characterised by conventional statistical physics...

Variational quantum algorithms that are used for quantum machine learning rely on the ability to automatically differentiate parametrized quantum circuits with respect to underlying parameters. Here we propose the rules for differentiating quantum circuits (unitaries) with arbitrary generators. Unlike the standard parameter-shift rule valid for uni...

Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization. Many problems appearing in science and engineering can be rewritten as a set of differential equations. Quantu...

We propose a quantum protocol that allows preparing a ground state (GS) of the honeycomb Kitaev model. Our approach efficiently uses underlying symmetries and techniques from topological error correction. It is based on the stabilization procedure, the developed centralizer ansatz, and utilizes the vortex basis description as the most advantageous...

We propose a quantum algorithm for sampling from a solution of stochastic differential equations (SDEs). Using differentiable quantum circuits (DQCs) with a feature map encoding of latent variables, we represent the quantile function for an underlying probability distribution and extract samples as DQC expectation values. Using quantile mechanics w...

Variational quantum algorithms that are used for quantum machine learning rely on the ability to automatically differentiate parametrized quantum circuits with respect to underlying parameters. Here, we propose the rules for differentiating quantum circuits (unitaries) with arbitrary generators. Unlike the standard parameter shift rule valid for un...

The Hamiltonian operator plays a central role in quantum theory being a generator of unitary quantum dynamics. Its expectation value describes the energy of a quantum system. Typically being a nonunitary operator, the action of the Hamiltonian is either encoded using complex ancilla-based circuits, or implemented effectively as a sum of Pauli strin...

We study a doped transition metal dichalcogenide monolayer in an optical microcavity. Using the microscopic theory, we simulate spectra of quasiparticles emerging due to the interaction of material excitations and a high-finesse optical mode, providing a comprehensive analysis of optical spectra as a function of Fermi energy and predicting several...

Photonic platforms are an excellent setting for quantum technologies because weak photon-environment coupling ensures long coherence times. The second key ingredient for quantum photonics is interactions between photons, which can be provided by optical nonlinearities in the form of cross-phase-modulation (XPM). This approach underpins many propose...

We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to represent function derivatives in an analytical form as differentiable quantum circuits (DQCs), thus avoiding inacc...

We study phase transitions in a lattice of square-arranged driven-dissipative polariton condensates with nearest-neighbour coupling. Simulating the polarization (spin) dynamics of the polariton lattice, we observe regions of qualitatively different steady-state behaviour which can be identified in time-integrated measurements. The transition betwee...

We consider a nonlinearly coupled electromechanical system, and develop a quantitative theory for two-phonon cooling. In the presence of two-phonon cooling, the mechanical Hilbert space is effectively reduced to its ground and first excited states, thus forming a mechanical qubit. This allows for performing quantum operations at the level of indivi...

We propose a quantum inverse iteration algorithm, which can be used to estimate ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the Hamiltonian inverse to an initial state prepares the approximate ground state. To apply the inverse Hamiltonian...

We study a 2D system of trion polaritons at the quantum level and demonstrate that for monolayer semiconductors they can exhibit a strongly nonlinear optical response. The effect is due to the composite nature of trion-based excitations resulting in their nontrivial quantum statistical properties, and enhanced phase space filling effects. We presen...

The Hamiltonian operator plays a central role in quantum theory being a generator of unitary quantum dynamics. Its expectation value describes the energy of a quantum system. Typically being a non-unitary operator, the action of the Hamiltonian is either encoded using complex ancilla-based circuits, or implemented effectively as a sum of Pauli stri...

Highly nonlinear optical materials with strong effective photon-photon interactions are required for ultrafast and quantum optical signal processing circuitry. Here we report strong Kerr-like nonlinearities by employing efficient optical transitions of charged excitons (trions) observed in semiconducting transition metal dichalcogenides (TMDCs). By...

Variational quantum eigensolver (VQE) emerged as a first practical algorithm for near-term quantum computers. Its success largely relies on the chosen variational ansatz, corresponding to a quantum circuit that prepares an approximate ground state of a Hamiltonian. Typically, it either aims to achieve high representation accuracy (at the expense of...

We analyze the effective Hamiltonian for the 2T discrete time crystal (2T-DTC or DTC). This effective Hamiltonian is given by spin 1/2 many-body Hamiltonian which includes all-to-all coupling terms, thus being of infinite range. We describe the possible structure of the Hamiltonian, including many-body localized version which prevents thermalizatio...

In the note by Khemani et al. [arXiv:2001.11037] the authors express conceptual disagreement with our recent paper on quantum time crystals [Phys. Rev. Lett. 123, 210602]. They criticise the idealized nature of the considered quantum time crystal, and make several points about properties of Hamiltonians presented in our work. In this reply we answe...

We study a system of a transition metal dichalcogenide (TMD) monolayer placed in an optical resonator, where strong light-matter coupling between excitons and photons is achieved. We present quantitative theory of the nonlinear optical response for exciton-polaritons for the case of doped TMD monolayer, and analyze in detail two sources of nonlinea...

We study a system of a transition metal dichalcogenide (TMD) monolayer placed in an optical resonator, where the strong light-matter coupling between excitons and photons is achieved. We present quantitative theory of the nonlinear optical response for exciton-polaritons for the case of a doped TMD monolayer, and analyze in detail two sources of no...

It is shown theoretically that the strong coupling of electrons in a bulk gapless semiconductor (HgTe) to a circularly polarized high-frequency electromagnetic field induces topological states on the surface of the semiconductor. Their branches lie near the center of the Brillouin zone and have the Dirac dispersion. Thus, the light-induced topologi...

Bose-Einstein condensates of exciton-polaritons in inorganic semiconductor microcavities are known to possess strong interparticle interactions attributed to their excitonic component. The interactions play a crucial role in the nonlinear dynamics of such systems and can be witnessed as the energy blueshifts of polariton states. However, the locali...

Strong light-matter coupling of a photon mode to tightly bound Frenkel excitons in organic materials has emerged as a versatile, room-temperature platform to study nonlinear many-particle physics and bosonic condensation. However, various aspects of the optical response of Frenkel excitons in this regime remained largely unexplored. Here, a hemisph...

We develop the theory describing the topological electronic states on the surface of a gapless strained semiconductor arisen from the mixing of conduction and valence bands. It follows from the present theory that the strain-induced band gap in the Brillouin zone center of the semiconductor results in the surface electronic states with the Dirac li...

Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where an external drive allows us to break discrete TTS, ultimately leading to Floquet time crystals. At the same time, genuine time crystals for closed quantum systems are believed to be imposs...

Highly nonlinear optical materials with strong effective photon-photon interactions (Kerr-like nonlinearity) are required in the development of novel quantum sources of light as well as for ultrafast and quantum optical signal processing circuitry. Here we report very large Kerr-like nonlinearities by employing strong optical transitions of charged...

We study a 2D system of trion-polaritons at the quantum level and demonstrate that for monolayer semiconductors they can exhibit a strongly nonlinear optical response. The effect is due to the composite nature of trion-based excitations resulting in their nontrivial quantum statistical properties, and enhanced phase space filling effects. We presen...

We propose a scheme for the spatial exciton energy control and exciton routing in a transition-metal dichalcogenide (TMD) monolayer which lies on a quantum paraelectric substrate. It relies on the ultrasensitive response of the substrate dielectric permittivity to temperature changes, allowing for spatially inhomogeneous screening of Coulomb intera...

Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where external drive allows to break discrete TTS, ultimately leading to Floquet time crystals. At the same time, genuine time crystals for closed quantum systems are believed to be impossible....

The strong light-matter coupling of a microcavity mode to tightly bound Frenkel excitons in organic materials emerged as a versatile, room-temperature compatible platform to study nonlinear many-particle physics and bosonic condensation. However, various aspects of the optical response of Frenkel excitons in this regime remained largely unexplored....

We study theoretically a lattice of locally bistable driven-dissipative nonlinear cavities. The system is found to resemble the classical Ising model and enables its effective simulation. First, we benchmark the performance of driven-dissipative nonlinear cavities for spin-glass problems, and study the scaling of the ground-state-energy deviation a...

We report on the origin of energy-shifts in organic polariton condensates. The localised nature of Frenkel excitons in molecular semiconductors precludes interparticle Coulomb exchange interactions -the latter being the dominant mechanism for blueshifts in inorganic semiconductor microcavities that bear Wannier-Mott excitons. We examine the contrib...

We report on the origin of energy-shifts in organic polariton condensates. The localised nature of Frenkel excitons in molecular semiconductors precludes interparticle Coulomb exchange interactions -the latter being the dominant mechanism for blueshifts in inorganic semiconductor microcavities that bear Wannier-Mott excitons. We examine the contrib...

We present the theory describing the various surface electronic states arisen from the mixing of conduction and valence bands in a strained mercury telluride (HgTe) bulk material. We demonstrate that the strain-induced band gap in the Brillouin zone center of HgTe results in the surface states of two different kinds. Surface states of the first kin...

We developed the theory which describes the Floquet engineering of surface electronic modes in bulk mercury telluride (HgTe) by a circularly polarized electromagnetic field. The analysis shows that the field results in the appearance of the surface states which arise from the mixing of conduction and valence bands of HgTe. Their branches lie near t...

We propose a scheme for the spatial exciton binding energy control and exciton routing in transition metal dichalcogenide (TMD) monolayer which lies on a quantum paraelectric substrate. It relies on the ultrasensitive response of the substrate dielectric permittivity to temperature changes, allowing for spatially inhomogeneous screening of Coulomb...

We propose a quantum protocol for estimating the ground state energy (GSE) of a quantum system. It is based on the inverse power iteration method, where the initial guess for the ground state energy given by the classical Hartree-Fock solution is progressively improved by the application of the Hamiltonian inverse. The latter is constructed using a...

We analyze theoretically a network of all-to-all coupled polariton modes, realized by a trapped polariton condensate excited by a multifrequency laser source. In the low-density regime the system dynamically finds a state with maximal gain defined by the average intensities (weights) of the excitation beams, analogous to active mode locking in lase...

The fields of opto- and electromechanics have facilitated numerous advances in the areas of precision measurement and sensing, ultimately driving the studies of mechanical systems into the quantum regime. To date, however, the quantization of the mechanical motion and the associated quantum jumps between phonon states remains elusive. For optomecha...

We present a scheme to generate an artificial gauge field for the system of neutral bosons, represented by polaritons in micropillars arranged into a square lattice. The splitting between the two polarizations of the micropillars breaks the time-reversal symmetry (TRS) and results in the effective phase-dependent hopping between cavities. This can...

A lattice of locally bistable driven-dissipative cavity polaritons is found theoretically to effectively simulate the Ising model, also enabling an effective transverse field. We benchmark the system performance for spin glass problems, and study the scaling of the ground state energy deviation and success probability as a function of system size....

We analyze theoretically a network of all-to-all coupled polariton modes, realized by a trapped polariton condensate excited by a comb of different frequencies. In the low-density regime the system dynamically finds a state with maximal gain defined by the average intensities (weights) of the excitation beams, analogous to active mode locking in la...

We developed the theory of dipolaritons in semiconductor quantum wells irradiated by an off-resonant electromagnetic wave (dressing field). Solving the Floquet problem for the dressed dipolaritons, we demonstrated that the field drastically modifies all dipolaritonic properties. In particular, the dressing field strongly effects on terahertz emissi...

In this work, we propose a method to improve electro-optical and structural parameters of light-absorbing kesterite materials. It relies on the application of weak power hydrogen plasma discharges using electromagnetic field of radio frequency range, which improves homogeneity of the samples. The method allows to reduce strain of light absorbers an...

We study theoretically the Coulomb interaction between excitons in transition metal dichalcogenide (TMD) monolayers. We calculate direct and exchange interaction for both ground and excited states of excitons. The screening of the Coulomb interaction, specific to monolayer structures, leads to the unique behavior of the exciton-exciton scattering f...

We propose a quantum algorithm for simulating spin models based on periodic modulation of transmon qubits. Using Floquet theory we derive an effective time-averaged Hamiltonian, which is of the general XYZ class, different from the isotropic XY Hamiltonian typically realised by the physical setup. As an example, we provide a simple recipe to constr...

We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance freque...

We analyze theoretically the Coulomb scattering processes of highly excited excitons in the direct-band-gap semiconductor quantum wells. We find that contrary to the interaction of ground-state excitons, the electron and hole exchange interaction between excited excitons has an attractive character both for s- and p-type two-dimensional (2D) excito...

We propose a microwave frequency single photon transistor which can operate under continuous wave probing, and represents an efficient single microwave photon detector. It can be realized using an impedance matched system of a three level artificial ladder-type atom coupled to two microwave cavities connected to input/output waveguides. Using class...

We analyze theoretically the Coulomb scattering processes of highly excited excitons in the direct bandgap semiconductor quantum wells. We find that contrary to the interaction of ground state excitons the electron and hole exchange interaction between excited excitons has an attractive character both for $s$- and $p$-type 2D excitons. Moreover, we...

We propose a continuous variable analog of quantum controlled-NOT gates based on a system of exciton-polaritons in semiconductor microcavities. This can be realized by the engineering of parametric interaction between control and target polariton modes, which can be varied in time. As an explicit setup we use a system of dipolaritons, which allows...

We revisit the physics of electron gas bilayers in the quantum Hall regime (MacDonald A. and Eisenstein J., Nature, 432 (2004) 691; Eisenstein J., Science, 305 (2004) 950), where transport and tunneling measurements provided evidence of a superfluid phase being present in the system. Previously, this behavior was explained by the possible formation...

We study, theoretically and numerically, the onset and development of modulational instability in an incoherently pumped spatially homogeneous polariton condensate. Within the framework of mean-field theory, we identify regimes of modulational instability in two cases: (1) strong feedback between the condensate and reservoir, which may occur in sca...