Quantum Physics

Noisy intermediate-scale quantum (NISQ) computers could solve quantum-mechanical simulation problems that are beyond the capabilities of classical computers. However, NISQ devices experience significant errors which, if not corrected, can render physical quantities measured in these simulations inaccurate or meaningless. Here we describe a method of reducing these errors which is tailored to quantum algorithms for simulating fermionic systems. The method is based on executing quantum circuits in the model of fermionic linear optics, which are known to be efficiently simulable classically, to infer the relationship between exact and noisy measurement outcomes, and hence undo the effect of noise. We validated our method by applying it to the VQE algorithm for estimating ground state energies of instances of the Fermi-Hubbard model. In classical numerical simulations of 12-qubit examples with physically realistic levels of depolarising noise, errors were reduced by a factor of around 34 compared with the uncorrected case. Smaller experiments on quantum hardware demonstrate an average reduction in errors by a factor of 10 or more.

Dynamical decoupling (DD) is a widely-used quantum control technique that takes advantage of temporal symmetries in order to partially suppress quantum errors without the need resource-intensive error detection and correction protocols. This and other open-loop error mitigation techniques are critical for quantum information processing in the era of Noisy Intermediate-Scale Quantum technology. However, despite its utility, dynamical decoupling does not address errors which occur at unstructured times during a circuit, including certain commonly-encountered noise mechanisms such as cross-talk and imperfectly calibrated control pulses. Here, we introduce and demonstrate an alternative technique - `quantum measurement emulation' (QME) - that effectively emulates the measurement of stabilizer operators via stochastic gate application, leading to a first-order insensitivity to coherent errors. The QME protocol enables error suppression based on the stabilizer code formalism without the need for costly measurements and feedback, and it is particularly well-suited to discrete coherent errors that are challenging for DD to address.

Characterising the input-output photon-number distribution of an unknown optical quantum channel is an important task for many applications in quantum information processing. Ideally, this would require deterministic photon-number sources and photon-number-resolving detectors, but these technologies are still work-in-progress. In this work, we propose a general method to rigorously bound the input-output photon number distribution of an unknown optical channel using standard optical devices such as coherent light sources and non-photon-number-resolving detectors/homodyne detectors. To demonstrate the broad utility of our method, we consider the security analysis of practical quantum key distribution systems based on calibrated single-photon detectors and an experimental proposal to implement time-correlated single photon counting technology using homodyne detectors instead of single-photon detectors.

It has been shown that some non-Gaussian states are useful in quantum metrology. In this paper, we consider an estimation problem which is not well studied in previous researches-an estimation of displacement that follows a Gaussian distribution when post-selection of the measurement outcome is allowed. We derive a lower bound for the estimation error when only Gaussian states and Gaussian operations are used. We show that this bound can be beaten using only linear optics and simple non-Gaussian states such as single photon states. We also obtain a lower bound for the estimation error when the maximum photon number of the sensor state is given, using a generalized version of Van Trees inequality. Our result further reveals the limit of methods using Gaussian states and the role of non-Gaussianity in quantum metrology.

Quantum computing is among the most significant technologies to emerge in recent decades, offering the promise of paradigm-shifting computational capacity with significant ethical consequences. On a technical level, the unique features of quantum computation have technical consequences for the imposition of fairness and ethical criteria on computation. Despite its significance, little if no structured research has been undertaken into the ethical implications of quantum technologies. In this paper, we fill this gap in the literature by presenting the first roadmap for ethical quantum computing setting out prospective research programmes. In doing so, we inaugurate the cross-disciplinary field of the ethics of quantum computing.

In this paper, we have studied the performance and role of local optimizers in quantum variational circuits. We studied the performance of the two most popular optimizers and compared their results with some popular classical machine learning algorithms. The classical algorithms we used in our study are support vector machine (SVM), gradient boosting (GB), and random forest (RF). These were compared with a variational quantum classifier (VQC) using two sets of local optimizers viz AQGD and COBYLA. For experimenting with VQC, IBM Quantum Experience and IBM Qiskit was used while for classical machine learning models, sci-kit learn was used. The results show that machine learning on noisy immediate scale quantum machines can produce comparable results as on classical machines. For our experiments, we have used a popular restaurant sentiment analysis dataset. The extracted features from this dataset and then after applying PCA reduced the feature set into 5 features. Quantum ML models were trained using 100 epochs and 150 epochs on using EfficientSU2 variational circuit. Overall, four Quantum ML models were trained and three Classical ML models were trained. The performance of the trained models was evaluated using standard evaluation measures viz, Accuracy, Precision, Recall, F-Score. In all the cases AQGD optimizer-based model with 100 Epochs performed better than all other models. It produced an accuracy of 77% and an F-Score of 0.785 which were highest across all the trained models.

Systems with non-Hermitian skin effects are very sensitive to the imposed boundary conditions and lattice size, and thus an important question is whether non-Hermitian skin effects can survive when deviating from the open boundary condition. To unveil the origin of boundary sensitivity, we present exact solutions for one-dimensional non-Hermitian models with generalized boundary conditions and study rigorously the interplay effect of lattice size and boundary terms. Besides the open boundary condition, we identify the existence of non-Hermitian skin effect when one of the boundary hopping terms vanishes. Apart from this critical line on the boundary parameter space, we find that the skin effect is fragile under any tiny boundary perturbation in the thermodynamic limit, although it can survive in a finite size system. Moreover, we demonstrate that the non-Hermitian Su-Schreieffer-Heeger model exhibits a new phase diagram in the boundary critical line, which is different from either open or periodical boundary case.

We study the reduced dynamics of open quantum spin chains of arbitrary length N with nearest neighbour XX interactions, immersed within an external constant magnetic field along the z direction, whose end spins are weakly coupled to heat baths at different temperatures, via energy preserving couplings. We find the analytic expression of the unique stationary state of the master equation obtained in the so-called global approach based on the spectralization of the full chain Hamiltonian. Hinging upon the explicit stationary state, we reveal the presence of sink and source terms in the spin-flow continuity equation and compare their behaviour with that of the stationary heat flow. Moreover, we also obtain analytic expressions for the steady state two-spin reduced density matrices and for their concurrence. We then set up an algorithm suited to compute the stationary bipartite entanglement along the chain and to study its dependence on the Hamiltonian parameters and on the bath temperatures.

We propose a variational approach to the dynamics of the Bose-Hubbard model beyond the mean field approximation. To develop a numerical scheme, we use a discrete overcomplete set of Glauber coherent states and its connection to the generalized coherent states studied in depth by Perelomov [A. Perelomov, Generalized Coherent States and Their Applications, Springer-Verlag (Berlin, 1986)]. The variational equations of motion of the generalized coherent state parameters as well as of the coefficients in an expansion of the wavefunction in terms of those states are derived and solved for many-particle problems with large particle numbers S and increasing mode number M. For M = 6 it is revealed that the number of parameters that have to be propagated is more than one order of magnitude less than in an expansion in terms of Fock states.

After propagating through a random amplifying medium, a squeezed state commonly shows excess noise above the shot-noise level. Since large noise can significantly reduce the signal-to-noise ratio, it is detrimental for precision measurement. To circumvent this problem, we propose a noise-reduction scheme using wavefront shaping. It is demonstrated that the average output quantum noise can be effectively suppressed even beyond the shot-noise limit. Both the decrease on amplification strength and the increase on input squeezing strength can give rise to a decrease in the suppressed average quantum noise. Our results not only show the feasibility of manipulating the output quantum noise of random amplifying media, but also indicate potential applications in quantum information processing in complex environments, such as, quantum imaging, quantum communication, and quantum key distribution.