We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the quantum Fourier transform and quantum addition. Embedding these algorithms in the parity encoding reduces the circuit depth compared to conventional gate-based implementations while keeping the multiqubit gate counts comparable. We further propose simple implementations of multiqubit gates in tailored encodings and an efficient strategy to prepare graph states.

Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in a multitude of quantum algorithms. Simultaneously measuring sets of Pauli operators allows for fewer measurements and an overall speedup of the measurement process. Using results from coloring random graphs, we give evidence for an upper bound on the expected minimum number of simultaneously measurable parts necessary to partition a set of Pauli operators. By expanding our gate set to allow multiqubit Clifford gates before measurement, we were able to cut down the number of measurements considerably compared to previous approaches. We conjecture that this improvement is, in general, linear with respect to the lengths of the Pauli operators. We conclude by demonstrating the feasibility of this approach by implementing the variational quantum eigensolver on the Aspen-4-4Q-A quantum processor unit. In doing so, we calculate the ground-state energies of ${\mathrm{H}}_2$ using fewer measurements than is possible with single-qubit gates with no statistically significant difference in accuracy.

Quantum addition circuits are considered being of two types: (1) Toffoli-adder circuits which use only classical reversible gates (controlled-not and Toffoli), and (2) QFT-adder circuits based on the quantum Fourier transformation. We present a systematic translation of the QFT addition circuit into a Toffoli-based adder. This result shows that QFT addition has fundamentally the same fault-tolerance cost (e.g., T count) as the most cost-efficient Toffoli adder: instead of using approximate decompositions of the gates from the QFT circuit, it is more efficient to merge gates. In order to achieve this, we formulated circuit identities for multicontrolled gates and apply the identities algorithmically. The employed techniques can be used to automate quantum circuit optimization heuristics.

It is shown that above-threshold-ionization peaks disappear when the kinetic energy associated with the nondipole radiation-pressure-induced photoelectron momentum in the laser propagation direction becomes comparable to the photon energy, and how peaks can be made to reappear if knowledge of the length and direction of the photoelectron momentum is at hand and an emission-direction-dependent momentum shift is accounted for. In this sense appropriate analysis of the nondipole effects restores the energy-conserving signature of the above-threshold-ionization peaks. The reported findings should be observable with intense midinfrared laser pulses.

Turbulent fluid dynamics typically involves excitations on many different length scales. Classical incompressible fluids can be cleanly represented in Fourier space enabling spectral analysis of energy cascades and other turbulence phenomena. In quantum fluids, additional phase information and singular behavior near vortex cores thwarts the direct extension of standard spectral techniques. We develop a formal and numerical spectral analysis for $\text{U}\left(1\right)$ symmetry-breaking quantum fluids suitable for analyzing turbulent flows, with specific application to the Gross–Pitaevskii fluid. Our analysis builds naturally on the canonical approach to spectral analysis of velocity fields in compressible quantum fluids and establishes a clear correspondence between energy spectral densities, power spectral densities, and autocorrelation functions, applicable to energy residing in velocity, quantum pressure, interaction, and potential energy of the fluid. Our formulation includes all quantum phase information and also enables arbitrary resolution spectral analysis, a valuable feature for numerical analysis. A central vortex in a trapped planar Bose–Einstein condensate provides an analytically tractable example with spectral features of interest in both the infrared and ultraviolet regimes. Sampled distributions modeling the dipole gas, plasma, and clustered regimes exhibit velocity correlation length increasing with vortex energy, consistent with known qualitative behavior across the vortex clustering transition. The spectral analysis of compressible quantum fluids presented here offers a rigorous tool for analyzing quantum features of superfluid turbulence in atomic or polariton condensates.

In addition to the reduction in the experimental complexity, generating correlated photonic pairs using nonlinear interactions in a synthetic lattice also benefits the high tunability of all relevant parameters. Here we found that the two-photon correlation can be modulated by using a synthetic lattice composed of the orbital angular momentum of light with a nonlinear Kerr interaction on a single site. By calculating the $S$ matrix for single-photon and two-photon scattering, we analyze the transmission and correlation properties of the outgoing photons. The presence of finite bandwidth enables the complete transfer of a single incident photon into the synthetic lattice inside the cavity. For two incident photons, the nonlinear Kerr interaction can lead to various correlated photonic pairs. The spectrum of the correlated outgoing fields can be controlled by changing the total energy of the incident photons or altering the interaction parameters. In addition, the presence of completely transferring the single incident photon provides an ideal starting point for detecting the correlated properties between the outgoing photons even for very weak interactions. The findings of the present study provide a new perspective for engineering the correlation properties of outgoing photons in synthetic systems.

Future quantum networks will require the ability to produce matter-photon entanglement at photon frequencies not naturally emitted from the matter qubit. This allows for a hybrid network architecture, where these photons can couple to other tools and quantum technologies useful for tasks such as multiplexing, routing, and storage, but which operate at wavelengths different from that of the matter qubit source, while also reducing network losses. Here, we demonstrate entanglement between a trapped ion and a 780-nm photon, a wavelength that can interact with neutral-Rb-based quantum networking devices. A single barium ion is used to produce 493-nm photons, entangled with the ion, which are then frequency converted to 780 nm while preserving the entanglement. We generate ion-photon entanglement with fidelities $\ge 0.93$(2) and $\ge 0.84$(2) for 493-nm and 780-nm photons respectively with the fidelity drop arising predominantly from a reduction in the signal-noise of our detectors at 780 nm compared with at 493 nm.

We propose a teleportation-based scheme to implement a universal set of quantum gates with a four-component cat code, assisted by appropriate entangled resource states and photon-number-resolving detection. The four-component cat code features the ability to recover from single-photon loss. Here we propose a concrete procedure to correct the single-photon loss, including detecting the single-photon-loss event and recovering the initial states. By concatenating with standard qubit error-correcting codes, we estimate the loss threshold for fault-tolerant quantum computation and obtain a significant improvement over the two-component cat code.

Two-XUV-photon double ionization of Ne, induced by an intense few-pulse attosecond train with a ∼4 fs envelope duration is investigated experimentally and theoretically. The experiment is performed at ELI-ALPS (Extreme Light Infrastructure Attosecond Light Pulse Source) utilizing the recently constructed 10 Hz gas phase high-order harmonic generation SYLOS GHHG-COMPACT beamline. A total pulse energy up to ∼1 μJ generated in argon in conjunction with high-reflectivity optics in the XUV region allowed the observation of the doubly charged state of Ne induced by 40 eV central XUV-photon energies. The interaction of the intense attosecond pulse train with Ne is also theoretically studied via second-order time-dependent perturbation theory equations of motion. The results of this work, combined with the feasibility of conducting XUV-pump–XUV-probe experiments, constitute a powerful tool for many potential applications. Those include attosecond pulse metrology as well as time-resolved investigations of the dynamics underlying direct and sequential double ionization and their electron correlation effects.

Variational quantum algorithms are the centerpiece of modern quantum programming. These algorithms involve training parametrized quantum circuits using a classical coprocessor, an approach adapted partly from classical machine learning. An important subclass of these algorithms, designed for combinatorial optimization on current quantum hardware, is the quantum approximate optimization algorithm (QAOA). Despite efforts to realize deeper circuits, experimental state-of-the-art implementations are limited to a fixed depth. However, it is known that problem density—a problem constraint to a variable ratio—induces underparametrization in fixed depth QAOA. Density-dependent performance has been reported in the literature, yet the circuit depth required to achieve fixed performance (henceforth called critical depth) remained unknown. Here, we propose a predictive model, based on a logistic saturation conjecture for critical depth scaling with respect to density. Focusing on random instances of MAX-2-SAT, we test our predictive model against simulated data with up to 15 qubits. We report the average critical depth, required to attain a success probability of 0.7, saturates at a value of 10 for densities beyond 4. We observe the predictive model to describe the simulated data within a $3\sigma$ confidence interval. Furthermore, based on the model, a linear trend for the critical depth with respect to problem size is recovered for the range of 5–15 qubits.

We explore the fundamental origin of the quantum advantage behind random access code. We propose new temporal inequalities compatible with noninvasive-realist models and show that any nonzero quantum advantage of $n\mapsto 1$ random access code in the presence of shared randomness is equivalent to the violation of the corresponding temporal inequality. As a consequence of this connection, we also prove that the maximal success probability of $n\mapsto 1$ random access code can be obtained when the maximal violation of the corresponding inequality is achieved. We further show that any nonzero quantum advantage of $n\mapsto 1$ random access code, or in other words, any nonzero violation of the corresponding temporal inequality, can certify genuine randomness.

Most previous efforts on quantum error correction focused on either extending classical error-correction schemes to the quantum regime by performing a perfect correction on a subset of errors or seeking a recovery operation to maximize the fidelity between an input state and its corresponding output state of a noisy channel. There are few results concerning quantum error precompensation. Here we design an error-precompensated input state for an arbitrary quantum noisy channel and a given target output state. By following a procedure, the required input state, if it exists, can be analytically obtained in single-partite systems. Furthermore, we also present semidefinite programs to numerically obtain the error-precompensated input states with maximal fidelities between the target state and the output state. The numerical results coincide with the analytical results.

Accurate quantum control is a key technology for realizing quantum information processing, such as quantum communication and quantum computation. In reality, a quantum state under control suffers from undesirable effects caused by systematic errors. A composite pulse (CP) is used to eliminate the effects of systematic errors during control. One-qubit control, which is the most fundamental in quantum control, is typically affected by two errors: pulse length error and off-resonance error (ORE). In this paper, we focus on ORE-robust CPs and systematically construct symmetric ones comprising three elementary operations in order to understand their properties. We find an infinitely large number of ORE-robust CPs, including the well-known CORPSE family, and evaluate their performance according to gate infidelity and operation time, both of which are important for the realization of accurate quantum control.

Improved values of hyperfine coefficients related to the electronic spin-orbit and electron-nucleus spin-spin tensor interactions in the ${\mathrm{HD}}^{+}$ molecular ion are obtained through numerical calculation of relativistic corrections at the $m{\alpha }^6$ order and radiative corrections at the $m{\alpha }^{7}ln\left(\alpha \right)$ order. The theoretical accuracy is improved by more than one order of magnitude. Some deviations with recent high-precision rovibrational spectroscopy experiments are observed, in contrast with the good agreement obtained in ${\mathrm{H}}_2^{+}$.

Configuration interaction calculations are performed to determine the dipole polarizabilities and tune-out wavelengths for the $2{}^3{S}_1$ state in ${\mathrm{Li}}^{+}$ ion. The finite nuclear mass correction is given by including the mass shift operator in the Dirac-Coulomb-Breit Hamiltonian directly, while the QED correction to dynamic dipole polarizabilities is evaluated by using the perturbation theory. The tune-out wavelengths for the $2{}^3{S}_1(M_J=0)$ and $2{}^3{S}_1(M_J=\pm 1)$ states are 159.620 55(6) nm and 159.631 14(6) nm, respectively. And the QED correction for 159 nm tune-out wavelength is 43 ppm. In addition, we obtain the static dipole polarizability for the $2{}^3{S}_1(M_J=\pm 1)$ state to be 46.857 03(4) a.u., in which the contribution from QED is 70 ppm. The 159 nm tune-out wavelength and the static dipole polarizability of $2{}^3{S}_1$ state might provide a test of atomic structure theory.

The dynamics of nanoplasma produced by an intense near-infrared pulse was investigated by time-resolved soft x-ray photoelectron spectroscopy. The pump-probe electron spectra indicate transient evolution of the electronic states of the constituent atoms and ions during plasma formation and disintegration. The delay dependence of photoelectron yields supports two-step fragmentation of laser-heated clusters, i.e., rapid explosion of surface ions followed by slow expansion of neutral atoms. The speed of the neutral core expansion was evaluated by comparing the experimental data with a model of uniform neutral core expansion.

We theoretically investigate the nonlinear response of bent graphene in the presence of artificially enhanced spin-orbit coupling, which can occur either via adatom deposition or by placing the sheet of bent graphene in contact with a spin-orbit-active substrate. We discuss the interplay between the spin-orbit coupling and the artificial magnetic field generated by the bending for the cases of both Rashba and intrinsic spin-orbit coupling. For the latter, we introduce a spin-field interaction Hamiltonian addressing directly the electron spin as a degree of freedom. Our findings reveal that in this case, by controlling the amount of spin-orbit coupling, it is possible to significantly tune the spectrum of the nonlinear signal, achieving, in principle, efficient conversion of light from the terahertz to UV region.

Of late, there has been an upsurge of interest in studying the sequential sharing of various forms of quantum correlations, viz., nonlocality, preparation contextuality, coherence, and entanglement. In this work, we explore the sequential sharing of nonlocality in a quantum network. We first consider the simplest case of the two-input bilocality scenario that features two independent sources and three parties, including two edge parties and a central party. We demonstrate that, in the symmetric case when the sharing is considered for both the edge parties, the nonlocality can be shared by, at most, two sequential observers per edge party. However, in the asymmetric case, when the sharing across one edge party is considered, we show that, at most, six sequential observers can share the nonlocality in the network. We extend our investigation to the two-input $n$-local scenario in the star-network configuration that features an arbitrary $n$ number of edge parties and one central party. In the asymmetric case, we demonstrate that the network nonlocality can be shared by an unbounded number of sequential observers across one edge party for a suitably large value of $n$. Further, we generalize our study for an arbitrary $m$ input $n$-local scenario in the star-network configuration. We show that, even for an arbitrary $m$ input scenario, the nonlocality can be shared by an unbounded number of sequential observers. However, increasing the input $m$, one has to employ a larger number of edge parties $n$ than that of the two-input case to demonstrate the sharing of an unbounded number of sequential observers.