XY Interaction Research Articles

Synthesis of energy-conserving quantum circuits with XY interaction

Abstract We study quantum circuits constructed from $\sqrt{iSWAP}$ gates and, more
generally, from the entangling gates that can be realized with the XX+YY
interaction alone. Such gates preserve the Hamming weight of states in the
computational basis, which means they respect the global U(1) symmetry
corresponding to rotations around the z axis. Equivalently, assuming that the
intrinsic Hamiltonian of each qubit in the system is the Pauli Z operator, they
conserve the total energy of the system. We develop efficient methods for
synthesizing circuits realizing any desired energy-conserving unitary using
XX+YY interaction with or without single-qubit rotations around the z-axis.
Interestingly, implementing generic energy-conserving unitaries, such as CCZ
and Fredkin gates, with 2-local energy-conserving gates requires the use of
ancilla qubits. When single-qubit rotations around the z-axis are permitted,
our scheme requires only a single ancilla qubit, whereas with the XX+YY
interaction alone, it requires 2 ancilla qubits. In addition to exact
realizations, we also consider approximate realizations and show how a general
energy-conserving unitary can be synthesized using only a sequence of
$\sqrt{iSWAP}$ gates and 2 ancillary qubits, with arbitrarily small error,
which can be bounded via the Solovay-Kitaev theorem. Our methods are also
applicable for synthesizing energy-conserving unitaries when, rather than the
XX+YY interaction, one has access to any other energy-conserving 2-body
interaction that is not diagonal in the computational basis, such as the
Heisenberg exchange interaction. We briefly discuss the applications of these
circuits in the context of quantum computing, quantum thermodynamics, and
quantum clocks.

Ion trap long-range XY model for quantum state transfer and optimal spatial search

Linear ion trap chains are a promising platform for quantum computation and simulation. The XY model with long-range interactions can be implemented with a single side-band Mølmer–Sørensen scheme, giving interactions that decay as , where parameterises the interaction range. Lower leads to longer range interactions, allowing faster long-range gate operations for quantum computing. However, decreasing causes an increased generation of coherent phonons and appears to dephase the effective XY interaction model. We characterise and show how to correct for this effect completely, allowing lower interactions to be coherently implemented. Ion trap chains are thus shown to be a viable platform for spatial quantum search in optimal time, for N ions. Finally, we introduce a quantum state transfer protocol, with a qubit encoding that maintains a high fidelity.

σ‐Hole intermolecular interactions between carbon oxides and dihalogens: Ab‐initio investigations

Recently, halogen bonding (XB) has received increased attention as a new type of non-covalent interaction widely present in nature. In this work, quantum chemical calculations at DFT level have been carried out to investigate halogen bonding interactions between COn (n= 1 or 2) and dihalogen molecules XY (X=F, Cl, Br, I and Y=Cl, Br, I). Highly accurate all-electron data, estimated by CCSD(T) calculations, were used to benchmark the different levels of computational methods with the objective of finding the best accuracy/computational cost. Molecular electrostatic potential, interaction energy values, charge transfer, UV spectra, and natural bond orbital (NBO) analysis were determined to better understand the nature of the XB interaction. Density of states (DOS) and projected DOS were also computed. Hence, according to these results, the magnitude of the halogen bonding is affected by the halogen polarizability and electronegativity, where for the more polarizable and less electronegative halogen atoms, the σ-hole is bigger. Furthermore, for the halogen-bonded complexes involving CO and XY, the OC∙∙∙XY interaction is stronger than the CO∙∙∙XY interaction. Thus, the results presented here can establish fundamental characteristics of halogen bonding in media, which would be very helpful for applying this noncovalent interaction for the sustainable capture of carbon oxides.

Many-body localization of Z3 Fock parafermions

We study the effects of a random magnetic field on a one-dimensional (1D) spin-1 chain with correlated nearest-neighbor XY interaction. We show that this spin model can be exactly mapped onto the 1D disordered tight-binding model of ${\mathbb{Z}}_{3}$ Fock parafermions (FPFs), exotic anyonic quasiparticles that generalize usual spinless fermions. Thus, we have a peculiar case of a disordered Hamiltonian that despite being bilinear in the creation and annihilation operators, exhibits a many-body localization (MBL) transition owing to the nontrivial statistics of FPFs. This is in sharp contrast to conventional bosonic and fermionic quadratic disordered Hamiltonians that show single-particle (Anderson) localization. We perform finite-size exact diagonalization calculations of level-spacing statistics, fractal dimensions, and entanglement entropy, and provide convincing evidence for the MBL transition at finite disorder strength.

Nonadiabatic geometric quantum computation of W-state codes using invariant-based reverse engineering

In this paper, we propose a protocol to realize nonadiabatic geometric quantum computation (NGQC)of W-state codes in a spin system using invariant-based reverse engineering. The Heisenberg XY interaction of spin qubits provides a two-dimensional computational subspace spanned by a pair of W states. By applying a time-dependent magnetic on the spin qubits, we realize the effective Pauli operations for the computational subspace. Assisted by the invariant-based reverse engineering, the waveform of the control field is designed and the evolution paths for the NGQC is found. The performance of the protocol under the influence of experimental imperfections is estimated by the numerical simulations with available parameters. The results demonstrate that the protocol is robust against systematic error, random noise and decoherence. Therefore, the protocol may be promising to implement fast and robust manipulation of W states in spin systems.

High-capacity and high-power collective charging with spin chargers.

Quantum battery works as a micro- or nanodevice to store and redistribute energy at the quantum level. Here we propose a spin-charger protocol, in which the battery cells are charged by a finite number of spins through a general Heisenberg XY interaction. Under the isotropic interaction, the spin-charger protocol is endowed with a higher capacity in terms of the maximum stored energy than the conventional protocols, where the battery is charged by a continuous-variable system, e.g., a cavity mode. By tuning the charger size, a tradeoff between the maximum stored energy and the average charging power is found in comparison to the cavity-charger protocol in the Tavis-Cummings model. Quantum advantage of our protocol is manifested by the scaling behavior of the optimal average power with respect to the battery size, in comparing the collective charging scheme to its parallel counterpart. We also discuss the detrimental effect on the charging performance from the anisotropic interaction between the battery and the charger, the nonideal initial states for both of them, and the crosstalk among the charger spins. A strong charger-charger interaction can be used to decouple the battery and the charger. Our findings about the advantages of the spin-charger protocol over the conventional cavity-charger protocols, including the high capacity of energy storage and the superior power law in the collective charging, provide an insight to exploit an efficient quantum battery based on the spin-spin-environment model.

Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology.

We introduce the concept of a Floquet gauge pump whereby a dynamically engineered Floquet Hamiltonian is employed to reveal the inherent degeneracy of the ground state in interacting systems. We demonstrate this concept in a one-dimensional XY model with periodically driven couplings and transverse field. In the high-frequency limit, we obtain the Floquet Hamiltonian consisting of the static XY and dynamically generated Dzyaloshinsky-Moriya interaction (DMI) terms. The dynamically generated magnetization current depends on the phases of complex coupling terms, with the XY interaction as the real and DMI as the imaginary part. As these phases are cycled, the current reveals the ground-state degeneracies that distinguish the ordered and disordered phases. We discuss experimental requirements needed to realize the Floquet gauge pump in a synthetic quantum spin system of interacting trapped ions.

Single-photon generation of entangled triplet state in an atomic spin dimer

We show that the entanglement between two atomic spins, coupled via XY interaction, can be achieved with the aid of a single photon in a controllable manner. Assuming a constant spin-photon coupling, two distinct cases are considered — excitation with a constant and with a linear time-dependent photon frequency. We demonstrate that these problems reduce to the study of the well known Jaynes-Cummings and Jaynes-Cummings – Landau-Zener models, respectively, where the two-level system is formed by the zero-momentum mode states of the dimer. Owing to the exact solubility of both models, by tuning the relevant parameters, one can design and coherently control the dynamics of the excitation process. For instance, one can adiabatically switch from an atomic spin system initialized in a state with both spins down to the maximally entangled triplet state.

Temperature estimation in a quantum spin bath through entangled and separable two-qubit probes

We investigate the two-qubit thermometry of a thermal spins bath using a pair of qubits in entangled or product states as a quantum probe. The probe system is coupled to the bath via a Heisenberg XY interaction. We evaluate the precision of the procedure by recourse to the quantum Fisher information and the corresponding quantum signal-to-noise ratio. We demonstrate that the use of entangled Bell states does not necessarily lead to improvements in the estimation procedure. For both short- and long-time interactions, we found that only a product state always allows us to achieve the largest estimation precision as compared to entangled Bell states.

Implementation of XY entangling gates with a single calibrated pulse

Near-term applications of quantum information processors will rely on optimized circuit implementations to minimize gate depth and therefore mitigate the impact of gate errors in noisy intermediate-scale quantum (NISQ) computers. More expressive gate sets can significantly reduce the gate depth of generic circuits. Similarly, structured algorithms can benefit from a gate set that more directly matches the symmetries of the problem. The XY interaction generates a family of gates that provides expressiveness well tailored to quantum chemistry as well as to combinatorial optimization problems, while also offering reductions in circuit depth for more generic circuits. Here we implement the full family of XY entangling gates in a transmon-based superconducting qubit architecture. We use a composite pulse scheme that requires calibration of only a single gate pulse and maintains constant gate time for all members of the family. This allows us to maintain a high fidelity implementation of the gate across all entangling angles. The average fidelity of gates sampled from this family ranges from $95.67 \pm 0.60\%$ to $99.01 \pm 0.15\%$, with a median fidelity of $97.35 \pm 0.17\%$, which approaches the coherence-limited gate fidelity of the qubit pair. We furthermore demonstrate the utility of XY in a quantum approximation optimization algorithm in enabling circuit depth reductions as compared to the CZ only case.

High-Contrast ZZ Interaction Using Superconducting Qubits with Opposite-Sign Anharmonicity.

For building a scalable quantum processor with superconducting qubits, ZZ interaction is of great concern because its residual has a crucial impact to two-qubit gate fidelity. Two-qubit gates with fidelity meeting the criterion of fault-tolerant quantum computation have been demonstrated using ZZ interaction. However, as the performance of quantum processors improves, the residual static ZZ can become a performance-limiting factor for quantum gate operation and quantum error correction. Here, we introduce a superconducting architecture using qubits with opposite-sign anharmonicity, a transmon qubit, and a C-shunt flux qubit, to address this issue. We theoretically demonstrate that by coupling the two types of qubits, the high-contrast ZZ interaction can be realized. Thus, we can control the interaction with a high on-off ratio to implement two-qubit controlled-Z gates, or suppress it during two-qubit gate operation using XY interaction (e.g., an iSWAP gate). The proposed architecture can also be scaled up to multiqubit cases. In a fixed coupled system, ZZ crosstalk related to neighboring spectator qubits could also be heavily suppressed.

A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY-interactions on a Cayley tree

The main aim of the present paper by means of the quantum Markov chain (QMC) approach is to establish the existence of a phase transition for the quantum Ising model with competing XY interaction. In this scheme, the C*-algebraic approach is employed to the phase transition problem. Note that these kinds of models do not have one-dimensional analogs, i.e., the considered model persists only on trees. It turns out that if the Ising part interactions vanish, then the model with only competing XY-interactions on the Cayley tree of order two does not have a phase transition. By phase transition, we mean the existence of two distinct QMCs that are not quasi-equivalent and their supports do not overlap. Moreover, it is also shown that the QMC associated with the model has a clustering property, which implies that the von Neumann algebras corresponding to the states are factors.

Steady states of a driven dissipative dipolar XXZ chain

We study theoretically a driven dissipative one-dimensional XXZ spin-1/2 chain with dipole coupling and a tunable strength of the Ising and XY interaction. Within a mean-field approximation, we find a rich phase diagram with uniform, spin density wave, antiferromagnetic and oscillatory phases, as well as regions of phase bistability. We study the phase diagram of small quantum systems using exact diagonalisation, and compare the results to the mean-field theory. We find that while expectation values only capture the uniform phases of the mean-field theory, fluctuations about these expectation values give signatures of spatially non-uniform phases and bistabilities. We find these signatures for all ratios of the Ising to XY interaction, showing that they appear to be general features of spin-1/2 systems.

How Far Can One Push the Noble Gases Towards Bonding?: A Personal Account.

Noble gases (Ngs) are the least reactive elements in the periodic table towards chemical bond formation when compared with other elements because of their completely filled valence electronic configuration. Very often, extreme conditions like low temperatures, high pressures and very reactive reagents are required for them to form meaningful chemical bonds with other elements. In this personal account, we summarize our works to date on Ng complexes where we attempted to theoretically predict viable Ng complexes having strong bonding to synthesize them under close to ambient conditions. Our works cover three different types of Ng complexes, viz., non-insertion of NgXY type, insertion of XNgY type and Ng encapsulated cage complexes where X and Y can represent any atom or group of atoms. While the first category of Ng complexes can be thermochemically stable at a certain temperature depending on the strength of the Ng-X bond, the latter two categories are kinetically stable, and therefore, their viability and the corresponding conditions depend on the size of the activation barrier associated with the release of Ng atom(s). Our major focus was devoted to understand the bonding situation in these complexes by employing the available state-of-the-art theoretic tools like natural bond orbital, electron density, and energy decomposition analyses in combination with the natural orbital for chemical valence theory. Intriguingly, these three types of complexes represent three different types of bonding scenarios. In NgXY, the strength of the donor-acceptor Ng→XY interaction depends on the polarizing power of binding the X center to draw the rather rigid electron density of Ng towards itself, and sometimes involvement of such orbitals becomes large enough, particularly for heavier Ng elements, to consider them as covalent bonds. On the other hand, in most of the XNgY cases, Ng forms an electron-shared covalent bond with X while interacting electrostatically with Y representing itself as [XNg]+Y−. Nevertheless, in some of the rare cases like NCNgNSi, both the C-Ng and Ng-N bonds can be represented as electron-shared covalent bonds. On the other hand, a cage host is an excellent moiety to examine the limits that can be pushed to attain bonding between two Ng atoms (even for He) at high pressure. The confinement effect by a small cage-like B12N12 can even induce some covalent interaction within two He atoms in the He2@B12N12 complex.

Decay rates and energies of free magnons and bound states in dissipative XXZ chains

Chains of coupled two-level atoms behave as one-dimensional quantum spin systems, exhibiting free magnons and magnon bound states. While these excitations are well studied for closed systems, little consideration has been given to how they are altered by the presence of an environment. This will be especially important in systems that exhibit nonlocal dissipation, e.g., systems in which the magnons decay due to optical emission. In this paper, we consider free magnon excitations and two-magnon bound states in an XXZ chain with nonlocal dissipation. We prove that while the energy of the bound state can lie outside the two-magnon continuum of energies, the decay rate of the bound state has to always lie within the two-magnon continuum of decay rates. We then derive analytically the bound-state solutions for a system where both the XY interaction and nonlocal dissipation are nearest neighbor or next-nearest neighbor, finding that the inclusion of nonlocal dissipation allows more freedom in engineering the energy and decay rate dispersions for the bound states. Finally, we numerically study a model of an experimental setup that should allow the realization of dissipative bound states by using Rydberg-dressed atoms coupled to a photonic crystal waveguide. We demonstrate that this model can exhibit many key features of our simpler models.

Steady-state measurement-induced nonlocality in thermal reservoir

We examined measurement-induced nonlocality (MIN) of a central system for which every of the constituent qubit is embedded in its respective independent thermal reservoir. By introducing anisotropy to the Heisenberg XY interaction of the qubits, we showed that the strength of the MIN can be enhanced apparently. The anisotropy of the spin interaction can also be employed to generate MIN from the initial zero-MIN states. In the infinite-time limit, the steady-state MIN is independent of the initial states and is determined solely by the anisotropic parameter of the system and the decoherence factor of the thermal reservoir.

Quantum information transmission through a qubit chain with quasi-local dissipation

We study quantum information transmission in a Heisenberg-XY chain where qubits are affected by quasi-local environment action and compare it with the case of local action of the environment. We find that for open boundary conditions the former situation always improves quantum state transfer process, especially for short chains. In contrast, for closed boundary conditions quasi-local environment results advantageous in the strong noise regime. When the noise strength is comparable with the XY interaction strength, the state transfer fidelity through chain of odd/even number of qubits in presence of quasi-local environment results smaller/greater than that in presence of local environment.

Realization of universal nonadiabatic geometric control on decoherence-free qubits in the XY model

A fundamental requirement of quantum information processing is the protection from the adverse effects of decoherence and noise. Decoherence-free subspaces and geometric processing are important steps of quantum information protection. Here, we provide a new experimentally feasible scheme to combine decoherence-free subspaces with nonadiabatic geometric manipulations to attain a universal quantum computation. The proposed scheme is different from previous proposals and is based on the typical XY interaction coupling, which can be set up in various nano-engineered systems and therefore open up for realization of nonadiabatic holonomic quantum computation in decoherence-free subspaces.

Exact phase boundaries and topological phase transitions of the XYZ spin chain.

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the XYZ spin chain. First, we identify the Ising order along x[over ̂] or y[over ̂] as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the XY interaction and the coupling Δ of the Δσ^{z}σ^{z} interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the XYZ spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1, depending on whether the Ising order parameter is along x[over ̂] or y[over ̂] directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the XYZ model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the XYZ model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

Universal feedback control of two-qubit entanglement

We consider two-qubit undergoing local dissipation and subject to local driving. We then determine the optimal Markovian feedback action to preserve initial entanglement as well as to create stationary entanglement with the help of an XY interaction Hamiltonian. Such feedback actions are worked out in a way not depending on the initial two-qubit state, whence called universal.