Qubit Interactions Research Articles

Arbitrary controlled-phase gate on fluxonium qubits using differential ac Stark shifts

Large scale quantum computing motivates the invention of two-qubit gate schemes that not only maximize the gate fidelity but also draw minimal resources. In the case of superconducting qubits, the weak anharmonicity of transmons imposes profound constraints on the gate design, leading to increased complexity of devices and control protocols. Here we demonstrate a resource-efficient control over the interaction of strongly-anharmonic fluxonium qubits. Namely, applying an off-resonant drive to noncomputational transitions in a pair of capacitively-coupled fluxoniums induces a $\text{ZZ}$ interaction due to unequal ac Stark shifts of the computational levels. With a continuous choice of frequency and amplitude, the drive can either cancel the static $\text{ZZ}$ term or increase it by an order of magnitude to enable a controlled-phase (CP) gate with an arbitrary programmed phase shift. The cross-entropy benchmarking of these non-Clifford operations yields a sub $1%$ error, limited solely by incoherent processes. Our result demonstrates the advantages of strongly-anharmonic circuits over transmons in designing the next generation of quantum processors.

Nonclassicality dynamics of a dissipative cavity field containing two qubits with Kerr medium: Linear and Wehrl phase entropies

An analytical solution for a dissipative cavity field interacting with two qubits (TQs) in presence of Kerr-like medium is obtained. The super-operator method is used to obtaining the field density matrix elements under the dispersive approximation. Linear entropy is calculated to determine the entanglement between the cavity field and the TQs. Moreover, the Wehrl entropy and Wehrl phase distribution are discussed to discover the nonclassicality dynamics of a dissipative cavity field. It is found that the Kerr medium and the dissipation reduce the generated quantum coherence due to the qubit–cavity interactions. It is possible to control the ability of cavity–qubit interactions to generate quantum coherence by the mean photon number of the initial coherent cavity state. Moreover, the nonclassicality of the initial coherent state reduces the dissipative and the Kerr medium effects.

Parallel Gate Operations Fidelity in a Linear Array of Flip‐Flop Qubits

AbstractQuantum computers based on silicon are promising candidates for long term universal quantum computation due to the long coherence times of electron and nuclear spin states. Furthermore, the continuous progress of micro‐ and nano‐electronics, also related to the scaling of metal–oxide–semiconductor systems, makes it possible to control the displacement of single dopants thus suggesting their exploitation as qubit holders. Flip‐flop qubit is a donor based qubit where interactions between qubits are achievable for distance up to several hundred nanometers. In this work, a linear array of flip‐flop qubits is considered and the unwanted mutual qubit interactions due to the simultaneous application of two one‐qubit and two two‐qubit gates are included in the quantum gate simulations. In particular, by studying the parallel execution of couples of one‐qubit gates, namely and , and of couples of two‐qubit gate, that is, , a safe inter‐qubit distance is found where unwanted qubit interactions are negligible thus leading to parallel gates fidelity up to 99.9%.

Hamiltonian simulation algorithms for near-term quantum hardware

The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In this work, we develop quantum algorithms for Hamiltonian simulation "one level below” the circuit model, exploiting the underlying control over qubit interactions available in most quantum hardware and deriving analytic circuit identities for synthesising multi-qubit evolutions from two-qubit interactions. We then analyse the impact of these techniques under the standard error model where errors occur per gate, and an error model with a constant error rate per unit time. To quantify the benefits of this approach, we apply it to time-dynamics simulation of the 2D spin Fermi-Hubbard model. Combined with new error bounds for Trotter product formulas tailored to the non-asymptotic regime and an analysis of error propagation, we find that e.g. for a 5 × 5 Fermi-Hubbard lattice we reduce the circuit depth from 1, 243, 586 using the best previous fermion encoding and error bounds in the literature, to 3, 209 in the per-gate error model, or the circuit-depth-equivalent to 259 in the per-time error model. This brings Hamiltonian simulation, previously beyond reach of current hardware for non-trivial examples, significantly closer to being feasible in the NISQ era.

Impact of Spectators on a Two-Qubit Gate in a Tunable Coupling Superconducting Circuit

Cross-resonance (CR) gates have emerged as a promising scheme for fault-tolerant quantum computation with fixed-frequency qubits. We experimentally implement an entangling CR gate by using a microwave-only control in a tunable coupling superconducting circuit, where the tunable coupler provides extra degrees of freedom to verify optimal conditions for constructing a CR gate. By developing a three-qubit Hamiltonian tomography protocol, we systematically investigate the dependency of gate fidelities on spurious qubit interactions and present the first experimental approach to the evaluation of the perturbation impact arising from spectator qubits. Our results reveal that the spectator qubits lead to reductions in CR gate fidelity dependent on ZZ interactions and particular frequency detunings between spectator and gate qubits. The target spectator demonstrates a more serious impact than the control spectator under a standard echo pulse scheme, whereas the degradation of gate fidelity is observed up to 22.5% as both the spectators are present with a modest ZZ coupling to the computational qubits. Our experiments uncover an optimal CR operation regime, and the method we develop here can readily be applied to improving other kinds of two-qubit gates in large-scale quantum circuits.

Synchronizing Two Superconducting Qubits through a Dissipating Resonator.

A system consisting of two qubits and a resonator is considered in the presence of different sources of noise, bringing to light the possibility of making the two qubits evolve in a synchronized way. A direct qubit–qubit interaction turns out to be a crucial ingredient, as well as the dissipation processes involving the resonator. The detrimental role of the local dephasing of the qubits is also taken into account.

The Brain and the New Foundations of Mathematics

Many concepts in mathematics are not fully defined, and their properties are implicit, which leads to paradoxes. New foundations of mathematics were formulated based on the concept of innate programs of behavior and thinking. The basic axiom of mathematics is proposed, according to which any mathematical object has a physical carrier. This carrier can store and process only a finite amount of information. As a result of the D-procedure (encoding of any mathematical objects and operations on them in the form of qubits), a mathematical object is digitized. As a consequence, the basis of mathematics is the interaction of brain qubits, which can only implement arithmetic operations on numbers. A proof in mathematics is an algorithm for finding the correct statement from a list of already-existing statements. Some mathematical paradoxes (e.g., Banach–Tarski and Russell) and Smale’s 18th problem are solved by means of the D-procedure. The axiom of choice is a consequence of the equivalence of physical states, the choice among which can be made randomly. The proposed mathematics is constructive in the sense that any mathematical object exists if it is physically realized. The consistency of mathematics is due to directed evolution, which results in effective structures. Computing with qubits is based on the nontrivial quantum effects of biologically important molecules in neurons and the brain.

The hybrid topological longitudinal transmon qubit

We introduce a new hybrid qubit consisting of a Majorana qubit interacting with a transmon longitudinally coupled to a resonator. To do so, we equip the longitudinal transmon qubit with topological quasiparticles, supported by an array of heterostructure nanowires, and derive charge- and phase-based interactions between the Majorana qubit and the resonator and transmon degrees of freedom. Inspecting the charge coupling, we demonstrate that the Majorana self-charging can be eliminated by a judicious choice of charge offset, thereby maintaining the Majorana degeneracy regardless of the quasiparticles spatial arrangement and parity configuration. We perform analytic and numerical calculations to derive the effective qubit–qubit interaction elements and discuss their potential utility for state readout and quantum error correction. Further, we find that select interactions depend strongly on the overall superconducting parity, which may provide a direct mechanism to characterize deleterious quasiparticle poisoning processes.

Effect of mechanical mode - qubit interaction on perfect optical non-reciprocity in double cavity system

Quantum devices exhibiting optical non-reciprocity are indispensable for quantum information processing and communication technology. In this paper we propose a double cavity optomechanical system where the movable mirror of the cavity is linearly coupled with a qubit placed inside the cavity. We study the effect of this mechanical mode - qubit linear interaction on time reversal symmetry i.e, optical non-reciprocity and prove that mechanical mode - qubit interaction can be used as a new tool to control optical non-reciprocity.

Substrate-controlled dynamics of spin qubits in low dimensional van der Waals materials

We report a theoretical study of the coherence dynamics of spin qubits in two-dimensional materials (2DMs) and van der Waals heterostructures, as a function of the host thickness and the composition of the surrounding environment. We focus on MoS2 and WS2, two promising systems for quantum technology applications, and we consider the decoherence arising from the interaction of the spin qubit with nuclear spins. We show that the Hahn-echo coherence time is determined by a complex interplay between the source of decoherence in the qubit host and in the environment, which in turn determines whether the noise evolution is in a classical or quantum mechanical regime. We suggest that the composition and thickness of van der Waals heterostructures encapsulating a qubit host can be engineered to maximize coherence times. Finally, we discuss how quantum sensors may be able to probe the dynamics of the nuclear bath in 2DMs.

Two-Qubit Local Fisher Information Correlation beyond Entanglement in a Nonlinear Generalized Cavity with an Intrinsic Decoherence.

In this paper, we study a Hamiltonian system constituted by two coupled two-level atoms (qubits) interacting with a nonlinear generalized cavity field. The nonclassical two-qubit correlation dynamics are investigated using Bures distance entanglement and local quantum Fisher information under the influences of intrinsic decoherence and qubit–qubit interaction. The effects of the superposition of two identical generalized coherent states and the initial coherent field intensity on the generated two-qubit correlations are investigated. Entanglement of sudden death and sudden birth of the Bures distance entanglement as well as the sudden changes in local Fisher information are observed. We show that the robustness, against decoherence, of the generated two-qubit correlations can be controlled by qubit–qubit coupling and the initial coherent cavity states.

Dynamics of entanglement and population inversion of two qubits in a hybrid nonlinear system

An analytical solution is obtained when the Kerr medium and Stark shift are considered as nonlinear interaction terms to the system containing two-qubit and two-mode electromagnetic field from the parametric amplifier. Dynamics of the population inversion, cavity–qubit and qubit–qubit entanglements are analyzed under the unitary cavity–qubit interaction, the Kerr medium and the Stark shift. The population inversion of a qubit presents periodic revivals and collapses. The results show that the entanglement and the population inversion as well as the inversion have the same stable intervals, that is, the collapse intervals. It is found that the Kerr medium and the Stark shift may lead to reduction of the periods and the amplitudes of the population inversion and the cavity–qubit/qubit–qubit entanglement. The deteriorated qubit–qubit/cavity–qubit entanglement and the population inversion, due to the Kerr medium, may be increased by increasing the Stark shift and vice versa.

Generation of all-to-all connections in a two-dimensional qubit array with two-body interactions

All-to-all connections are required in general quantum annealing machines to solve various combinatorial optimization problems. The Lechner, Hauke, and Zoller method, which is used to realize the all-to-all connections, requires many-body interactions in locally connected qubits. Because most of the qubit interactions are two-body interactions, Lechner also proposed the construction of each four-body interaction by six controlled-NOT (CNOT) gates between two qubits. However, it is difficult to construct many CNOT gates. Herein, we show more concrete sequences to produce four-body and three-body interactions based on a two-dimensional solid-state qubit system. We show that the number of operations needed to construct the many-body interactions can be reduced using appropriate pulse sequences. These findings will help reduce quantum computation costs for solving combinatorial problems.

Non-local correlation between two coupled qubits interacting nonlinearly with a two-mode cavity: Bell function, Trace norm and Bures distance quantifiers

In this paper, we study the dynamics of two coupled qubits interacting with a two-mode parametric amplifier cavity through the nonlinear interactions of the photon processes under the intrinsic decoherence. The nonlinear unitary interactions lead to generating different types of nonlocal correlations via Bell nonlocality, trace-norm measurement-induced non-locality (MIN), and Bures-distance entanglement. Based on the intrinsic decoherence, the two-qubit states have stationary amounts of the MIN-correlation and Bures distance entanglement with more stability. It is found that the qubit–qubit interaction coupling is affected as additional decoherence. It leads to more oscillations and stability. The enhancement of the amount of the generated nonlocal correlations depends on the superposition of Barut-Girardello coherent states. The phenomenon of sudden birth/death and the Bell non-locality can be enhanced when the two-mode parametric amplifier cavity is initially prepared in the coherent states.

Parallel single-shot measurement and coherent control of solid-state spins below the diffraction limit.

Solid-state spin defects are a promising platform for quantum science and technology. The realization of larger-scale quantum systems with solid-state defects will require high-fidelity control over multiple defects with nanoscale separations, with strong spin-spin interactions for multi-qubit logic operations and the creation of entangled states. We demonstrate an optical frequency-domain multiplexing technique, allowing high-fidelity initialization and single-shot spin measurement of six rare-earth (Er3+) ions, within the subwavelength volume of a single, silicon photonic crystal cavity. We also demonstrate subwavelength control over coherent spin rotations by using an optical AC Stark shift. Our approach may be scaled to large numbers of ions with arbitrarily small separation and is a step toward realizing strongly interacting atomic defect ensembles with applications to quantum information processing and fundamental studies of many-body dynamics.

Addressing the many and the individual

Quantum Systems The ability to coherently manipulate the quantum state of atomic defects in solid-state systems is a promising route to developing a platform for quantum technologies. A successful platform requires the interaction of many qubits in close proximity, as well as the ability to address each qubit individually, and, to date, such requirements have run counter to each other. Chen et al. devised an optical frequency-domain method with which they were able to simultaneously address many individual rare-earth ion defects (six at this point) with separations all within the diffraction limit of the control light. Because the approach is scalable to tens or hundreds of defects, it provides the prospect of realizing truly large-scale quantum processors. Science , this issue p. [592][1] [1]: /lookup/doi/10.1126/science.abc7821

Interaction of a superconducting qubit and a nonlinear field under energy dissipative effect: entanglement and nonclassical properties

The present manuscript studies the temporal behavior of quantum entanglement and nonclassical properties for a superconducting-qubit ( $$\hbox {SC}_{ \text {qubit}}$$ )- field system in the framework of deformed f-oscillator formalism. We introduce the nonlinear Jaynes-Cummings model by using the deformation of the mode field operators. Such a generalization of the Jaynes Cummings model that considers the interaction of a $$\hbox {SC}_{\text {qubit}}$$ with an electromagnetic field in the presence of a nonlinear Kerr-like medium and energy dissipation. We examine the effect of the detuning and decay parameters on the degree of the quantum entanglement, population inversion and field photon statistics. Finally, the relationship among quantum quantifiers is explored according to the optimal choice of the main parameters of the physical model.

Spin-Bath Dynamics in a Quantum Resonator-Qubit System: Effect of a Mechanical Resonator Coupled to a Central Qubit

In line with an experimentally feasible protocol was proposed by A. Asadian et al. [ PRL 112, 190402 (2014)], we introduce a pure dephasing model where the interaction of the central qubit with a nano-mechanical resonator is affected by a spin-bath to study the dynamics of resonator-qubit entangled states. We show that how system-bath coupling as well as the coupling among the bath’s spins, initial semi-classical states of the phonon as well as the initial states of the bath, modify the entanglement of the system using measures like concurrence. To gain insight into the effect of these correlations, we study the dynamics of the mentioned setup both with and without initial correlations for arbitrary system-environment coupling strengths. It is also shown that stable entanglement, which is dependent on correlated initial states of the system-bath, their coupling strength, and bath temperature, occurs even in the presence of decoherence.

Elementary quantum gates between long-distance qubits mediated by a resonator

We propose a scheme to realize Controlled-NOT, Controlled-V, Controlled- $$V^{\dag }$$ gate based on the indirect coupling of two qubits which are coupled to a common resonator. Based on the state-of-the-art controllability of longitudinal and transverse coupling between a qubit and a resonator, we let the control qubit couple to the resonator longitudinally and the target qubit couple to the resonator transversely. One can get the fidelity of these gates (as well as the synthesized Toffoli gate) over 99% within effective gate timescales. The proposed gate scheme is possible for the experimental setups where the effective qubit–resonator coupling strength is far bigger than the cavity decay rate and the dephasing rate of the qubits and applicable to quantum circuit synthesizing and long-distance qubit interaction.

Analyzing Heuristic-based Randomized Search Strategies for the Quantum Circuit Compilation Problem

In this work we investigate the performance of greedy randomised search (GRS) techniques to the problem of compiling quantum circuits to emerging quantum hardware. Quantum computing (QC) represents the next big step towards power consumption minimisation and CPU speed boost in the future of computing machines. Quantum computing uses quantum gates that manipulate multi-valued bits (qubits). A quantum circuit is composed of a number of qubits and a series of quantum gates that operate on those qubits, and whose execution realises a specific quantum algorithm. Current quantum computing technologies limit the qubit interaction distance allowing the execution of gates between adjacent qubits only. This has opened the way to the exploration of possible techniques aimed at guaranteeing nearest-neighbor (NN) compliance in any quantum circuit through the addition of a number of so-called swap gates between adjacent qubits. In addition, technological limitations (decoherence effect) impose that the overall duration (makespan) of the quantum circuit realization be minimized. One core contribution of the paper is the definition of two lexicographic ranking functions for quantum gate selection, using two keys: one key acts as a global closure metric to minimise the solution makespan; the second one is a local metric, which favours the mutual approach of the closest qstates pairs. We present a GRS procedure that synthesises NN-compliant quantum circuits realizations, starting from a set of benchmark instances of different size belonging to the Quantum Approximate Optimization Algorithm (QAOA) class tailored for the MaxCut problem. We propose a comparison between the presented meta-heuristics and the approaches used in the recent literature against the same benchmarks, both from the CPU efficiency and from the solution quality standpoint. In particular, we compare our approach against a reference benchmark initially proposed and subsequently expanded in [1] by considering: (i) variable qubit state initialisation and (ii) crosstalk constraints that further restrict parallel gate execution.