Preparation Of Entangled States Research Articles

Efficient quantum circuits based on the quantum natural gradient

Efficient preparation of arbitrary entangled quantum states is crucial for quantum computation. This is particularly important for noisy intermediate-scale quantum simulators relying on variational hybrid quantum-classical algorithms. To that end, we propose symmetry-conserving modified quantum approximate optimization algorithm (SCom-QAOA) circuits. The depths of these circuits depend not only on the desired fidelity to the target state but also on the amount of entanglement the state contains. The parameters of the SCom-QAOA circuits are optimized using the quantum natural gradient method based on the Fubini-Study metric. The SCom-QAOA circuit transforms an unentangled state into a ground state of a gapped one-dimensional Hamiltonian with a circuit depth that depends not on the system size but rather on the finite correlation length. In contrast, the circuit depth grows proportionally to the system size for preparing low-lying states of critical one-dimensional systems. Even in the latter case, SCom-QAOA circuits with depth less than the system size were sufficient to generate states with fidelity in excess of 99%, which is relevant for near-term applications. The proposed scheme enlarges the set of the initial states accessible for variational quantum algorithms and widens the scope of investigation of nonequilibrium phenomena in quantum simulators. Published by the American Physical Society 2024

Characterizing Matrix-Product States and Projected Entangled-Pair States Preparable via Measurement and Feedback

Preparing long-range entangled states poses significant challenges for near-term quantum devices. It is known that measurement and feedback (MF) can aid this task by allowing the preparation of certain paradigmatic long-range entangled states with only constant circuit depth. Here, we systematically explore the structure of states that can be prepared using constant-depth local circuits and a single MF round. Using the framework of tensor networks, the preparability under MF translates to tensor symmetries. We detail the structure of matrix-product states (MPSs) and projected entangled-pair states (PEPSs) that can be prepared using MF, revealing the coexistence of Clifford-like properties and magic. In one dimension, we show that states with Abelian-symmetry-protected topological order are a restricted class of MF-preparable states. In two dimensions, we parametrize a subset of states with Abelian topological order that are MF preparable. Finally, we discuss the analogous implementation of operators via MF, providing a structural theorem that connects to the well-known Clifford teleportation. Published by the American Physical Society 2024

Fast joint parity measurement via collective interactions induced by stimulated emission

Parity detection is essential in quantum error correction. Error syndromes coded in parity are detected routinely by sequential CNOT gates. Here, different from the standard CNOT-gate based scheme, we propose a reliable joint parity measurement (JPM) scheme inspired by stimulated emission. By controlling the collective behavior between data qubits and syndrome qubit, we realize the parity detection and experimentally implement the weight-2 and weight-4 JPM scheme in a tunable coupling superconducting circuit, which shows comparable performance to the CNOT scheme. Moreover, with the aid of the coupling tunability in quantum system, this scheme can be further utilized for specific joint entangling state preparation (JEP) with high fidelity, such as multiqubit entangled state preparation for non-adjacent qubits. This strategy, combined with the superconducting qubit system with tunable couplers, reveals tremendous potential and applications in the surface code architecture without adding extra circuit elements. Besides, the method we develop here can readily be applied in large-scale quantum computation and quantum simulation.

State carving in a chirally-coupled atom-nanophotonic cavity

Coherent quantum control of multiqubit systems represents one of the challenging tasks in quantum science and quantum technology. Here we theoretically investigate the reflectivity spectrum in an atom-nanophotonic cavity with collective nonreciprocal couplings. In the strong-coupling regime with a high cooperativity, we theoretically predict distinct on-resonance spectral dips owing to destructive interferences of chiral couplings. Due to the well-separated multiple dips in the spectrum, a contrasted reflectivity suggests a new control knob over the desired entangled state preparation in the basis of coupled and uncoupled states from the atoms’ internal hyperfine ground states. We propose to utilize such atom-nanophotonic cavity to quantum engineer the atomic internal states via photon-mediated dipole–dipole interactions in the coupled state and the chirality of decay channels, where the atomic Bell state and W states for arbitrary number of atoms can be tailored and heralded by state carving in the single-photon reflection spectrum. Our results pave the way toward quantum engineering of multiqubit states and offer new opportunities for coherent and scalable multipartite entanglement transport in atoms coupled to nanophotonic devices.

Preparation of two-qubit entangled states on a spin-1/2 Ising–Heisenberg diamond spin cluster by controlling the measurement

The preparation of entangled quantum states is an inherent and indispensable step for the implementation of many quantum information algorithms. Depending on the physical system, there are different ways to control and measure them, which allow one to achieve the predefined quantum states. The diamond spin cluster is the system that can be applied for this purpose. Moreover, such a system appears in chemical compounds such as the natural mineral azurite, where the Cu2+ are arranged in a spin-1/2 diamond chain. Herein, we propose the method of preparation of pure entangled states on the Ising–Heisenberg spin-1/2 diamond cluster. We suppose that the cluster consists of two central spins which are described by an anisotropic Heisenberg model and interact with the side spins via Ising interaction. Controlling the measurement direction of the side (central) spins allows us to achieve predefined pure quantum states of the central (side) spins. We show that this directly affects the entanglement and fidelity of the prepared states. For example, we obtain conditions and fidelities for preparations of the Bell states.

Strong Quantum Metrological Limit from Many-Body Physics.

Surpassing the standard quantum limit and even reaching the Heisenberg limit using quantum entanglement, represents the Holy Grail of quantum metrology. However, quantum entanglement is a valuable resource that does not come without a price. The exceptional time overhead for the preparation of large-scale entangled states raises disconcerting concerns about whether the Heisenberg limit is fundamentally achievable. Here, we find a universal speed limit set by the Lieb-Robinson light cone for the quantum Fisher information growth to characterize the metrological potential of quantum resource states during their preparation. Our main result establishes a strong precision limit of quantum metrology accounting for the complexity of many-body quantum resource state preparation and reveals a fundamental constraint for reaching the Heisenberg limit in a generic many-body lattice system with bounded one-site energy. It enables us to identify the essential features of quantum many-body systems that are crucial for achieving the quantum advantage of quantum metrology, and brings an interesting connection between many-body quantum dynamics and quantum metrology.

Stationary states of a dissipative two-qubit quantum channel and their applications for quantum machine learning

Entangled-state preparation and preservation are the cornerstones of any quantum information platform. However, the strongest adversaries in quantum information science are unwanted environmental effects such as decoherence and dissipation. Here, we address how to control and harness these unwanted effects that arise from the coupling of a system with its environment, to provide stationary entangled states for quantum machine learning (QML). To do so, we design a dissipative quantum channel, i.e., a two-qubit system interacting with a squeezed vacuum field reservoir, and study the output state of the channel by solving the corresponding master equation, especially, in the small squeezing regime. We show that the time-dependent output state of the channel is the so-called two-qubit X-states that generalize many families of entangled two-qubit states. Also, by considering a general Bell diagonal state as the initial state of the system, we reveal that this dissipative channel generates two well-known classes of entangled mixed state and Werner-like states in the steady-state regime. Moreover, this channel provides an efficient way to determine whether a given initial state results in a stationary entangled state or not. Finally, we examine the potential application of the designed two-qubit channel for QML. In this line, we propose a general theoretical scheme for quantum neural networks (QNNs) implemented with the variational quantum circuits, which encode data in continuous variables (CVs) of the two-qubit states. The linear (also referred to as affine) and nonlinear (activation function) transformations are enacted in the QNN using the stationary states of the two-qubit channel and measurement process, respectively. Finally, we proceed to test our proposed model by solving some supervised binary classification tasks. Integrating the non-unitary transformation and parallel-processed neural computing on such a two-qubit channel establishes the requirements for a meaningful QNN. Such a CV-QNN model with sufficient layers may execute any algorithm implementable on a universal CV quantum computer.

A secure deterministic remote state preparation via a seven-qubit entangled channel of a two-qubit entangled state under the impact of quantum noise

In this study, a deterministic remote state preparation protocol is presented for the preparation of arbitrary two-qubit entangled states through a seven-qubit entangled channel prepared from the state proposed by Borras et al. (2007). The implementation of any protocol for quantum communication is inherently susceptible to quantum noise, presenting a challenge to the reliability and security of quantum communication systems. The introduction of noise results in a transition from a pure to a mixed quantum state. This paper examines six distinct noise models, including bit-flip noise, phase-flip noise, bit-phase-flip noise, amplitude damping, phase damping, and depolarizing noise, and analyzes their impact on the entangled channel. The alterations to the density matrices resulting from the introduction of noise are evaluated. The fidelity between the original and remotely prepared quantum states is also analyzed and visually represented. Additionally, a thorough security analysis is conducted to demonstrate the robustness of the protocol against both internal and external attacks.

Measurement as a Shortcut to Long-Range Entangled Quantum Matter

The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback (``adaptive circuits'') can evade such restrictions. We introduce three classes of local adaptive circuits that enable low-depth preparation of long-range entangled quantum matter characterized by gapped topological orders and conformal field theories (CFTs). The three classes are inspired by distinct physical insights, including tensor-network constructions, multiscale entanglement renormalization ansatz (MERA), and parton constructions. A large class of topological orders, including chiral topological order, can be prepared in constant depth or time, and one-dimensional CFT states and non-abelian topological orders with both solvable and non-solvable groups can be prepared in depth scaling logarithmically with system size. We also build on a recently discovered correspondence between symmetry-protected topological phases and long-range entanglement to derive efficient protocols for preparing symmetry-enriched topological order and arbitrary CSS (Calderbank-Shor-Steane) codes. Our work illustrates the practical and conceptual versatility of measurement for state preparation.

Generation of Greenberger-Horne-Zeilinger States on Two-Dimensional Superconducting-Qubit Lattices via Parallel Multiqubit-Gate Operations

A recent major technological breakthrough in superconducting circuits is the realization of more than 50 qubits arranged on two-dimensional (2D) lattices with tunable nearest-neighbor couplings. We propose a protocol to generate Greenberger-Horne-Zeilinger (GHZ) states on 2D superconducting-qubit lattices by applying multiqubit controlled-$i$swap gates in parallel. The multiqubit gate can be naturally implemented based on an effective three-body interaction, which can be synthesized with appropriate detunings and coupling strengths between qubits. We simulate the preparation process of GHZ states with realistic parameters, and show a $37$-qubit GHZ state can be generated with a controlled-$i$swap depth of $3$. Our proposal provides a more promising method of generating GHZ states on the latest 2D superconducting-qubit architectures and will stimulate the preparation of multiqubit entangled states based on multiqubit gates.

Rapid Feedback Stabilization of Quantum Systems With Application to Preparation of Multiqubit Entangled States.

For stochastic quantum systems with measurement feedback, this article proposes a rapid switching control scheme based on state space partition and realizes the rapid stabilization of an eigenstate of an observable operator. Meanwhile, we apply the proposed scheme to the preparation of typical entangled states in multiqubit systems. In view of the convergence obstacle caused by the symmetric structure of the state space, especially in the case with degenerate observable operators, we first partition the state space into a subset containing the target state and its complement to distinguish the target state from its antipodal points, and then design the corresponding control laws in these two subsets, respectively, by using different Lyapunov functions. The interaction Hamiltonians are also constructed to drive the system state to the desired subset first, and further to the target state. In particular, the control law designed in the undesired subset guarantees the strictly monotonic descent of the corresponding Lyapunov function, which makes the system trajectory switch between the two subsets at most twice and has the potential to speed up the convergence process. We also prove the stability of the closed-loop system with the proposed switching control law based on the stochastic Lyapunov stability theory. By applying the proposed switching control scheme to a three-qubit system, we achieve the preparation of a GHZ state and a W state.

Preparation and Analysis of Two-Dimensional Four-Qubit Entangled States with Photon Polarization and Spatial Path

Entanglement states serve as the central resource for a number of important applications in quantum information science, including quantum key distribution, quantum precision measurement, and quantum computing. In pursuit of more promising applications, efforts have been made to generate entangled states with more qubits. However, the efficient creation of a high-fidelity multiparticle entanglement remains an outstanding challenge due to the difficulty that increases exponentially with the number of particles. We design an interferometer that is capable of coupling the polarization and spatial paths of photons and prepare 2-D four-qubit GHZ entanglement states. Using quantum state tomography, entanglement witness, and the violation of Ardehali inequality against local realism, the properties of the prepared 2-D four-qubit entangled state are analyzed. The experimental results show that the prepared four-photon system is an entangled state with high fidelity.

Two-dimensional quantum motion of a levitated nanosphere

We report on the two-dimensional (2D) dynamics of a levitated nanoparticle in an optical cavity. The motion of the nanosphere is strongly coupled to the cavity field by coherent scattering and heavily cooled in the plane orthogonal to the tweezer axis. Due to the characteristics of the 2D motion and the strong optomechanical coupling, the motional sideband asymmetry that reveals the quantum nature of the dynamics is not limited to mere scale factors between Stokes and anti-Stokes peaks, as customary in quantum optomechanics, but assumes a peculiar spectral dependence. We introduce and discuss an effective thermal occupancy that quantifies how close the system is to a minimum uncertainty state and allows us to consistently characterize the particle motion. By rotating the polarization angle of the tweezer beam we tune the system from a 1D cooling regime, where we achieve a best thermal occupancy of $0.51\ifmmode\pm\else\textpm\fi{}0.05$, to a regime in which the fully 2D dynamics of the particle exhibit strong nonclassical properties. We achieve a strong 2D confinement with thermal occupancy of $3.4\ifmmode\pm\else\textpm\fi{}0.4$ along the warmest direction and around one in the orthogonal one. These results represent a major improvement over previous experiments considering both the 1D and the 2D motion and pave the way toward the preparation of tripartite optomechanical entangled states and novel applications to directional force and displacement quantum sensing.

Stabilizing volume-law entangled states of fermions and qubits using local dissipation

We analyze a general method for the dissipative preparation and stabilization of volume-law entangled states of fermionic and qubit lattice systems in 1D (and higher dimensions for fermions). Our approach requires minimal resources: nearest-neighbour Hamiltonian interactions that obey a suitable chiral symmetry, and the realization of just a single, spatially-localized dissipative pairing interaction. In the case of a qubit array, the dissipative model we study is not integrable and maps to an interacting fermionic problem. Nonetheless, we analytically show the existence of a unique pure entangled steady state (a so-called rainbow state). Our ideas are compatible with a number of experimental platforms, including superconducting circuits and trapped ions.

Hybrid controlled-sum gate with one superconducting qutrit and one cat-state qutrit and application in hybrid entangled state preparation

Compared with a qubit, a qudit (i.e., $d$-level or $d$-state quantum system) provides a larger Hilbert space to store and process information. On the other hand, qudit-based hybrid quantum computing usually requires performing hybrid quantum gates with qudits different in their nature or in their encoding format. In this work, we consider the qutrit case, i.e., the case for a qudit with $d$=3. We propose a simple method to realize a hybrid quantum controlled-SUM gate with one superconducting (SC) qutrit and a cat-state qutrit. This gate plus single-qutrit gates form a universal set of ternary logic gates for quantum computing with qutrits. Our proposal is based on circuit QED and operates essentially by employing a SC ququart (a four-level quantum system) dispersively coupled to a microwave cavity. The gate implementation is quite simple because it only requires a single basic operation. Neither classical pulse nor measurement is needed. The auxiliary higher energy level of the SC ququart is virtually excited during the gate operation, thus decoherence from this level is greatly suppressed. As an application of this gate, we discuss the generation of a hybrid maximally-entangled state of one SC qutrit and one cat-state qutrit. We further analyze the experimental feasibility of creating such hybrid entangled state in circuit QED. This proposal is quite general and can be extended to accomplish the same task in a wide range of physical system, such as a four-level natural or artificial atom coupled to an optical or microwave cavity.

Power-law decay of entanglement quantifiers in a single agent coupled to a many-body system

Manipulating many body quantum systems is a challenge. A useful way to achieve it would be to entangle the system to a diluted system, with a small particle number. Preparation of such entangled states can be facilitated as ground state of a many body Hamiltonian or the steady state of a many body open quantum system. Here we study two-site lattice models with a conserved boson number, biased to display a large occupancy in one of the sites. The Von Neumann entanglement entropy as well as the Logarithmic negativity show a typical power law decay in $R$, the occupancy ratio between the two sites. These results imply that it is feasible to entangle a large many body system to a single atom, as recently reported experimentally.

Stroboscopic aliasing in long-range interacting quantum systems

We unveil a mechanism for generating oscillations with arbitrary multiplets of the period of a given external drive, in long-range interacting quantum many-particle spin systems. These oscillations break discrete time translation symmetry as in time crystals, but they are understood via two intertwined stroboscopic effects similar to the aliasing resulting from video taping a single fast rotating helicopter blade. The first effect is similar to a single blade appearing as multiple blades due to a frame rate that is in resonance with the frequency of the helicopter blades' rotation; the second is akin to the optical appearance of the helicopter blades moving in reverse direction. Analogously to other dynamically stabilized states in interacting quantum many-body systems, this stroboscopic aliasing is robust to detuning and excursions from a chosen set of driving parameters, and it offers a novel route for engineering dynamical n-tuplets in long-range quantum simulators, with potential applications to spin squeezing generation and entangled state preparation.

Coupling-modulation–mediated generation of stable entanglement of superconducting qubits via dissipation

We propose an experimentally feasible scheme for the dissipative generation of stable entanglement of superconducting qubits via coupling modulation without applying any drives on qubits and resonator. Firstly, we study the circuit of one superconducting transmission line resonator coupled to two separated qubits via two superconducting quantum interference devices (SUQIDs). By modulating the inductance of the SQUIDs via external fluxes, we can tailor an appropriate qubit-resonator coupling with both red- and blue-sideband interactions. Combined with the photon loss of the resonator, the two qubits can be autonomously steered into a long-lived entangled state with high fidelity. Moreover, we extend the model to one resonator coupled to two separated qubit chains, each of which contains N linearly coupled superconducting qubits. We show that the lossy resonator can drive the whole system into a unique dark state, i.e., a series of N entangled pairs of qubits across the chains can be stabilized at the stationary state. So, the present work enables the preparation of a stable long-range entangled state between the two qubits in the end sites of the chains, which plays an important role for implementing scalable quantum computation and quantum communication.

Entanglement preparation and nonreciprocal excitation evolution in giant atoms by controllable dissipation and coupling

We investigate the dynamics of giant atom(s) in a waveguide QED scenario, where the atom couples to the coupled resonator waveguide via two sites. For a single giant atom setup, we find that the atomic dissipation rate can be adjusted by tuning its size. For the two giant atoms system, the waveguide will induce the controllable individual and collective dissipation as well as effective inter-atom coupling. As a result, we can theoretically realize the robust entangled state preparation and non-reciprocal excitation evolution. We hope our study can be applied in quantum information processing based on photonic and acoustic waveguide setup.

Minimally entangled state preparation of localized wave functions on quantum computers

Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires $O({2}^{{n}_{Q}})$ entangling gates on a quantum computer with ${n}_{Q}$ qubits per site. It is conceivable that instead initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a noninteracting scalar field theory, initializing to a symmetric exponential wave function requires ${n}_{Q}\ensuremath{-}1$ entangling gates, the minimal number necessary to create an entangled state of all ${n}_{Q}$ qubits. This is compared with the ${2}^{{n}_{Q}\ensuremath{-}1}+{n}_{Q}\ensuremath{-}3+{\ensuremath{\delta}}_{{n}_{Q},1}$ required for a symmetric Gaussian wave function. In this work, we explore the initialization of one-site (${n}_{Q}=4$), two-site (${n}_{Q}=3$), and three-site (${n}_{Q}=3$) noninteracting scalar field theories with symmetric exponential wave functions using IBM's quantum simulators and quantum devices (Poughkeepsie and Tokyo). With the digitizations attainable with ${n}_{Q}=3,4$, these tensor-product wave functions are found to have large overlap with a Gaussian wave function and provide a suitable low-noise initialization for improvement and Somma inflation. In performing these simulations, we have employed a workflow that interleaves calibrations to mitigate systematic errors in production. The calibrations allow tolerance cuts on gate performance including the fidelity of the symmetrizing Hadamard gate, both in vacuum (${|\mathbf{0}\ensuremath{\rangle}}^{\ensuremath{\bigotimes}{n}_{Q}}$) and in medium (${n}_{Q}\ensuremath{-}1$ qubits initialized to an exponential function). The results obtained in this work are relevant to systems beyond scalar field theories, such as the deuteron radial wave function, two- and three-dimensional Cartesian-space wave functions, and nonrelativistic multinucleon systems built on a localized eigenbasis.