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arXiv:2104.14310 · Physical Review A

Preparing Dicke states in a spin ensemble using phase estimation

Yang Wang, Barbara M. Terhal

Published Sep 9, 2021• 29 citations
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Abstract

We present a Dicke state preparation scheme which uses global control of $N$ spin qubits: our scheme is based on the standard phase estimation algorithm, which estimates the eigenvalue of a unitary operator. The scheme prepares a Dicke state nondeterministically by collectively coupling the spins to an ancilla qubit via a $ZZ$ interaction, using $\ensuremath{\lceil}{log}_{2}N\ensuremath{\rceil}+1$ ancilla qubit measurements. The preparation of such Dicke states can be useful if the spins in the ensemble are used for magnetic sensing: we discuss a possible realization using an ensemble of electronic spins located at diamond nitrogen-vacancy centers coupled to a single superconducting flux qubit. We also analyze the effect of noise and limitations in our scheme.

DOI
10.1103/physreva.104.032407

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We present a Dicke state preparation scheme which uses global control of NNN spin qubits: our scheme is based on the standard phase estimation algorithm, which estimates the eigenvalue of a unitary operator. The scheme prepares a Dicke state nondeterministically by collectively coupling the spins to an ancilla qubit via a ZZZZZZ interaction, using \ensuremath⌈log2N\ensuremath⌉+1\ensuremath{\lceil}{log}_{2}N\ensuremath{\rceil}+1\ensuremath⌈log2​N\ensuremath⌉+1 ancilla qubit measurements. The preparation of such Dicke states can be useful if the spins in the ensemble are used for magnetic sensing: we discuss a possible realization using an ensemble of electronic spins located at diamond nitrogen-vacancy centers coupled to a single superconducting flux qubit. We also analyze the effect of noise and limitations in our scheme.
Abstract We propose a potentially practical scheme for creating macroscopic entangled coherent state between two separate nitrogen-vacancy center spin ensembles placed near a superconducting flux qubit. Through the collective magnetic coupling and the in situ tunability of the flux qubit, the arbitrary entangled coherent states of spin ensembles can be achieved with high success possibilities under the influence from decoherence of the flux qubit and spin ensembles. The experimental feasibility and challenge are justified using currently available technology.
Quantum phase estimation (QPE) is a crucial subroutine in many quantum algorithms. It is used to estimate the eigenvalues of a unitary operator acting on a target quantum system. Conventional QPE is often expensive to implement because it requires a large number of ancilla qubits and the ability to perform quantum Fourier transform. Recent developments in iterative QPE reduce the implementation cost by repetitive uses of a single ancilla and classical postprocessing. However, both conventional and iterative schemes often require preparation of the target system in an eigenstate of the unitary operator, while it remains ambiguous to achieve QPE of multiple eigenvalues with no need of initial-state preparation. Here we clarify this issue by developing a theoretical framework based on sequential quantum channels for iterative QPE. We find that QPE of multiple eigenvalues can be efficiently realized for arbitrary initial target system state by actively utilizing the measurement backaction of iterative QPE on the target system with a long coherence time. Specifically, we investigate two iterative QPE schemes based on sequential Ramsey interferometry measurements (RIMs) of an ancilla qubit: (a) the repetitive scheme, which conducts repetitive RIMs to achieve the standard quantum limit in estimating the eigenvalues; (b) the adaptive scheme, which adjusts the parameters of each RIM based on prior measurement outcomes to attain the Heisenberg limit. In both schemes, sequential ancilla measurements generate sequential quantum channels on the target system, gradually steering it to the eigenstates of the estimated unitary operator, while the measurement statistics of the ancilla can reveal the embedded information about its eigenvalues with proper postprocessing. We demonstrate the analysis by simulating a central spin model and evaluate the performance and noise resilience of both schemes.
We propose a strategy to generate a many-body entangled state in a collection of randomly placed, dipolarly coupled electronic spins in the solid state. By using coherent control to restrict the evolution into a suitable collective subspace, this method enables the preparation of GHZ-like and spin-squeezed states even for randomly positioned spins, while in addition protecting the entangled states against decoherence. We consider the application of this squeezing method to improve the sensitivity of nanoscale magnetometer based on nitrogen-vacancy spin qubits in diamond.
Quantum states with conserved total spins, or spin eigenfunctions, are important for studying quantum chemistry and quantum manybody physics problems. A typical class of spin eigenfunctions are Dicke states, which attain maximal spins. While we already have many efficient quantum algorithms to prepare Dicke states, it is not yet clear if we could do so for arbitrary spin eigenfunctions deterministically. Generalizing Bärtschi and Eidenbenz's elegant algorithms for Dicke state preparation, we successfully prepare arbitrary spin eigenfunctions characterized by branching paths and binary spin trees. As a byproduct, we also develop the corresponding classical algorithms to reconstruct all these spin states.
Generalized Dicke models can be implemented in hybrid quantum systems built from ensembles of nitrogen-vacancy (NV) centers in diamond coupled to superconducting microwave cavities. By engineering cavity assisted Raman transitions between two spin states of the NV defect, a fully tunable model for collective light-matter interactions in the ultrastrong coupling limit can be obtained. Our analysis of the resulting nonequilibrium phases for a single cavity and for coupled cavity arrays shows that different superradiant phase transitions can be observed using existing experimental technologies, even in the presence of large inhomogeneous broadening of the spin ensemble. The phase diagram of the Dicke lattice model displays distinct features induced by dissipation, which can serve as a genuine experimental signature for phase transitions in driven open quantum systems.
There has been an extensive development in the use of multi-partite entanglement as a resource for various quantum information processing tasks. In this paper we focus on preparing arbitrary spin eigenstates whose subset contain important entangled resources like Dicke states as well as some other sub-radiant states that are difficult to prepare. Leveraging on the symmetry of these states we consider uniform pairwise exchange coupling between every pair of qubits. Starting from a product state of a given spin eigenstate with a single qubit state, another spin eigenstate can be prepared using simple time evolutions. This expansion paves a deterministic approach to prepare arbitrary Dicke states in linear steps. We discuss an improvement in this cost building up on a previous work for W states deterministic preparation in logarithmic circuit depth. The modified algorithm requires several iterations of pumping spin angular momentum into the system and is akin to the amplitude amplification in Grover search. As a use case to demonstrate the proposed scheme, we choose a system of non-interacting static spin qubits connected to a ferromagnetic reservoir. The flying qubits emerging from the reservoir locally interact with static qubits successively, mediating an in-direct exchange interaction between all the pairs.