Quantum state preparation of spin eigenstates including the Dicke states with generalized all-coupled interaction in a spintronic quantum computing architecture
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.
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.
The W state is a symmetrically entangled multipartite state where a single excitation is shared by all parties. It is an important resource for various quantum algorithms and communication systems, and hence, its preparation is of immense interest to the quantum information community. We examine here a deterministic scheme to prepare a W state of an n-qubit system with all-to-all pairwise exchange interaction between n qubits. This relies on sharing superposed excitations of a smaller number of q qubits among others. We present a bound on the maximal jumps from q to n and formalize a scheme to generate the Wn state in O(logn) stages. We demonstrate this scheme in the context of spin-torque-based quantum computing architecture that is characterized by repeated interactions between static and flying qubits.
The n-qubit k-weight Dicke states ∣Dkn⟩, defined as the uniform superposition of all computational basis states with exactly k qubits in state ∣1⟩, form a basis of the symmetric subspace and represent an important class of entangled quantum states with broad applications in quantum computing. We propose deterministic quantum circuits for Dicke state preparation under two commonly seen qubit connectivity constraints: 1. All-to-all qubit connectivity: our circuit has depth O(log(k)log(n/k)+k), which improves the previous best bound of O(klog(n/k)). 2. Grid qubit connectivity ((n1×n2)-grid, n1≤n2): (a) For k≥n2/n1, we design a circuit with depth O(klog(n/k)+n2), surpassing the prior O(nk) bound. (b) For k<n2/n1, we design an optimal-depth circuit with depth O(n2). Furthermore, we establish the depth lower bounds of Ω(log(n)) for all-to-all qubit connectivity and Ω(n2) for (n1×n2)-grid connectivity constraints, demonstrating the near-optimality of our constructions.
Efficient preparation of Dicke states and, more generally, permutation-symmetric states is important for quantum metrology, quantum networking, and collective quantum information processing. Measurements and classical feedforward enable low-depth preparations of these states, with a cost of ancillary qubits. In this work, we introduce an exact constant-depth adaptive preparation protocol for arbitrary Dicke-(n,k) states and further symmetric states. We first provide a protocol preparing the uniform subset superposition state, as a primitive, using constant-depth adaptive circuit with O(k2log2n) ancillary qubits and success probability at least 1/k. This yields an exact, probabilistic, constant-depth Dicke-state preparation protocol using O(n2+k2log2n+knlognloglogn) ancillary qubits. Parallel repetition suppresses the failure probability exponentially without increasing the quantum depth. Moreover, the uniform subset superposition state is also of independent interest as the uniform vertex state of the Johnson graph and as the compact uniform subset state appearing in quantum-walk and topological-data-analysis algorithms. We further establish a general lifting framework that coherently combines clean unitary Dicke-state preparation circuits to prepare arbitrary symmetric states with only polynomial ancillary overhead. Combined with recent constant-depth unitary Dicke-state constructions, this gives an exact constant-depth preparation protocol for arbitrary n-qubit symmetric states using O(n3logn) ancillary qubits.
Dicke states ∣J=N/2,m⟩ of a collection of N atoms were central to Dicke's theory of superradiance. Except for the fully polarized end states, they are entangled many-body states; in particular, the single-excitation Dicke state is the W state well known in quantum information science. However, deterministic preparation of Dicke states with a prescribed spin projection remains challenging, especially without relying on postselection or heralding. Here we present a detuning-programmed Hamiltonian protocol using atoms or qubits in a dispersive cavity subject to a coherent transverse drive. In the absence of the drive, the off-resonant cavity produces an effective collective-spin interaction. By combining this cavity-mediated interaction with the coherent drive, tuning the atom--drive detuning enables the protocol, in principle, to target any allowed Dicke state along the symmetric Dicke ladder. Starting from the transverse-drive ground state, adiabatic ground-state interpolation prepares the selected Dicke state by ramping down the drive strength while ramping up the cavity-mediated interaction. After preparation, tuning the cavity into resonance with the atoms or qubits provides a direct way to probe the collective-emission response of the prepared Dicke state. We discuss implementation with superconducting circuit QED and show that the prepared states, especially the central Dicke state with m=0, provide resources for quantum sensing with Heisenberg-limited scaling.
We introduce protocols to prepare many-body quantum states with quantum circuits assisted by local operations and classical communication. We show that by lifting the requirement of exact preparation, one can substantially save resources. In particular, the so-called W and, more generally, Dicke states require a circuit depth and number of ancillas per site that are independent of the system size. As a by-product of our work, we introduce an efficient scheme to implement certain nonlocal, non-Clifford unitary operators. We also discuss how similar ideas may be applied in the preparation of eigenstates of well-known spin models, both free and interacting.
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.