Simple ways of preparing qudit Dicke states

Abstract

Dicke states are permutation-invariant superpositions of qubit computational basis states, which play a prominent role in quantum information science. We consider here two higher-dimensional generalizations of these states: $SU(2)$ spin-$s$ Dicke states and $SU(d)$ Dicke states. We present various ways of preparing both types of qudit Dicke states on a qudit quantum computer, using two main approaches: a deterministic approach, based on exact canonical matrix product state representations; and a probabilistic approach, based on quantum phase estimation. The quantum circuits are explicit and straightforward, and are arguably simpler than those previously reported.

25 pages, 9 figures, implementations of circuits in cirq are available on GitHub; v2: references added

References in corpus (17)

• High-Fidelity Qutrit Entangling Gates for Superconducting Circuits
• Efficient Long-Range Entanglement using Dynamic Circuits
• Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements
• Universal qudit gate synthesis for transmons
• Experimental Realization of Two Qutrits Gate with Tunable Coupling in Superconducting Circuits
• Quantum Error Correction of Qudits Beyond Break-even
• Performing SU($d$) operations and rudimentary algorithms in a superconducting transmon qudit for $d=3$ and $d=4$
• Approximating many-body quantum states with quantum circuits and measurements
• State preparation by shallow circuits using feed forward
• Complete unitary qutrit control in ultracold atoms
• Measurement-Based Long-Range Entangling Gates in Constant Depth
• Qudit Dicke state preparation
• Global Variational Quantum Circuits for Arbitrary Symmetric State Preparation
• Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage
• Spin-s Dicke states and their preparation
• Dicke states as matrix product states
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward

Cited by in corpus (1)

• Spin-$s$ $U(1)$-eigenstate preparation