Qubit encodings for lattices of dipolar planar rotors

• URL: http://arxiv.org/abs/2507.17952v1
• Date: Wed, 23 Jul 2025 21:48:20 GMT
• Title: Qubit encodings for lattices of dipolar planar rotors
• Authors: Muhammad Shaeer Moeed, James Brown, Alexander Ibrahim, Estevao Vilas Boas De Oliveira, Pierre-Nicholas Roy,
• Abstract summary: We investigate two qubit representations of the planar rotor lattice Hamiltonian.<n>The first representation is realized by decomposing the rotor Hamiltonian projectors in binary and mapping them to spin-1/2 projectors.<n>The second approach relies on embedding the planar rotor lattice Hilbert space in a larger space and recovering the relevant qubit encoded system as a quotient space projecting down to the physical degrees of freedom.
• Score: 39.58317527488534
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Near term quantum devices have recently garnered significant interest as promising candidates for investigating difficult-to-probe regimes in many-body physics. To this end, various qubit encoding schemes targeting second quantized Hamiltonians have been proposed and optimized. In this work, we investigate two qubit representations of the planar rotor lattice Hamiltonian. The first representation is realized by decomposing the rotor Hamiltonian projectors in binary and mapping them to spin-1/2 projectors. The second approach relies on embedding the planar rotor lattice Hilbert space in a larger space and recovering the relevant qubit encoded system as a quotient space projecting down to the physical degrees of freedom. This is typically called the unary mapping and is used for bosonic systems. We establish the veracity of the two encoding approaches using sparse diagonalization on small chains and discuss quantum phase estimation resource requirements to simulate small planar rotor lattices on near-term quantum devices.

Related papers

• Systematic input scheme of many-boson Hamiltonians with applications to the two-dimensional $φ^4$ theory [0.0]
  We present our discussion of this input scheme based on the light-front Hamiltonian of the two-dimensional $phi 4$ theory. In our input scheme, we employ a set of quantum registers, where each register encodes the occupation of a distinct boson mode as binaries. We present the spectral calculations of the Hamiltonian utilizing the hybrid quantum-classical symmetry-adapted quantum Krylov subspace diagonalization algorithm.
  arXiv  Detail & Related papers  (2024-07-18T16:47:53Z)
• Single-modulated-pulse two-qubit gates for Rydberg atoms with noncyclic geometric control [4.902211702175651]
  We present a convenient approach for implementing a two-qubit controlled-phase gate using Rydberg blockade. The robustness of the proposal against systematic errors will be remarkably improved due to the geometric characteristic. The proposed scheme will provide an analytical waveforms for arbitrary two-qubit gates and may have important use in the experiments of atomic arrays.
  arXiv  Detail & Related papers  (2024-02-02T03:08:56Z)
• Qubit Gate Operations in Elliptically Trapped Polariton Condensates [0.0]
  We consider bosonic condensates of exciton-polaritons optically confined in elliptical traps. We describe a set of universal single-qubit gates resulting in a controllable shift of the Bloch vector. We discuss the applicability of our qubit proposal in the context of DiVincenzo's criteria for the realization of local quantum computing processes.
  arXiv  Detail & Related papers  (2023-09-29T16:04:47Z)
• Low-depth simulations of fermionic systems on square-grid quantum hardware [0.0]
  We present a strategy for mapping fermionic systems to quantum hardware with square qubit connectivity. We report unprecedentedly low circuit depths per single Trotter layer with up to a $70 %$ improvement upon previous state-of-the-art.
  arXiv  Detail & Related papers  (2023-02-03T17:08:26Z)
• Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer [0.0]
  Fermionic ansatz state preparation is a critical subroutine in many quantum algorithms such as Variational Quantum Eigensolver for quantum chemistry and condensed matter applications. Inspired by data-loading circuits developed for quantum machine learning, we propose an alternate paradigm that provides shallower, yet scalable $mathcalO(d log2N)$ two-qubit gate depth circuits to prepare such states with d-fermions.
  arXiv  Detail & Related papers  (2023-01-18T12:43:18Z)
• Penrose dodecahedron, Witting configuration and quantum entanglement [55.2480439325792]
  A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose. The model was later reformulated using so-called Witting configuration with 40 rays in 4D Hilbert space. Two entangled systems with quantum states described by Witting configurations are discussed in presented work.
  arXiv  Detail & Related papers  (2022-08-29T14:46:44Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• Quantum algorithms for grid-based variational time evolution [36.136619420474766]
  We propose a variational quantum algorithm for performing quantum dynamics in first quantization. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
  arXiv  Detail & Related papers  (2022-03-04T19:00:45Z)
• A quantum processor based on coherent transport of entangled atom arrays [44.62475518267084]
  We show a quantum processor with dynamic, nonlocal connectivity, in which entangled qubits are coherently transported in a highly parallel manner. We use this architecture to realize programmable generation of entangled graph states such as cluster states and a 7-qubit Steane code state.
  arXiv  Detail & Related papers  (2021-12-07T19:00:00Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit [62.997667081978825]
  We present a circuit design composed of a non-reciprocal device and Josephson junctions whose ground space is doubly degenerate and the ground states are approximate codewords of the Gottesman-Kitaev-Preskill (GKP) code. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction.
  arXiv  Detail & Related papers  (2020-02-18T16:45:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.