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arXiv:quant-ph/0109083 · Physical Review Letters

Quantum Computation with Trapped Polar Molecules

David P. DeMille

Published Jan 24, 2002• 1,354 citations
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Abstract

We propose a novel physical realization of a quantum computer. The qubits are electric dipole moments of ultracold diatomic molecules, oriented along or against an external electric field. Individual molecules are held in a 1D trap array, with an electric field gradient allowing spectroscopic addressing of each site. Bits are coupled via the electric dipole-dipole interaction. Using technologies similar to those already demonstrated, this design can plausibly lead to a quantum computer with greater, approximately > or = 10(4) qubits, which can perform approximately 10(5) CNOT gates in the anticipated decoherence time of approximately 5 s.

DOI
10.1103/physrevlett.88.067901

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We propose a novel physical realization of a quantum computer. The qubits are electric dipole moments of ultracold diatomic molecules, oriented along or against an external electric field. Individual molecules are held in a 1D trap array, with an electric field gradient allowing spectroscopic addressing of each site. Bits are coupled via the electric dipole-dipole interaction. Using technologies similar to those already demonstrated, this design can plausibly lead to a quantum computer with greater, approximately > or = 10(4) qubits, which can perform approximately 10(5) CNOT gates in the anticipated decoherence time of approximately 5 s.
In proposals for quantum computers using arrays of trapped ultracold polar molecules as qubits, a strong external field with appreciable gradient is imposed in order to prevent quenching of the dipole moments by rotation and to distinguish among the qubit sites. That field induces the molecular dipoles to undergo pendular oscillations, which markedly affect the qubit states and the dipole-dipole interaction. We evaluate entanglement of the pendular qubit states for two linear dipoles, characterized by pairwise concurrence, as a function of the molecular dipole moment and rotational constant, strengths of the external field and the dipole-dipole coupling, and ambient temperature. We also evaluate a key frequency shift, △ω, produced by the dipole-dipole interaction. Under conditions envisioned for the proposed quantum computers, both the concurrence and △ω become very small for the ground eigenstate. In principle, such weak entanglement can be sufficient for operation of logic gates, provided the resolution is high enough to detect the △ω shift unambiguously. In practice, however, for many candidate polar molecules it appears a challenging task to attain adequate resolution. Simple approximate formulas fitted to our numerical results are provided from which the concurrence and △ω shift can be obtained in terms of unitless reduced variables.
In proposals for quantum computers using arrays of trapped ultracold polar molecules as qubits, a strong external field with appreciable gradient is imposed in order to prevent quenching of the dipole moments by rotation and to distinguish among the qubit sites. That field induces the molecular dipoles to undergo pendular oscillations, which markedly affect the qubit states and the dipole-dipole interaction. We evaluate entanglement of the pendular qubit states for two linear dipoles, characterized by pairwise concurrence, as a function of the molecular dipole moment and rotational constant, strengths of the external field and the dipole-dipole coupling, and ambient temperature. We also evaluate a key frequency shift, △ω, produced by the dipole-dipole interaction. Under conditions envisioned for the proposed quantum computers, both the concurrence and △ω become very small for the ground eigenstate. In principle, such weak entanglement can be sufficient for operation of logic gates, provided the resolution is high enough to detect the △ω shift unambiguously. In practice, however, for many candidate polar molecules it appears a challenging task to attain adequate resolution. Simple approximate formulas fitted to our numerical results are provided from which the concurrence and △ω shift can be obtained in terms of unitless reduced variables.
Arrays of trapped ultracold molecules represent a promising platform for implementing a universal quantum computer. DeMille [Phys. Rev. Lett. 88, 067901 (2002)] has detailed a prototype design based on Stark states of polar (1)Σ molecules as qubits. Herein, we consider an array of polar (2)Σ molecules which are, in addition, inherently paramagnetic and whose Hund's case (b) free-rotor pair-eigenstates are Bell states. We show that by subjecting the array to combinations of concurrent homogeneous and inhomogeneous electric and magnetic fields, the entanglement of the array's Stark and Zeeman states can be tuned and the qubit sites addressed. Two schemes for implementing an optically controlled CNOT gate are proposed and their feasibility discussed in the face of the broadening of spectral lines due to dipole-dipole coupling and the inhomogeneity of the electric and magnetic fields.
Proposals for quantum computing using rotational states of polar molecules as qubits have previously considered only diatomic molecules. For these the Stark effect is second-order, so a sizable external electric field is required to produce the requisite dipole moments in the laboratory frame. Here we consider use of polar symmetric top molecules. These offer advantages resulting from a first-order Stark effect, which renders the effective dipole moments nearly independent of the field strength. That permits use of much lower external field strengths for addressing sites. Moreover, for a particular choice of qubits, the electric dipole interactions become isomorphous with NMR systems for which many techniques enhancing logic gate operations have been developed. Also inviting is the wider chemical scope, since many symmetric top organic molecules provide options for auxiliary storage qubits in spin and hyperfine structure or in internal rotation states.
Abstract We investigate several aspects of realizing quantum computation using entangled polar molecules in pendular states. Quantum algorithms typically start from a product state and we show that up to a negligible error, the ground states of polar molecule arrays can be considered as the unentangled qubit basis state . This state can be prepared by simply allowing the system to reach thermal equilibrium at low temperature (<1 mK). We also evaluate entanglement, characterized by concurrence of pendular state qubits in dipole arrays as governed by the external electric field, dipole–dipole coupling and number N of molecules in the array. In the parameter regime that we consider for quantum computing, we find that qubit entanglement is modest, typically no greater than 10−4, confirming the negligible entanglement in the ground state. We discuss methods for realizing quantum computation in the gate model, measurement‐based model, instantaneous quantum polynomial time circuits and the adiabatic model using polar molecules in pendular states.
Optically trapped ultracold polar molecules can have multiple long-lived states for coding quantum information, and can exhibit electric dipole-dipole interactions~(DDI) which enables entanglement generation. The general understanding on the quantized motion~(QM) of molecules in the traps is that it causes fluctuation of DDI. Here, we find that the molecular QM can realize an asymmetric quantum Rabi model, which is of specific importance in the study of fundamental physics. The molecular QM can also lead to an exotic trap-dipole resonance, resulting in excess population loss to uncoupled motional states, and, hence, should be avoided in a general quantum control over polar molecules. To examine the impact of QM on quantum computing based on polar molecules, we introduce two gate protocols, a fast iSWAP gate which can be realized by a global microwave pulse of pulse area smaller than 2π2π2π, and a controlled-phase gate with an arbitrary controlled phase, and find that both gates can attain a high fidelity.