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arXiv:2210.06212 · Physical Review Research

Optical multiqubit gate operations on an excitation-blockaded atomic quantum register

Adam Kinos, Klaus Mølmer

Published Mar 27, 2023• 9 citations
arXivHTMLPDF

Abstract

We consider a multiqubit system of atoms or ions with two computational ground states and an interacting excited state in the so-called blockade regime, such that only one qubit can be excited at any one time. Examples of such systems are rare-earth-ion-doped crystals and neutral atoms trapped in tweezer arrays. We present a simple laser excitation protocol that yields a complex phase factor on any desired multiqubit product state, and which can be used to implement multiqubit gates such as the $n$-bit Toffoli gates. The operation is performed using only two pulses, where each pulse simultaneously address all qubits involved in the operation. By relying on the well-established complex hyperbolic secant pulse shape, our scheme is also robust and permits complete transfers to and from the excited states despite variations in Rabi frequencies and transition frequencies. A detailed analysis of the multiqubit gate performance is provided.

DOI
10.1103/physrevresearch.5.013205

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We consider a multiqubit system of atoms or ions with two computational ground states and an interacting excited state in the so-called blockade regime, such that only one qubit can be excited at any one time. Examples of such systems are rare-earth-ion-doped crystals and neutral atoms trapped in tweezer arrays. We present a simple laser excitation protocol that yields a complex phase factor on any desired multiqubit product state, and which can be used to implement multiqubit gates such as the nnn-bit Toffoli gates. The operation is performed using only two pulses, where each pulse simultaneously address all qubits involved in the operation. By relying on the well-established complex hyperbolic secant pulse shape, our scheme is also robust and permits complete transfers to and from the excited states despite variations in Rabi frequencies and transition frequencies. A detailed analysis of the multiqubit gate performance is provided.
We propose an efficient protocol to realize multi-qubit gates in arrays of neutral atoms. The atoms encode qubits in the long-lived hyperfine sublevels of the ground electronic state. To realize the gate, we apply a global laser pulse to transfer the atoms to a Rydberg state with strong blockade interaction that suppresses simultaneous excitation of neighboring atoms arranged in a star-graph configuration. The number of Rydberg excitations, and thereby the parity of the resulting state, depends on the multiqubit input state. Upon changing the sign of the interaction and de-exciting the atoms with an identical laser pulse, the system acquires a geometric phase that depends only on the parity of the excited state, while the dynamical phase is completely canceled. Using single qubit rotations, this transformation can be converted to the C k Z or C k NOT quantum gate for k + 1 atoms. We also present extensions of the scheme to implement quantum gates between distant atomic qubits connected by a quantum bus consisting of a chain of atoms.
We report the implementation of universal two- and three-qubit entangling gates on neutral-atom qubits encoded in long-lived hyperfine ground states. The gates are mediated by excitation to strongly interacting Rydberg states and are implemented in parallel on several clusters of atoms in a one-dimensional array of optical tweezers. Specifically, we realize the controlled-phase gate, enacted by a novel, fast protocol involving only global coupling of two qubits to Rydberg states. We benchmark this operation by preparing Bell states with fidelity F≥95.0(2)%, and extract gate fidelity ≥97.4(3)%, averaged across five atom pairs. In addition, we report a proof-of-principle implementation of the three-qubit Toffoli gate, in which two control atoms simultaneously constrain the behavior of one target atom. These experiments demonstrate key ingredients for high-fidelity quantum information processing in a scalable neutral-atom platform.
Abstract Multi-qubit quantum gates are the most important building blocks for quantum computation. In this article, we propose a scheme for realizing the Toffoli gate in a linear neutral atom array. Two ground-state hyperfine levels of the atoms are considered as qubit states. Our method relies on the strong and long-range interactions between atoms due to Rydberg excitations and the occurrence of dark states in the target qubit, with both control and target qubits being individually addressed with laser pulses. Our gate protocol enables precise control over the quantum states of individual qubits, effectively suppressing undesirable transitions to ensure high-fidelity gate performance. We also implement two-atom Rydberg antiblockade mechanism to avoid any unwanted population blockage in the control atoms to get the best fidelity. At zero temperature, the gate fidelity is estimated to be about 99.16% for realistic laser power omitting the motional state of the atoms when the interatomic distance ( l ) 6.55 μ m. We construct a C n NOT gate with n > 2 in a 2D atomic array by exploiting the n -atom Rydberg antiblockade (RAB) mechanism, which allows n atoms within the blockade radius to be simultaneously excited to the Rydberg states. In particular, we simulate C 3 NOT gate with about 98.37 % fidelity. We further analyze the gate error by decreasing the interatomic distance and find that gate fidelity improves more rapidly for larger n with increased interaction potential. We find that more than 99 % fidelity can be achieved for C 3 NOT gate for l < 6.2 μ m, implying that our proposed scheme promising and reliable for multi-qubit controlled NOT gates. For a finite temperature ( ∼ 30 μ K), including the Doppler dephasing, we simulate our gates to achieve 98.90% and 98.54 % fidelity for the Toffoli gate and C 3
We present a theoretical study of finite-blockade dynamics in a symmetric three-neutral-atom system, providing a framework for understanding high-fidelity multiqubit quantum operations. The transition from the finite- to the strong-blockade regime is systematically investigated to examine the effects of finite Rydberg blockade. Using a single Gaussian laser pulse, we analyze the complete gate dynamics while explicitly accounting for population leakage into non-computational Rydberg states. By exploiting the permutation symmetry of the system, we construct a symmetry-adapted Hamiltonian that reduces the computational complexity while preserving the exact dynamics. This enables a systematic investigation of the interplay among the Rabi frequency, laser detuning, and Rydberg blockade strength, leading to the identification of optimal operating regimes with high fidelity, fast gate operation, and suppressed leakage. We further quantify the dominant error mechanisms, including phase errors, population leakage, and finite Rydberg-state lifetimes, and evaluate their impact on the gate fidelity. Our results demonstrate experimentally accessible high-fidelity gate operation and provide practical guidelines for multi-qubit quantum computing.
We propose how to realize a multiqubit tunable phase gate of one qubit simultaneously controlling nnn qubits with four-level quantum systems in a cavity or coupled to a resonator. Each of the nnn two-qubit controlled-phase (cp) gates involved in this multiqubit phase gate has a shared control qubit but a different target qubit. In this proposal, the two lowest levels of each system represent the two logical states of a qubit while the two higher-energy intermediate levels are used for the gate implementation. The method presented here operates essentially by creating a single photon through the control qubit, which then induces a phase shift to the state of each target qubit. The phase shifts on each target qubit can be adjusted by changing the Rabi frequencies of the pulses applied to the target qubit systems. The operation time for the gate implementation is independent of the number of qubits, and neither adjustment of the qubit level spacings nor adjustment of the cavity mode frequency during the gate operation is required by this proposal. It is also noted that this approach can be applied to implement certain types of significant multiqubit phase gates (e.g., the multiqubit phase gate consisting of nnn two-qubit cp gates which are key elements in quantum Fourier transforms). A possible physical implementation of our approach is presented. Our proposal is quite general and can be applied to physical systems such as various types of superconducting devices coupled to a resonator and trapped atoms in a cavity.