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Scientific Reports

Ultrafast Ramsey interferometry to implement cold atomic qubit gates

Jongseok Lim, Han-gyeol Lee, Sangkyung Lee, Chang-Yong Park, Jaewook Ahn

Published Jul 29, 2014• 23 citations
Publisher

Abstract

Quantum computing is based on unitary operations in a two-level quantum system, a qubit, as the fundamental building block, and the ability to perform qubit operations in an amount of time that is considerably shorter than the coherence time is an essential requirement for quantum computation. Here, we present an experimental demonstration of arbitrary single-qubit SU(2) quantum gate operations achieved at a terahertz clock speed. Implemented by coherent control methods of tailored ultrafast laser interaction with cold rubidium atomic qubits, Bloch vector manipulation about all three rotational axes was successfully demonstrated. The dynamic evolution of the qubits was successfully measured by devised femtosecond Ramsey interferometry. We anticipate this demonstration to be a starting point to process quantum algorithm in a simplified manner by a programmed sequence of femtosecond laser pulses.

DOI
10.1038/srep05867

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Bulletin of the American Physical Society•Jan 1, 2016•13 citations
Quantum computing is based on unitary operations in a two-level quantum system, a qubit, as the fundamental building block, and the ability to perform qubit operations in an amount of time that is considerably shorter than the coherence time is an essential requirement for quantum computation. Here, we present an experimental demonstration of arbitrary single-qubit SU(2) quantum gate operations achieved at a terahertz clock speed. Implemented by coherent control methods of tailored ultrafast laser interaction with cold rubidium atomic qubits, Bloch vector manipulation about all three rotational axes was successfully demonstrated. The dynamic evolution of the qubits was successfully measured by devised femtosecond Ramsey interferometry. We anticipate this demonstration to be a starting point to process quantum algorithm in a simplified manner by a programmed sequence of femtosecond laser pulses.
Extremely fast qubit controls can greatly reduce the calculation time in quantum computation, and potentially resolve the finite-time decoherence issues in many physical systems. Here, we propose and experimentally demonstrate pico-second time-scale controls of atomic clock state qubits, using Berry-phase gates implemented with a pair of chirped laser pulses. While conventional methods of microwave or Raman transitions do not allow atomic qubit controls within a time faster than the hyperfine free evolution period, our approach of ultrafast Berry-phase gates accomplishes fast clock-state operations. We also achieves operational robustness against laser parametric noises, since geometric phases are determined by adiabatic evolution pathway only, without being affected by any dynamic details. The experimental implementation is conducted with two linearly polarized, chirped ultrafast optical pulses, interacting with five single rubidium atoms in an array of optical tweezer dipole traps, to demonstrate the proposed ultrafast clock-state gates and their operational robustness.
With carefully prepared resonant laser-controlled pulses, the two quantum states of a cold ensemble of sodium atoms were manipulated by pure geometric rotations of the Bloch vector around axes 2 and 3 on the Bloch sphere. The fidelity for two geometric rotations was improved to be 90%. A universal single-qubit operation on the ground-state wave function was demonstrated by a pure geometric operation and the phase shift due to the rotation around axis 3 was measured using a geometric atom interferometer.
We propose and demonstrate the Kramers-Henneberger KH) atom as a novel qubit platform for ultrafast single-qubit gate operations. In the KH frame, the time-averaged strong laser field engineers a double-well potential whose two lowest eigenstates define the qubit basis, so that the computational structure is created and maintained by the driving field itself. A weak resonant control field drives coherent gate operations: full time-dependent Schrödinger equation simulations with the complete time-dependent KH potential confirm a Z gate and S gate of the order of femtoseconds, six orders of magnitude faster than laser-driven superconducting qubit gates. Decoherence characterisation gives longer decoherence times than those required for the gate operations. The complete six-gate single-qubit set is demonstrated in the time-averaged two-level limit, with strong agreement between the full and time-averaged descriptions confirming that fidelity is limited by structured leakage rather than stochastic decoherence. In principle, this is an error channel suppressible through pulse engineering. These results constitute the first demonstration of coherent single-qubit gates in a strong-field setting, with a clear pathway toward attosecond-scale operations.
One of the major problems in building a quantum computer is the development of scalable and robust methods to entangle many qubits. Quantum computers based on trapped atomic ions are one of the most mature and promising platforms for quantum information processing, exhibiting excellent coherence properties, near-perfect qubit detection efficiency, and high-fidelity entangling gates. Entangling operations between multiple ions in a chain typically rely on qubit state-dependent forces that modulate their Coulomb-coupled normal modes of motion. However, scaling these operations to large qubit numbers in a single chain must account for the increasing complexity of the normal mode spectrum, and can result in a gate time slowdown or added complexity of the control forces. In this thesis, I present an alternative route to the scalability problem using optical interactions faster than any state evolution. The experiments shown here represent a proof of principle for quantum manipulation of atoms in the strong coupling regime. This work relies on spin dependent forces (SDK) with short laser pulses and use it as our fundamental building block for thermometry and non-trivial motional state preparation. Together with a robust stabilization of the ion trap and high light collection efficiency, we demonstrate two-ion entanglement with ten ultrafast pulses. Due to the nature of the interaction, the demonstrated entangling operation can be made arbitrarily fast only limited by laser engineering.
Arbitrary rotation of a qubit can be performed with a three-pulse sequence, for example, ZYZZYZZYZ rotations. However, this requires precise control of the relative phase and timing between the pulses, making it technically challenging in optical implementation in a short time scale. Here we show any ZYZZYZZYZ rotations can be implemented with a single laser pulse, that is, a chirped pulse with a temporal hole. The hole of this shaped pulse induces a nonadiabatic interaction in the middle of the adiabatic evolution of the chirped pulse, converting the central part of an otherwise simple ZZZ rotation to a YYY rotation, constructing ZYZZYZZYZ rotations. The result of our experiment performed with shaped femtosecond laser pulses and cold rubidium atoms shows strong agreement with the theory.
Quantum computers can solve certain problems more efficiently compared to conventional classical methods. In the endeavor to build a quantum computer, several competing platforms have emerged that can implement certain quantum algorithms using a few qubits. However, the demonstrations so far have been done usually by tailoring the hardware to meet the requirements of a particular algorithm implemented for a limited number of instances. Although such proof of principal implementations are important to verify the working of algorithms on a physical system, they further need to have the potential to serve as a general purpose quantum computer allowing the flexibility required for running multiple algorithms and be scaled up to host more qubits. Here we demonstrate a small programmable quantum computer based on five trapped atomic ions each of which serves as a qubit. By optically resolving each ion we can individually address them in order to perform a complete set of single-qubit and fully connected two-qubit quantum gates and alsoperform efficient individual qubit measurements. We implement a computation architecture that accepts an algorithm from a user interface in the form of a standard logic gate sequence and decomposes it into fundamental quantum operations that are native to the hardware using a set of compilation instructions that are defined within the software. These operations are then effected through a pattern of laser pulses that perform coherent rotations on targeted qubits in the chain. The architecture implemented in the experiment therefore gives us unprecedented flexibility in the programming of any quantum algorithm while staying blind to the underlying hardware. As a demonstration we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms on the five-qubit processor and achieve average success rates of 95 and 90 percent, respectively. We also implement a five-qubit coherent quantum Fourier transform and examine its performance in the period finding and phase estimation protocol. We find fidelities of 84 and 62 percent, respectively. While maintaining the same computation architecture the system can be scaled to more ions using resources that scale favorably (O(N^2)) with the number of qubits N.