Quantum Computing with Trapped Ions

Typical qubit gate operations are binary, involving operations with up to just two qubits. While this can be universal, it is more efficient for almost all quantum circuits to directly entangle qubits with N-body interactions. With trapped ions, gates are typically realized by applying optical state-dependent displacements to the ions.  By instead using state-dependent squeezing forces, the workhorse quantum gate between pairs of trapped ions is extended to an N-qubit gate. This is an important shortcut for most quantum circuits such as quantum error-correction encoding and quantum optimization circuits, while also providing direct N-body interactions for quantum simulations of many-body quantum systems.

• “Demonstration of three- and four-body interactions between trapped-ion spins,” Or Katz, Lei Feng, Andrew Risinger, Christopher Monroe, Marko Cetina, Nature Physics 19, 1452 (2023); arXiv:2209.05691.
• “Programmable N-body interactions with trapped ions,” O. Katz, M. Cetina, and C. Monroe, Phys. Rev. X Quantum 4, 030311 (2023); arXiv:2207.10550.
• “N-body interactions between trapped ion qubits via spin-dependent squeezing,” O. Katz, M. Cetina, and C. Monroe, Phys. Rev. Lett. 129, 063603 (2022).

1D systems exhibiting a continuous symmetry can host exotic quantum phases of matter with true long-range order, but they require long-range interactions. We individually control all the spins in a chain of trapped ions, and their inherent long-range interactions allow the study of such CSB phases with up to 23 spin/qubits.

• “Continuous Symmetry Breaking in a Trapped-Ion Spin Chain,” L. Feng, O. Katz, C. Haack, M. Maghrebi, A. V. Gorshkov, Z. Gong, M. Cetina, and C. Monroe, arXiv:2211.01275 (2022).
• See related work with neutral atom arrays: C. Chen, … N. Y. Yao, A. Broeways, “Continuous Symmetry Breaking in a Two-dimensional Rydberg Array,” arXiv:2207.12930 (2022).

We have demonstrated two examples of quantum circuits that allow a verifier to certify a quantum computer, without the verifier having a quantum computer himself. The protocols rely on interactions between prover and verifier and are an extension of “interactive proofs” used in computer science. We demonstrate quantum circuits based on a particular cryptographic function as well as a “learning with errors” model, both passing the threshold for quantum behavior. Importantly, this requires measurement of a subset of qubits and subsequent coherent feedback on the remaining qubits, which we demonstrate in the trapped ion system of up to 15 qubits.

• “Experimental Implementation of an Efficient Test of Quantumness,” L. Lewis, D. Zhu, A. Gheorghiu, C. Noel, O. Katz, B. Harraz, Q. Wang, A. Risinger, L. Feng, D. Biswas, L. Egan, T. Vidick, M. Cetina, and C. Monroe, arXiv:2209.14316 (2022).
• “Interactive Protocols for Classically-Verifiable Quantum Advantage,” D. Zhu, G. D. Kahanamoku-Meyer, L. Lewis, C. Noel, O. Katz, B. Harraz, Q. Wang, A. Risinger, L. Feng, D. Biswas, L. Egan, A. Gheorghiu, Y. Nam, T. Vidick, U. Vazirani, N. Y. Yao, M. Cetina, and C. Monroe arXiv:2112.05156 (2022).

• “Fault-Tolerant Operation of a Quantum Error-Correction Code,” L. N. Egan, D. M. Debroy, C. Noel, A. Risinger, D. Zhu, D. Biswas, M. Newman, M. Li, K. R. Brown, M. Cetina, and C. Monroe, Nature 598, 281 (2021).
• See also related work by other ion trap groups:
  •  C. Ryan, et al., “Realization of Real-Time Fault-Tolerant Quantum Error Correction,” Phys. Rev. X, 041058 (2021) [Quantinuum, Inc.]
  •  “Demonstration of fault-tolerant universal quantum gate operations,” L. Postler, et al., Nature 605, 675 (2022) [Univ. Innsbruck]

We train a small quantum computer to perform “generative modeling” of a particular class of quantum states in one of the first demonstrations of machine learning techniques applied to a quantum computer.  Multiple layers of a standard quantum circuit are generated, with the many classical parameters defining the circuit optimized to minimize a cost function.  We use different types of classical optimization subroutines, showing that in some cases, the classical optimizer is the performance bottleneck.

In a related experiment, we use a variational technique (quantum approximate optimization algorithm or QAOA) to generate “Thermofield Double States.”  These states are pairwise entangled across a ladder network when considered as a whole, but become identical thermal mixed states when considered individually, and their evolution scrambles qubits (see below). TFD states are relevant to theories of quantum gravity and wormholes, where the role of traversing a wormhole takes the form of quantum teleportation across the circuit.

• Training of Quantum Circuits on a Hybrid Quantum Computer, D. Zhu, et al., Science Advances 5, eaaw9918 (2019).
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• Variational Generation of Thermofield Double States and Critical Ground States with a Quantum Computer, D. Zhu, et al., arXiv 1905.02699 (2019).

Quantum scrambling is the complete diffusion of information throughout a quantum system.  The system is not just entangled, but it is entangled at all depth levels throughout the whole system.  Scrambling is also thought to be the fate of information introduced into a black hole, and is a perfect example of the connection between quantum information and cosmology.  But scrambling it is very difficult to measure, because the space of quantum states is exponentially large.

We didn’t create a black hole in the lab, but instead implemented a 7-qubit circuit on our universal quantum computer that for the first time shows the unambiguous detection of scrambling. The signature is a successful teleportation of information across the circuit.

• “Verified Quantum Information Scrambling,” K. A Landsman, C. Figgatt, T. Schuster, N. M. Linke, B. Yoshida, N. Y. Yao, C. Monroe, Nature 567, 61 (2019).
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Profs. Christopher Monroe and Michael Raymer spearheaded the U.S. National Quantum Initiative (NQI), on behalf of the National Photoninics Initiative (NPI).

On May 18, 2018, Monroe testified at the U.S. House of Representatives Committee on Energy and Commerce, “Disruptor Series” hearing on Quantum Computing, then on Oct 24, 2017 at the U.S. House of Representatives Committee on Science, Space and Technology, hearing on American Leadership in Quantum Technology

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U.S. National Quantum Initiative

In one of the largest quantum simulations ever performed, up to 53 trapped ion qubits have been used to simulate properties of many body magnetic interactions.  The qubits are each prepared with individual control, and measured in a single shot with nearly 100% efficiency.  This allows the observation of arbitrary correlation functions that cannot be calculated.  This restricted quantum computer becomes fully programmable and reconfigurable with straightforward modifications in the control lasers.

• “Observation of a Many-Body Dynamical Phase Transition in a 53-Qubit Quantum Simulator,” J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. B. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Nature 551, 601 (2017)
• News Release

Connectivity between qubits in a quantum computer may be as important as clock speed and gate fidelity when it comes time to build large-scale quantum computers. We run several quantum algorithms on two 5-qubit programmable quantum computers: our fully-connected ion trap system, and the IBM Quantum Experience superconducting system.  The performance is seen to mirror the connectivity of the systems, with the ion trap system out-performing the superconducting system on all results, but particularly when the algorithm demands more connections.  This first comparison of algorithms on different platforms shows the power of having a programmable and reconfigurable system, which will be critical to successfully adapt to new quantum algorithms as they are discovered.

• “Experimental Comparison of Two Quantum Computing Architectures,” N. M. Linke, D. Maslov, M. Roetteler, S. Debnath, C. Figgatt, K. A. Landsman, K. Wright, C. Monroe, Proc. Natl. Acad. Sci. 114, 13 (2017). [News Release]
• “Comparison of Cloud-Based Ion Trap and Superconducting Quantum Computer Architectures,” S. Blinov, B. Wu, and C. Monroe, AVS Quantum Sci. 3, 033801 (2021)

In a delicate balance between strong interactions, weak disorder, and a periodic driving force, a collection of trapped ions qubits has been made to pulsate with a period that is relatively insensitive to the drive. This is a time crystal, where the stable pulses emerge and break time symmetry – just like a freezing liquid breaks spatial symmetry and forms a spatial crystal. Trapped ion qubits can pulsate on their own with excellent passive stability, but this observation may guide the stabilization of complex solid-state systems, where true quantum behavior is usually masked by defects and impurities.

• “Observation of a Discrete Time Crystal,” J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I.-D. Potirniche, A. C. Potter, A. Vishwanath, N. Y. Yao, C. Monroe, Nature 543, 217 (2017).
• Nature news article on time crystals
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