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1. Entangled quantum cellular automata, physical complexity, and Goldilocks rules

   Logan E. Hillberry, Matthew T. ( May 2020 , ArXivorg)

   Cellular automata are interacting classical bits that display diverse behaviors, from fractals to random-number generators to Turing-complete computation. We introduce entangled quantum cellular automata subject to Goldilocks rules, tradeoffs of the kind underpinning biological, social, and economic complexity. Tweaking digital and analog quantum-computing protocols generates persistent entropy fluctuations; robust dynamical features, including an entangled breather; and network structure and dynamics consistent with complexity. Present-day quantum platforms---Rydberg arrays, trapped ions, and superconducting qubits---can implement Goldilocks protocols, which generate quantum many-body states with rich entanglement and structure. Moreover, the complexity studies reported here underscore an emerging idea in many-body quantum physics: some systems fall outside the integrable/chaotic dichotomy. 

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2. Efficient Simulation of Random States and Random Unitaries

   https://doi.org/10.1007/978-3-030-45727-3_26  

   Gorjan Alagic, Christian Majenz ( May 2020 , Annual International Conference on the Theory and Applications of Cryptographic Techniques (Eurocrypt))

   We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered for restricted adversaries. Against adversaries with an a priori bound on the number of queries, it is well-known that t-designs suffice. Against polynomial-time adversaries, one can use pseudorandom states (PRS) and pseudorandom unitaries (PRU), as defined in a recent work of Ji, Liu, and Song; unfortunately, no provably secure construction is known for PRUs. In our setting, we are concerned with unbounded adversaries. Nonetheless, we are able to give stateful quantum algorithms which simulate the ideal object in both settings of interest. In the case of Haar-random states, our simulator is polynomial-time, has negligible error, and can also simulate verification and reflection through the simulated state. This yields an immediate application to quantum money: a money scheme which is information-theoretically unforgeable and untraceable. In the case of Haar-random unitaries, our simulator takes polynomial space, but simulates both forward and inverse access with zero error. These results can be seen as the first significant steps in developing a theory of lazy sampling for random quantum objects. 

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3. A quantum processor based on coherent transport of entangled atom arrays

   https://doi.org/10.1038/s41586-022-04592-6  

   Bluvstein, Dolev ; Levine, Harry ; Semeghini, Giulia ; Wang, Tout T. ; Ebadi, Sepehr ; Kalinowski, Marcin ; Keesling, Alexander ; Maskara, Nishad ; Pichler, Hannes ; Greiner, Markus ; et al ( April 2022 , Nature)

   Abstract The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems 1,2 . In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation 3–5 . We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state 6,7 . Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits 8 and a toric code state on a torus with sixteen data and eight ancillary qubits 9 . Finally, we use this architecture to realize a hybrid analogue–digital evolution 2 and use it for measuring entanglement entropy in quantum simulations 10–12 , experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars 13,14 . Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology. 

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4. Compiling Quantum Circuits for Dynamically Field-Programmable Neutral Atoms Array Processors

   https://doi.org/10.22331/q-2024-03-14-1281  

   Tan, Daniel Bochen ; Bluvstein, Dolev ; Lukin, Mikhail D ; Cong, Jason ( March 2024 , Quantum)

   Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a promising platform for quantum information processing. In DPQA, atomic qubits are selectively loaded into arrays of optical traps that can be reconfigured during the computation itself. Leveraging qubit transport and parallel, entangling quantum operations, different pairs of qubits, even those initially far away, can be entangled at different stages of the quantum program execution. Such reconfigurability and non-local connectivity present new challenges for compilation, especially in the layout synthesis step which places and routes the qubits and schedules the gates. In this paper, we consider a DPQA architecture that contains multiple arrays and supports 2D array movements, representing cutting-edge experimental platforms. Within this architecture, we discretize the state space and formulate layout synthesis as a satisfiability modulo theories problem, which can be solved by existing solvers optimally in terms of circuit depth. For a set of benchmark circuits generated by random graphs with complex connectivities, our compiler OLSQ-DPQA reduces the number of two-qubit entangling gates on small problem instances by 1.7x compared to optimal compilation results on a fixed planar architecture. To further improve scalability and practicality of the method, we introduce a greedy heuristic inspired by the iterative peeling approach in classical integrated circuit routing. Using a hybrid approach that combined the greedy and optimal methods, we demonstrate that our DPQA-based compiled circuits feature reduced scaling overhead compared to a grid fixed architecture, resulting in 5.1X less two-qubit gates for 90 qubit quantum circuits. These methods enable programmable, complex quantum circuits with neutral atom quantum computers, as well as informing both future compilers and future hardware choices.

    

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5. Logical quantum processor based on reconfigurable atom arrays

   https://doi.org/10.1038/s41586-023-06927-3  

   Bluvstein, Dolev ; Evered, Simon J. ; Geim, Alexandra A. ; Li, Sophie H. ; Zhou, Hengyun ; Manovitz, Tom ; Ebadi, Sepehr ; Cain, Madelyn ; Kalinowski, Marcin ; Hangleiter, Dominik ; et al ( December 2023 , Nature)

   Suppressing errors is the central challenge for useful quantum computing¹, requiring quantum error correction (QEC)^2–6for large-scale processing. However, the overhead in the realization of error-corrected ‘logical’ qubits, in which information is encoded across many physical qubits for redundancy^2–4, poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays⁷, our system combines high two-qubit gate fidelities⁸, arbitrary connectivity^7,9, as well as fully programmable single-qubit rotations and mid-circuit readout^10–15. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code⁶distance fromd = 3 tod = 7, preparation of colour-code qubits with break-even fidelities⁵, fault-tolerant creation of logical Greenberger–Horne–Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks^16,17, we realize computationally complex sampling circuits¹⁸with up to 48 logical qubits entangled with hypercube connectivity¹⁹with 228 logical two-qubit gates and 48 logical CCZ gates²⁰. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling^21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.

    

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