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      <title>RydbergAtoms</title>
      <link>https://umqt.phys.strath.ac.uk/tag/rydbergatoms/</link>
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    <item>
      <title>Cs Atom Array @ 7K</title>
      <link>https://umqt.phys.strath.ac.uk/ryd-posts/25-11-19-cryogenic-cs-array/</link>
      <pubDate>Wed, 19 Nov 2025 00:00:00 +0000</pubDate>
      <guid>https://umqt.phys.strath.ac.uk/ryd-posts/25-11-19-cryogenic-cs-array/</guid>
      <description>&lt;p&gt;We have demonstrated single atom trapping of Cs in a 940nm tweezer array within the 7K region of our cryostat. Next steps will see installation of 810nm trap beams for Rb and evaluation of cryogenic lifetimes.&lt;/p&gt;
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      <title>Sparse Graph Optimization using Weighted Quantum Wires in Rydberg Atom Arrays</title>
      <link>https://umqt.phys.strath.ac.uk/ryd-posts/25-11-05-experimental-quantum-wires/</link>
      <pubDate>Wed, 05 Nov 2025 00:00:00 +0000</pubDate>
      <guid>https://umqt.phys.strath.ac.uk/ryd-posts/25-11-05-experimental-quantum-wires/</guid>
      <description>&lt;h2 id=&#34;overview&#34;&gt;Overview&lt;/h2&gt;
&lt;p&gt;Neutral atom arrays provide a versatile platform to implement coherent quantum annealing as an approach to solving hard combinatorial optimization problems. In this work we present and experimentally demonstrate an efficient encoding scheme based on chains of Rydberg-blockaded atoms, which we call quantum wires, to natively embed maximum weighted independent set (MWIS) and quadratic unconstrained binary optimization (QUBO) problems on a neutral atom architecture. For graphs with quasi-unit-disk connectivity, in which only a few long-range edges are required, our approach requires a significantly lower overhead in the number of ancilla qubits than previous proposals, facilitating the implementation on currently available hardware. To demonstrate the approach, we perform weighted-graph annealing on a programmable atom array using local light shifts to encode problem-specific weights across graphs of varying sizes. This approach successfully identifies the solutions to the original MWIS and QUBO graph instances. Our work expands the operational toolkit of near-term neutral atom arrays, enhancing their potential for scalable quantum optimization. For more details see &lt;a href=&#34;https://arxiv.org/abs/2503.17115&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;arXiv:2503.17115&lt;/a&gt;.&lt;/p&gt;
&lt;h2 id=&#34;weighted-quantum-wires&#34;&gt;Weighted Quantum Wires&lt;/h2&gt;







































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                &lt;img src=&#34;images/quantum-wires.png&#34; 
                    alt=&#34;Weighted Quantum Wires (a) Basic construction of a wire to connect two nodes with weights α and β in MWIS and QUBO problems. The energy diagram shows the ordering of the eigenstates for an MWIS implementation. (b, c) Wire constructions to delocalise triangular and all-to-all square interactions between vertices in MWIS problems. (d) Generalization of the crossing gadget introduced in [33] to allow for arbitrary weights of the nodes.&#34; width=&#34;120%&#34; /&gt;
            &lt;/center&gt;&lt;figcaption class=&#34;figcaption&#34;&gt;
            &lt;p&gt;&lt;strong&gt;Weighted Quantum Wires&lt;/strong&gt; (a) Basic construction of a wire to connect two nodes with weights α and β in MWIS and QUBO problems. The energy diagram shows the ordering of the eigenstates for an MWIS implementation. (b, c) Wire constructions to delocalise triangular and all-to-all square interactions between vertices in MWIS problems. (d) Generalization of the crossing gadget introduced in [33] to allow for arbitrary weights of the nodes.
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      <title>Rb/Cs Dual Species MOTs @ 7K</title>
      <link>https://umqt.phys.strath.ac.uk/ryd-posts/25-04-13-cryogenic-dual-species-mot/</link>
      <pubDate>Sun, 13 Apr 2025 00:00:00 +0000</pubDate>
      <guid>https://umqt.phys.strath.ac.uk/ryd-posts/25-04-13-cryogenic-dual-species-mot/</guid>
      <description>&lt;p&gt;We have demonstrated a bi-chromatic dual species magneto-optical trap enabling simultaneous cooling of Rb and Cs within the 7K region of our cryostat. Following this project milestone our aim now is to get the atoms loaded into arrays of species-selective optical traps ready to begin work on inter-species gate operations.&lt;/p&gt;
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      <title>Graph Colouring via Quantum Optimization on a Rydberg-Qudit Atom Array</title>
      <link>https://umqt.phys.strath.ac.uk/ryd-posts/25-04-11-graph-colouring-with-rydberg-qudits/</link>
      <pubDate>Fri, 11 Apr 2025 00:00:00 +0000</pubDate>
      <guid>https://umqt.phys.strath.ac.uk/ryd-posts/25-04-11-graph-colouring-with-rydberg-qudits/</guid>
      <description>&lt;h2 id=&#34;summary&#34;&gt;Summary&lt;/h2&gt;
&lt;p&gt;We propose a new approach to natively embedding graph colouring problems onto neutral atom arrays using multiple Rydberg states each representing a unique colour. Graph colouring arises in a wide range of industrially relevant optimisation problems from sharing data across a wifi network to scheduling tasks and planning workloads. Using multiple Rydberg states enables efficient encoding of this problem onto quantum hardware and provides a new direction for near-term applications of neutral atom quantum computing. For more details see &lt;a href=&#34;https://doi.org/10.48550/arXiv.2504.08598&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;arXiv.2504.08598&lt;/a&gt;.&lt;/p&gt;
&lt;h2 id=&#34;key-results&#34;&gt;Key Results&lt;/h2&gt;
&lt;p&gt;Neutral atom arrays have emerged as a versatile candidate for the embedding of hard classical optimization problems. Prior work has focused on mapping problems onto finding the maximum independent set of weighted or unweighted unit disk graphs. In this paper we introduce a new approach to solving natively-embedded vertex graph colouring problems by performing coherent annealing with Rydberg-qudit atoms, where different same-parity Rydberg levels represent a distinct label or colour. We demonstrate the ability to robustly find optimal graph colourings for chromatic numbers up to the number of distinct Rydberg states used, in our case k = 3. We analyse the impact of both the long-range potential tails and residual inter-state interactions, proposing encoding strategies that suppress errors in the resulting ground states. We discuss the experimental feasibility of this approach and propose extensions to solve higher chromatic number problems, providing a route towards direct solution of a wide range of real-world integer optimization problems using near-term neutral atom hardware. For more details see &lt;a href=&#34;https://doi.org/10.48550/arXiv.2504.08598&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;arXiv.2504.08598&lt;/a&gt;.&lt;/p&gt;
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      <title>Demonstration of weighted graph optimization on a Rydberg atom array using local light-shifts</title>
      <link>https://umqt.phys.strath.ac.uk/ryd-posts/24-07-24-speeding-up-readout/</link>
      <pubDate>Wed, 24 Jul 2024 00:00:00 +0000</pubDate>
      <guid>https://umqt.phys.strath.ac.uk/ryd-posts/24-07-24-speeding-up-readout/</guid>
      <description>&lt;p&gt;We present a scheme for speeding up quantum measurement. The scheme builds on previous protocols that entangle the system to be measured with ancillary systems. In the idealised situation of perfect entangling operations and no decoherence, it gives an exact space-time trade-off meaning the readout speed increases linearly with the number of ancilla. We verify this scheme is robust against experimental imperfections through numerical modelling of gate noise and readout errors, and under certain circumstances our scheme can even lead to better than linear improvement in the speed of measurement with the number of systems measured. This hardware-agnostic approach is broadly applicable to a range of quantum technology platforms and offers a route to accelerate midcircuit measurement as required for effective quantum error correction. For more details see &lt;a href=&#34;https://doi.org/10.1103/PhysRevLett.134.080801&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Phys. Rev. Lett. 134, 080801&lt;/a&gt; or &lt;a href=&#34;https://arxiv.org/abs/2407.17342&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;arXiv:2407.17342&lt;/a&gt;.&lt;/p&gt;
</description>
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      <title>Demonstration of weighted graph optimization on a Rydberg atom array using local light-shifts</title>
      <link>https://umqt.phys.strath.ac.uk/ryd-posts/24-04-04-graph-optimisation/</link>
      <pubDate>Thu, 04 Apr 2024 00:00:00 +0000</pubDate>
      <guid>https://umqt.phys.strath.ac.uk/ryd-posts/24-04-04-graph-optimisation/</guid>
      <description>&lt;h2 id=&#34;overview&#34;&gt;Overview&lt;/h2&gt;
&lt;p&gt;In this paper we present first demonstrations of weighted graph optimization on a Rydberg atom array using annealing with local light-shifts. We verify the ability to prepare weighted graphs in 1D and 2D arrays, including embedding a five vertex non-unit disk graph using nine physical qubits. We find common annealing ramps leading to preparation of the target ground state robustly over a substantial range of different graph weightings. This work provides a route to exploring large-scale optimization of non-planar weighted graphs relevant for solving relevant real-world problems. For more details see  &lt;a href=&#34;https://arxiv.org/abs/2404.02658&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;arXiv:2404.02658&lt;/a&gt;.&lt;/p&gt;
&lt;h2 id=&#34;graph-optimisation-using-neutral-atom-arrays&#34;&gt;Graph Optimisation using Neutral Atom Arrays&lt;/h2&gt;
&lt;p&gt;Neutral atom arrays have emerged as a versatile platform towards scalable quantum computation and optimisation, capable of implementing high fidelity digital gates and logical qubit encodings with arbitrary connectivity [1], as well as enabling solution of classical optimisation problems using analogue quantum annealing [2]. Early demonstrations of solving the Maximum Independent Set (MIS) problem using arrays of up to 289 qubits found for hard problems the quantum hardware offered a speedup over classical solvers [3], however recent analysis shows for MIS problems on unit disk graphs improved classical solvers can find solutions for thousands of qubits [4].&lt;/p&gt;
&lt;p&gt;A recent proposal from Nguyen et al. [5] shows that by introducing local light-shifts it is possible to extend beyond solving MIS to a wide range of problems including maximum weighted independent set (MWIS), quadratic unconstrained binary optimisation (QUBO) and even factorisation with at worst a quadratic overhead in qubit number. This approach uses gadgets to map a given problem onto a unit-disk graph (UDG) MWIS with local light-shifts to implement weightings. In this work, we implement the first experimental demonstrations of UDG-MWIS optimisation using local light-shifts.&lt;/p&gt;
&lt;h2 id=&#34;local-light-shifts&#34;&gt;Local Light-shifts&lt;/h2&gt;
&lt;p&gt;To implement weighted graph annealing with local light-shifts we use an additional laser and spatial light modulator (SLM) to project a secondary tweezer array onto the atoms with a programmable relative power. This light-shift potential allows us to precisely control the relative weight on each qubit, whilst performing global control of the laser intensity to enable simplified annealing protocols with a finite number of parameters. For our Cs atoms the 800 nm light causes a blue-shift (positive detuning), so annealing ramps are performed using a two-stage process where the global Rydberg excitation lasers are first ramped to resonance, then the light-shift intensity shaped to give smoothly evolving light shifts on each site with fixed relative weighting to ensure the groundstate of the combined atom-light interaction encodes the solution to the classical UDG-MWIS problem.&lt;/p&gt;
&lt;h2 id=&#34;weighted-1d-chains&#34;&gt;Weighted 1D Chains&lt;/h2&gt;
&lt;p&gt;To verify the ability to use local light-shifts we begin with a simple example of a weighted 1D chain. Using uniform weighting, for an odd chain the blockade condition should ensure all atoms on odd sites are Rydberg excited. Introducing a relative weighting of 2 onto the even sites changes the resulting groundstate and causes the inverted case of Rydberg excitation on even sites. Below we show results of optimising the annealing for the weighted graph, and demonstrate the same annealing ramp is able to simultaneously prepare the groundstate of the uniformly weighted graph, demonstrating the ability to adiabatically preprare the groundstate of the system.&lt;/p&gt;







































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                    alt=&#34;Optimisation with 1D weighted chains: (a) For a uniformly weighted, odd-length 1D graph the ground state is the Z2-ordered phase with Rydberg excitations on odd sites which corresponds to the unweighted MIS. Introducing a weighting with wi=2 on even sites results in an MWIS ground state with Rydberg excitations localised to the even sites which is no longer equivalent to the MIS solution. (b) Optimal annealing ramp for preparing the weighted ground state obtained via closed-loop optimization for N=9 atoms spaced by a=7 µm. Output state probability (c) and time evolution (d) for the unweighted graph showing the odd-ordered target ground state is prepared with 19(1)% probability. Output state probability (e) and time evolution (f) for the weighted graph showing even-ordered ground state is also prepared with 19(1)% probability.&#34; width=&#34;120%&#34; /&gt;
            &lt;/center&gt;&lt;figcaption class=&#34;figcaption&#34;&gt;
            &lt;p&gt;&lt;strong&gt;Optimisation with 1D weighted chains:&lt;/strong&gt; (a) For a uniformly weighted, odd-length 1D graph the ground state is the Z&lt;sub&gt;2&lt;/sub&gt;-ordered phase with Rydberg excitations on odd sites which corresponds to the unweighted MIS. Introducing a weighting with w&lt;sub&gt;i&lt;/sub&gt;=2 on even sites results in an MWIS ground state with Rydberg excitations localised to the even sites which is no longer equivalent to the MIS solution. (b) Optimal annealing ramp for preparing the weighted ground state obtained via closed-loop optimization for N=9 atoms spaced by a=7 µm. Output state probability (c) and time evolution (d) for the unweighted graph showing the odd-ordered target ground state is prepared with 19(1)% probability. Output state probability (e) and time evolution (f) for the weighted graph showing even-ordered ground state is also prepared with 19(1)% probability.
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&lt;h2 id=&#34;weighted-2d-graphs&#34;&gt;Weighted 2D Graphs&lt;/h2&gt;
&lt;p&gt;To demonstrate our ability to optimise for 2D graphs, we consider a simple 5-vertex weighted graph shown below, which can be mapped onto a UDG-MWIS graph with 9 atoms. We find annealing profiles that optimise this graph for the weightings (2,1,2,1,1) giving the correct groundstate solution as shown, and additionally find this same annealing profile works for a range of other weightings highlighting the versatility and robustness of the approach of using local light-shifts for solving graph optimisation problems.&lt;/p&gt;







































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                    alt=&#34;Optimisation of a 2D weighted graph: (a) The target 5-vertex weighted graph problem is embedded into UDG-MWIS form for encoding onto a neutral atom array using 9 qubits, with 5 qubits encoding the vertices and 4 additional atoms required to implement the coupling of vertices 1 and 3 to vertex 5 whilst maintaining the constraint that no vertices connected by an edge can be simultaneously excited. (b) Result showing annealing of a weighted graph problem where the neutral atom hardware is able to correctly identify the solution corresponding to vertices 1 and 3 having higher weighting than 2, 4 and 5.&#34; width=&#34;120%&#34; /&gt;
            &lt;/center&gt;&lt;figcaption class=&#34;figcaption&#34;&gt;
            &lt;p&gt;&lt;strong&gt;Optimisation of a 2D weighted graph:&lt;/strong&gt; (a) The target 5-vertex weighted graph problem is embedded into UDG-MWIS form for encoding onto a neutral atom array using 9 qubits, with 5 qubits encoding the vertices and 4 additional atoms required to implement the coupling of vertices 1 and 3 to vertex 5 whilst maintaining the constraint that no vertices connected by an edge can be simultaneously excited. (b) Result showing annealing of a weighted graph problem where the neutral atom hardware is able to correctly identify the solution corresponding to vertices 1 and 3 having higher weighting than 2, 4 and 5.
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&lt;h2 id=&#34;references&#34;&gt;References&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;[1] D. Bluvstein et al., Logical quantum processor based on reconfigurable atom arrays, &lt;a href=&#34;https://doi.org/10.1038/s41586-023-06927-3&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Nature 626, 58 (2024)&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;[2] M. Kim et al., Quantum computing with Rydberg atom graphs, &lt;a href=&#34;https://doi.org/10.1007/s40042-023-00774-1&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;J. Korean Phys. Soc. 82, 827 (2023)&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;[3] S. Ebadi et al., Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays, &lt;a href=&#34;https://doi.org/10.1126/science.abo6587&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Science 376, 1209 (2022)&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;[4] R.S. Abdrist et al., Hardness of the maximum-independent-set problem on unit-disk graphs and prospects for quantum speedups, &lt;a href=&#34;https://link.aps.org/doi/10.1103/PhysRevResearch.5.043277&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Phys. Rev. Research 5, 043277 (2023)&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;[5] M.-T. Nguyen et al., Quantum optimization with arbitrary connectivity using Rydberg atom arrays, &lt;a href=&#34;https://doi.org/10.1103/PRXQuantum.4.010316&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;PRX Quantum 5, 010316 (2023)&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
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      <title>Benchmarking the algorithmic performance of near-term neutral atom processors</title>
      <link>https://umqt.phys.strath.ac.uk/ryd-posts/24-02-03-algorithmic-benchmarking/</link>
      <pubDate>Tue, 13 Feb 2024 00:00:00 +0000</pubDate>
      <guid>https://umqt.phys.strath.ac.uk/ryd-posts/24-02-03-algorithmic-benchmarking/</guid>
      <description>&lt;p&gt;Neutral atom quantum processors provide a viable route to scalable quantum computing, with recent demonstrations of high-fidelity and parallel gate operations and initial implementation of quantum algorithms using both physical and logical qubit encodings. In this work we present a characterization of the algorithmic performance of near term Rydberg atom quantum computers through device simulation to enable comparison against competing architectures. We consider three different quantum algorithm related tests, exploiting the ability to dynamically update qubit connectivity and multi-qubit gates. We calculate a quantum volume of VQ=2&lt;sup&gt;9&lt;/sup&gt; for 9 qubit devices with realistic parameters, which is the maximum achievable value for this device size and establishes a lower bound for larger systems. We also simulate highly efficient implementations of both the Bernstein-Vazirani algorithm with &amp;gt;0.95 success probability for 9 data qubits and 1 ancilla qubit without loss correction, and Grover&amp;rsquo;s search algorithm with a loss-corrected success probability of 0.97 for an implementation of the algorithm using 6 data qubits and 3 ancilla qubits using native multi-qubit CCZ gates. Our results indicate Rydberg atom processors are a highly competitive near-term platform which, bolstered by the potential for further scalability, can pave the way toward useful quantum computation.&lt;/p&gt;
&lt;p&gt;For more details see  &lt;a href=&#34;https://doi.org/10.48550/arXiv.2402.02127&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;arXiv:2402.02127&lt;/a&gt;.&lt;/p&gt;
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      <title>Interspecies Förster resonances of Rb-Cs Rydberg d-states for enhanced multi-qubit gate fidelities</title>
      <link>https://umqt.phys.strath.ac.uk/ryd-posts/24-01-04-interspecies-forster-resonances/</link>
      <pubDate>Wed, 03 Jan 2024 00:00:00 +0000</pubDate>
      <guid>https://umqt.phys.strath.ac.uk/ryd-posts/24-01-04-interspecies-forster-resonances/</guid>
      <description>&lt;p&gt;We present an analysis of interspecies interactions between Rydberg d-states of rubidium and cesium. We identify the Förster resonance channels offering the strongest interspecies couplings, demonstrating the viability for performing high-fidelity two- and multi-qubit C&lt;sub&gt;k&lt;/sub&gt;Z gates up to k=4, including accounting for blockade errors evaluated via numerical diagonalization of the pair-potentials. Our results show d-state orbitals offer enhanced suppression of intraspecies couplings compared to s-states, making them well suited for use in large-scale neutral atom quantum processors. For more details see  &lt;a href=&#34;https://doi.org/10.48550/arXiv.2401.02308&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;arXiv:2401.02308&lt;/a&gt;.&lt;/p&gt;
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      <title>Randomised benchmarking and non-destructive readout</title>
      <link>https://umqt.phys.strath.ac.uk/ryd-posts/23-01-01-randomisedbenchmarking/</link>
      <pubDate>Wed, 25 Jan 2023 00:00:00 +0000</pubDate>
      <guid>https://umqt.phys.strath.ac.uk/ryd-posts/23-01-01-randomisedbenchmarking/</guid>
      <description>&lt;p&gt;We have demonstrated high-fidelity randomised benchmarking of single qubit microwave gates across an array of 225 atoms using conventional readout techniques using strings of up to 1000 random gates. We achieved an average gate error of 8×10&lt;sup&gt;-5&lt;/sup&gt; which is below the threshold for fault tolerant operations, highlighting the viability of neutral atoms for scalable computing.&lt;/p&gt;







































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&lt;p&gt;We further demonstrated non-destructive readout using state-selective imaging on the stretched state transition to enable post-selection for loss and avoiding the requirement to reload the arrays after every sequence.&lt;/p&gt;
&lt;p&gt;For more details see our paper &lt;a href=&#34;https://doi.org/10.1103/PhysRevLett.131.030602&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Phys. Rev. Lett. 131, 030602 (2023)&lt;/a&gt; [&lt;a href=&#34;https://arxiv.org/abs/2301.10510&#34; title=&#34;arXiv:2301.10510 (2023)&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;arXiv&lt;/a&gt;].&lt;/p&gt;
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      <title>High-fidelity multi-qubit gate operations</title>
      <link>https://umqt.phys.strath.ac.uk/ryd-posts/22-08-22-high-fidelity-multi-qubit/</link>
      <pubDate>Mon, 22 Aug 2022 00:00:00 +0000</pubDate>
      <guid>https://umqt.phys.strath.ac.uk/ryd-posts/22-08-22-high-fidelity-multi-qubit/</guid>
      <description>&lt;p&gt;We have developed a robust protocol for implementing high-fidelity multiqubit controlled phase gates (C&lt;sub&gt;k&lt;/sub&gt;Z) on neutral atom qubits coupled to highly excited Rydberg states.







































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                &lt;img src=&#34;images/levelscheme.png&#34; 
                    alt=&#34;Atomic level scheme We model gate fidelities for two-level excitation including the full intermediate state hyperfine structure.&#34; width=&#34;80%&#34; /&gt;
            &lt;/center&gt;&lt;figcaption class=&#34;figcaption&#34;&gt;
            &lt;p&gt;&lt;strong&gt;Atomic level scheme&lt;/strong&gt; We model gate fidelities for two-level excitation including the full intermediate state hyperfine structure.
            &lt;/p&gt;
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Our approach is based on extending adiabatic rapid passage (ARP) to two-photon excitation via a short-lived intermediate excited state common to alkali-atom Rydberg experiments, accounting for the full impact of spontaneous decay and differential AC Stark shifts from the complete manifold of hyperfine excited states. We evaluate and optimisze gate performance using optimal control techniques to calculate Rabi frequency and detuning parameters in time. For Cs and currently available laser frequencies and powers, a CCZ gate with fidelity F &amp;gt; 0.995 for three qubits.







































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    &lt;figure class=&#34;figure&#34; height=450px &gt;&lt;center&gt;
                &lt;img src=&#34;images/3Qgates.png&#34; 
                    alt=&#34;Three atom CCZ gate We show (a) optimal pulse parameters for the CCZ gate, (b) leakage errors from spontaneous decay and excitation of the intermediate excited state (c) Resulting phase and amplitude of the optimal gate sequence.&#34; width=&#34;80%&#34; /&gt;
            &lt;/center&gt;&lt;figcaption class=&#34;figcaption&#34;&gt;
            &lt;p&gt;&lt;strong&gt;Three atom CCZ gate&lt;/strong&gt; We show (a) optimal pulse parameters for the CCZ gate, (b) leakage errors from spontaneous decay and excitation of the intermediate excited state (c) Resulting phase and amplitude of the optimal gate sequence.
            &lt;/p&gt;
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This same technique can be used to find gates for four or more qubits, with the performance limitation imposed simply by the largest distance between any atom pair. For four qubits, this can be done using either a planar square geometry or in 3D with a pyramid offering CCCZ with F &amp;gt; 0.99 for four qubits is attainable in ∼ 1.8 μs via this protocol. Higher fidelities are accessible with future technologies, and our results highlight the utility of neutral atom arrays for the native implementation of multiqubit unitaries.&amp;quot;&lt;/p&gt;
&lt;p&gt;






































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                &lt;img src=&#34;images/4Qgates.png&#34; 
                    alt=&#34;Four atom CCCZ Gate Optimal pulse shapes for 4 qubits in different geometries.&#34; width=&#34;80%&#34; /&gt;
            &lt;/center&gt;&lt;figcaption class=&#34;figcaption&#34;&gt;
            &lt;p&gt;&lt;strong&gt;Four atom CCCZ Gate&lt;/strong&gt; Optimal pulse shapes for 4 qubits in different geometries.
            &lt;/p&gt;
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For more details see our paper in &lt;a href=&#34;https://iopscience.iop.org/article/10.1088/2058-9565/ac823a&#34; title=&#34;QST&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;QST&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;G. Pelegri, A. Daley and J.D. Pritchard, &lt;em&gt;High-fidelity multiqubit Rydberg gates via two-photon adiabatic rapid passage&lt;/em&gt;,
&lt;a href=&#34;https://iopscience.iop.org/article/10.1088/2058-9565/ac823a&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Quantum Sci. Technol. 7, 045020 (2022)&lt;/a&gt;&lt;/p&gt;
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