QC_Post | EQOP

Sparse Graph Optimization using Weighted Quantum Wires in Rydberg Atom Arrays

Wed, 05 Nov 2025 00:00:00 +0000

Overview

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 arXiv:2503.17115.

Weighted Quantum Wires

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.

Graph Colouring via Quantum Optimization on a Rydberg-Qudit Atom Array

Fri, 11 Apr 2025 00:00:00 +0000

Summary

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 arXiv.2504.08598.

Key Results

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 arXiv.2504.08598.

Demonstration of weighted graph optimization on a Rydberg atom array using local light-shifts

Wed, 24 Jul 2024 00:00:00 +0000

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 Phys. Rev. Lett. 134, 080801 or arXiv:2407.17342.

Demonstration of weighted graph optimization on a Rydberg atom array using local light-shifts

Thu, 04 Apr 2024 00:00:00 +0000

Overview

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 arXiv:2404.02658.

Graph Optimisation using Neutral Atom Arrays

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].

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.

Local Light-shifts

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.

Weighted 1D Chains

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.

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 w_i=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.

Weighted 2D Graphs

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.

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.

References

[1] D. Bluvstein et al., Logical quantum processor based on reconfigurable atom arrays, Nature 626, 58 (2024)
[2] M. Kim et al., Quantum computing with Rydberg atom graphs, J. Korean Phys. Soc. 82, 827 (2023)
[3] S. Ebadi et al., Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays, Science 376, 1209 (2022)
[4] R.S. Abdrist et al., Hardness of the maximum-independent-set problem on unit-disk graphs and prospects for quantum speedups, Phys. Rev. Research 5, 043277 (2023)
[5] M.-T. Nguyen et al., Quantum optimization with arbitrary connectivity using Rydberg atom arrays, PRX Quantum 5, 010316 (2023)

Benchmarking the algorithmic performance of near-term neutral atom processors

Tue, 13 Feb 2024 00:00:00 +0000

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=2⁹ 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 >0.95 success probability for 9 data qubits and 1 ancilla qubit without loss correction, and Grover’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.

For more details see arXiv:2402.02127.

Commensurate and incommensurate 1D interacting quantum systems

Thu, 11 Jan 2024 00:00:00 +0000

Hyperlink

Nat Communications 15, 474 (2024).

Abstract

We use dynamically varying microscopic light potentials in a quantum-gas microscope to study commensurate and incommensurate 1D systems of interacting bosonic atoms in an optical lattice. Such incommensurate systems are analogous to doped insulating states that exhibit atom transport and compressibility. Initially, a commensurate system with unit filling and fixed atom number is prepared between two potential barriers. We deterministically create an incommensurate system by dynamically changing the position of the barriers such that the number of available lattice sites is reduced while retaining the atom number. Our commensurate and incommensurate systems are characterised by measuring the distribution of particles and holes as a function of the lattice filling, and interaction strength, and we probe the particle mobility by applying a bias potential. Our work provides the foundation for preparation of low-entropy states with controlled filling in optical lattice experiments.

Interspecies Förster resonances of Rb-Cs Rydberg d-states for enhanced multi-qubit gate fidelities

Wed, 03 Jan 2024 00:00:00 +0000

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_kZ 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 arXiv:2401.02308.

Dr. Jonathan Pritchard awarded RAEng Senior Research Fellowship

Wed, 01 Mar 2023 00:00:00 +0000

Congratulations to Dr Jonathan Pritchard on receiving a prestigious RAEng Senior Research Fellowship with M Squared Lasers to develop fault-tolerant neutral atom quantum computers. For more information see the project page QuERy.

Accurate holographic light potentials using pixel crosstalk modelling

Fri, 24 Feb 2023 00:00:00 +0000

Hyperlink

Scientific Reports 13, 3252 (2023).

Abstract

Quantum-gas microscopes are used to study ultracold atoms in optical lattices at the singleparticle level. In these systems atoms are localised on lattice sites with separations close to or below the diffraction limit. To determine the lattice occupation with high fidelity, a deconvolution of the images is often required. We compare three different techniques, a local iterative deconvolution algorithm, Wiener deconvolution and the Lucy-Richardson algorithm, using simulated microscope images. We investigate how the reconstruction fidelity scales with varying signal-to-noise ratio, lattice filling fraction, varying fluorescence levels per atom, and imaging resolution. The results of this study identify the limits of singe-atom detection and provide quantitative fidelities which are applicable for different atomic species and quantum-gas microscope setups.

Randomised benchmarking and non-destructive readout

Wed, 25 Jan 2023 00:00:00 +0000

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^-5 which is below the threshold for fault tolerant operations, highlighting the viability of neutral atoms for scalable computing.

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.

For more details see our paper Phys. Rev. Lett. 131, 030602 (2023) [arXiv].

Two-Qubit EIT Gate Protocol

Tue, 22 Nov 2022 00:00:00 +0000

We have demonstrated the UK’s first neutral atom quantum gate using a novel protocol based on electromagnetically induced transparency (EIT) originally proposed by M. Müller, I. Lesanovsky and P. Zoller back in 2008, with our results published in Phys. Rev. Lett. 129, 200501 (2022).

EIT gate protocol (a) Control and target qubits in individual traps (b) Excitation pulse sequence (c) If the control qubit is in state |0>, the EIT condition on the target qubit prevents transfer whilst (d) if the control qubit is in |1> it is Rydberg excited, with interactions breaking the EIT condition and the target undergoes a Raman transition to implement a native CNOT gate.

We achieved a corrected CNOT gate fidelity of 0.82(6), mainly limited by available laser power, and used this gate to prepare a Bell state on two qubits.

EIT gate results (a) Raw and (b) Corrected gate matrices.

Bell State Preparation (a) Population and (b) Parity Oscillation of Bell states prepared using EIT gate protocol.

This provides a scalable gate protocol capable of performing a native CNOT gate and maps to CNOTN gates with N targets for stabiliser measurements in quantum error correction, for which we proposed with experimental upgrades including performing excitation via the inverted 7P1/2 transition to reach intrinsic fidelities F>0.998.

For more details see our paper Phys. Rev. Lett. 129, 200501 (2022).

High-fidelity multi-qubit gate operations

Mon, 22 Aug 2022 00:00:00 +0000

We have developed a robust protocol for implementing high-fidelity multiqubit controlled phase gates (C_kZ) on neutral atom qubits coupled to highly excited Rydberg states.

Atomic level scheme We model gate fidelities for two-level excitation including the full intermediate state hyperfine structure.

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 > 0.995 for three qubits.

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.

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 > 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."

Four atom CCCZ Gate Optimal pulse shapes for 4 qubits in different geometries.

For more details see our paper in QST.

G. Pelegri, A. Daley and J.D. Pritchard, High-fidelity multiqubit Rydberg gates via two-photon adiabatic rapid passage, Quantum Sci. Technol. 7, 045020 (2022)

Microwave preparation of two-dimensional fermionic spin mixtures

Wed, 02 Jan 2019 00:00:00 +0000

Hyperlink

New J. Phys. 21 013020 (2010).

Abstract

We present a method for preparing a single two-dimensional sample of a two-spin mixture of fermionic potassium in a single antinode of an optical lattice, in a quantum-gas microscope apparatus. Our technique relies on spatially-selective microwave transitions in a magnetic field gradient. Adiabatic transfer pulses were optimized for high efficiency and minimal atom loss and heating due to spin-changing collisions. We have measured the dynamics of those loss processes, which are more pronounced in the presence of a spin mixture. As the efficient preparation of atoms in a single antinode requires a homogeneous transverse magnetic field, we developed a method to image and minimize the magnetic field gradients in the focal plane of the microscope.

Sub-Doppler laser cooling of 40K

Wed, 12 Apr 2017 00:00:00 +0000

Abstract

Gray molasses is a powerful tool for sub-Doppler laser cooling of atoms to low temperatures. For alkaline atoms, this technique is commonly implemented with cooling lasers which are blue-detuned from either the D1 or D2 line. Here we show that efficient gray molasses can be implemented on the D2 line of 40K with red-detuned lasers. We obtained temperatures of $48(2),\mu {\rm{K}}$, which enables direct loading of $9.2(3)\times {10}^{6}$ atoms from a magneto-optical trap into an optical dipole trap. We support our findings by a one-dimensional model and three-dimensional numerical simulations of the optical Bloch equations which qualitatively reproduce the experimentally observed cooling effects.

Hyperlink

J. Phys. B: At. Mol. Opt. Phys. 50 095002 (2017).

Single-atom imaging of fermions in a quantum-gas microscope

Mon, 13 Jul 2015 00:00:00 +0000

Abstract

Single-atom-resolved detection in optical lattices using quantum-gas microscopes has enabled a new generation of experiments in the field of quantum simulation. Although such devices have been realized with bosonic species, a fermionic quantum-gas microscope has remained elusive. Here we demonstrate single-site- and single-atom-resolved fluorescence imaging of fermionic potassium-40 atoms in a quantum-gas microscope set-up, using electromagnetically-induced-transparency cooling. We detected on average 1,000 fluorescence photons from a single atom within 1.5 s, while keeping it close to the vibrational ground state of the optical lattice. A quantum simulator for fermions with single-particle access will be an excellent test bed to investigate phenomena and properties of strongly correlated fermionic quantum systems, allowing direct measurement of ordered quantum phases and out-of-equilibrium dynamics with access to quantities ranging from spin–spin correlation functions to many-particle entanglement12.

Hyperlink

Nature Physics 11, 738–742 (2015.