Motivated by far-reaching applications ranging from quantum simulations of complex processes in physics and chemistry to quantum information processing1, a broad effort is currently underway to build large-scale programmable quantum systems. Such systems provide insights into strongly correlated quantum matter2–6, while at the same time enabling new methods for computation7–10 and metrology11. Here we demonstrate a programmable quantum simulator based on deterministically prepared two-dimensional arrays of neutral atoms, featuring strong interactions controlled by coherent atomic excitation into Rydberg states12. Using this approach, we realize a quantum spin model with tunable interactions for system sizes ranging from 64 to 256 qubits. We benchmark the system by characterizing high-fidelity antiferromagnetically ordered states and demonstrating quantum critical dynamics consistent with an Ising quantum phase transition in (2 + 1) dimensions13. We then create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation14, experimentally map the phase diagram and investigate the role of quantum fluctuations. Offering a new lens into the study of complex quantum matter, these observations pave the way for investigations of exotic quantum phases, non-equilibrium entanglement dynamics and hardware-efficient realization of quantum algorithms. A programmable quantum simulator with 256 qubits is created using neutral atoms in two-dimensional optical tweezer arrays, demonstrating a quantum phase transition and revealing new quantum phases of matter.

Quantum phases of matter on a 256-atom programmable quantum simulator

Photons have been a flagship system for studying quantum mechanics, advancing quantum information science, and developing quantum technologies. Quantum entanglement, teleportation, quantum key distribution, and early quantum computing demonstrations were pioneered in this technology because photons represent a naturally mobile and low-noise system with quantum-limited detection readily available. The quantum states of individual photons can be manipulated with very high precision using interferometry, an experimental staple that has been under continuous development since the 19th century. The complexity of photonic quantum computing devices and protocol realizations has raced ahead as both underlying technologies and theoretical schemes have continued to develop. Today, photonic quantum computing represents an exciting path to medium- and large-scale processing. It promises to put aside its reputation for requiring excessive resource overheads due to inefficient two-qubit gates. Instead, the ability to generate large numbers of photons—and the development of integrated platforms, improved sources and detectors, novel noise-tolerant theoretical approaches, and more—have solidified it as a leading contender for both quantum information processing and quantum networking. Our concise review provides a flyover of some key aspects of the field, with a focus on experiment. Apart from being a short and accessible introduction, its many references to in-depth articles and longer specialist reviews serve as a launching point for deeper study of the field.

Photonic quantum information processing: A concise review

Photons have been a flagship system for studying quantum mechanics, advancing quantum information science, and developing quantum technologies. Quantum entanglement, teleportation, quantum key distribution and early quantum computing demonstrations were pioneered in this technology because photons represent a naturally mobile and low-noise system with quantum-limited detection readily available. The quantum states of individual photons can be manipulated with very high precision using interferometry, an experimental staple that has been under continuous development since the 19th century. The complexity of photonic quantum computing device and protocol realizations has raced ahead as both underlying technologies and theoretical schemes have continued to develop. Today, photonic quantum computing represents an exciting path to medium- and large-scale processing. It promises to out aside its reputation for requiring excessive resource overheads due to inefficient two-qubit gates. Instead, the ability to generate large numbers of photons---and the development of integrated platforms, improved sources and detectors, novel noise-tolerant theoretical approaches, and more---have solidified it as a leading contender for both quantum information processing and quantum networking. Our concise review provides a flyover of some key aspects of the field, with a focus on experiment. Apart from being a short and accessible introduction, its many references to in-depth articles and longer specialist reviews serve as a launching point for deeper study of the field.

Photonic quantum information processing: a concise review

Quantum information encoded in single trapped ions provides a promising avenue towards a scalable quantum computer. This contribution describes most of the necessary building blocks for such a device. Particular emphasis is given to the implementation of single-qubit and multi-qubit gate operations.

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Quantum computing with trapped ions

This topical review addresses how Rydberg atoms can serve as building blocks for emerging quantum technologies. Whereas the fabrication of large numbers of artificial quantum systems with the uniformity required for the most attractive applications is difficult if not impossible, atoms provide stable quantum systems which, for the same species and isotope, are all identical. Whilst atomic ground-states provide scalable quantum objects, their applications are limited by the range over which their properties can be varied. In contrast, Rydberg atoms offer strong and controllable atomic interactions that can be tuned by selecting states with different principal quantum number or orbital angular momentum. In addition Rydberg atoms are comparatively long-lived, and the large number of available energy levels and their separations allow coupling to electromagnetic fields spanning over 6 orders of magnitude in frequency. These features make Rydberg atoms highly desirable for developing new quantum technologies. After giving a brief introduction to how the properties of Rydberg atoms can be tuned, we give several examples of current areas where the unique advantages of Rydberg atom systems are being exploited to enable new applications in quantum computing, electromagnetic field sensing, and quantum optics.

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Rydberg atom quantum technologies

We present a blueprint for building a fault-tolerant universal quantum computer with Rydberg atoms. Our scheme, which is based on the surface code, uses individually addressable, optically trapped atoms as qubits and exploits electromagnetically induced transparency to perform the multiqubit gates required for error correction and computation. We discuss the advantages and challenges of using Rydberg atoms to build such a quantum computer, and we perform error correction simulations to obtain an error threshold for our scheme. Our findings suggest that Rydberg atoms are a promising candidate for quantum computation, but gate fidelities need to improve before fault-tolerant universal quantum computation can be achieved.

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Blueprint for fault-tolerant quantum computation with Rydberg atoms

Performing entangling gates between physical qubits is necessary for building a large-scale universal quantum computer, but in some physical implementations—for example, those that are based on linear optics or networks of ion traps—entangling gates can only be implemented probabilistically. In this work, we study the fault-tolerant performance of a topological cluster state scheme with local nondeterministic entanglement generation, where failed entangling gates (which correspond to bonds on the lattice representation of the cluster state) lead to a defective three-dimensional lattice with missing bonds. We present two approaches for dealing with missing bonds; the first is a nonadaptive scheme that requires no additional quantum processing, and the second is an adaptive scheme in which qubits can be measured in an alternative basis to effectively remove them from the lattice, hence eliminating their damaging effect and leading to better threshold performance. We find that a fault-tolerance threshold can still be observed with a bond-loss rate of 6.5% for the nonadaptive scheme, and a bond-loss rate as high as 14.5% for the adaptive scheme.

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Fault-tolerant quantum computation with nondeterministic entangling gates

The construction of topological error correction codes requires the ability to fabricate a lattice of physical qubits embedded on a manifold with a nontrivial topology such that the quantum information is encoded in the global degrees of freedom (i.e., the topology) of the manifold. However, the manufacturing of large-scale topological devices will undoubtedly suffer from fabrication errors—permanent faulty components such as missing physical qubits or failed entangling gates—introducing permanent defects into the topology of the lattice and hence significantly reducing the distance of the code and the quality of the encoded logical qubits. In this work we investigate how fabrication errors affect the performance of topological codes, using the surface code as the test bed. A known approach to mitigate defective lattices involves the use of primitive swap gates in a long sequence of syndrome extraction circuits. Instead, we show that in the presence of fabrication errors the syndrome can be determined using the supercheck operator approach and the outcome of the defective gauge stabilizer generators without any additional computational overhead or use of swap gates. We report numerical fault-tolerance thresholds in the presence of both qubit fabrication and gate fabrication errors using a circuit-based noise model and the minimum-weight perfect-matching decoder. Our numerical analysis is most applicable to two-dimensional chip-based technologies, but the techniques presented here can be readily extended to other topological architectures. We find that in the presence of 8% qubit fabrication errors, the surface code can still tolerate a computational error rate of up to 0.1%.

Fault-tolerance thresholds for the surface code with fabrication errors

In this thesis, we consider steps towards building a useful quantum computer in the presence of realistic errors. We start by presenting a novel scheme for fault-tolerant quantum computation with Rydberg atoms. The scheme uses topological error correction codes to provide fault-tolerance and utilises electromagnetically induced transparency to perform entangling gates between qubits. We examine the benefits of this scheme compared to alternative approaches, and we investigate the errors that are likely to occur and how these can be managed. We then consider how to perform quantum computation with a surface code based quantum computer that has permanently faulty components. We study both faulty links between qubits, which prevent qubits from interacting, and faulty qubits themselves; such faults could affect a wide variety of physical implementations, including schemes that use superconducting qubits and those that use trapped ions. The approach we propose for dealing with these faulty components requires minimal modification to the quantum operations required by the surface code and should therefore be implementable by almost all current and future proposals for surface code based quantum devices. Finally, we consider how to perform fault-tolerant quantum computation with components that fail probabilistically. This section is largely motivated by quantum computation with linear optics and therefore focuses on quantum computation with cluster states. We show that these probabilistic failures can be tolerated providing the failure rate is suitably low, and we present methods for increasing error thresholds in the presence of such errors.

James M. Auger

Papers

Blueprint for fault-tolerant quantum computation with Rydberg atoms

Fault-tolerant quantum computation with nondeterministic entangling gates

Fault-tolerance thresholds for the surface code with fabrication errors

Fault-tolerant Quantum Computation with Realistic Error Models

Fault-tolerant quantum computation with non-deterministic entangling gates