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A major challenge in quantum computing is to solve general problems with limited physical hardware. Here, we implement digitized adiabatic quantum computing, combining the generality of the adiabatic algorithm with the universality of the digital approach, using a superconducting circuit with nine qubits. We probe the adiabatic evolutions, and quantify the success of the algorithm for random spin problems. We find that the system can approximate the solutions to both frustrated Ising problems and problems with more complex interactions, with a performance that is comparable. The presented approach is compatible with small-scale systems as well as future error-corrected quantum computers.Quantum mechanics can help solve complex problems in physics [1], chemistry [2], and machine learning [3], provided they can be programmed in a physical device. In adiabatic quantum computing [4][5][6], the system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this analog method lies in its combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions, and noise. A complementary approach is digital quantum computing, where logic gates combine to form quantum circuit algorithms [7]. The digital approach allows for constructing arbitrary interactions and is compatible with error correction [8, 9], but requires devising tailor-made algorithms. Here, we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution, explore the scaling of errors with system size, and measure the influence of local fields. We conclude by having the full system find the solution to random Ising problems with frustration, and problems with more complex interactions. This digital quantum simulation [10][11][12][13] consists of up to nine qubits and up to 10 3 quantum logic gates. This demonstration of digitized quantum adiabatic computing in the solid state opens a path to solving complex problems, and we hope it will motivate further research into the efficient synthesis of adiabatic algorithms, on small-scale systems with noise as well as future large-scale quantum computers with error correction.A key challenge in adiabatic quantum computing is to construct a device that is capable of encoding problem Hamiltonians that are non-stoquastic [14]. Such Hamiltonians would allow for universal adiabatic quantum computing [15, 16] as well as improving the performance for difficult instances * Present address: IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA of classical optimization problems [17]. Additionally, simulating interacting fermions for physics and chemistry requires non-stoquastic Hamiltonians [1, 18]. In general, nonstoquastic Hamiltonians are more difficult to study classically, as Monte Carlo ...

The intriguing many-body phases of quantum matter arise from the interplay of particle interactions, spatial symmetries, and external fields [1]. Generating these phases in an engineered system could provide deeper insight into their nature and the potential for harnessing their unique properties [2][3][4][5][6][7]. However, concurrently bringing together the main ingredients for realizing manybody phenomena in a single experimental platform is a major challenge. Using superconducting qubits, we simultaneously realize synthetic magnetic fields and strong particle interactions, which are among the essential elements for studying quantum magnetism and fractional quantum Hall (FQH) phenomena [8, 9]. The artificial magnetic fields are synthesized by sinusoidally modulating the qubit couplings. In a closed loop formed by the three qubits, we observe the directional circulation of photons, a signature of broken time-reversal symmetry. We demonstrate strong interactions via the creation of photonvacancies, or "holes", which circulate in the opposite direction. The combination of these key elements results in chiral groundstate currents, the first direct measurement of persistent currents in low-lying eigenstates of strongly interacting bosons. The observation of chiral currents at such a small scale is interesting and suggests that the rich many-body physics could survive to smaller scales. We also motivate the feasibility of creating FQH states with near future superconducting technologies. Our work introduces an experimental platform for engineering quantum phases of strongly interacting photons and highlight a path toward realization of bosonic FQH states.It is commonly observed that when the number of particles in a system increases, complex phases can emerge which were absent in the system when it had fewer particles, i.e. the "more is different" [10]. This observation drives experimental efforts in synthetic quantum systems, where the primary goal is to engineer and utilize these emerging phases. However, it has generally been overlooked that these sought-after phases can only emerge from simultaneous realization and control of particle numbers, real-space arrangements, external fields, particle interactions, state preparation, and quantum measurement. The simultaneous realization of all these ingredients makes synthesizing many-body phases a holistic task, and hence constitutes a major experimental challenge. Engineering these factors, in particular synthesizing magnetic fields, have been performed in several platforms [4,[11][12][13][14][15][16][17][18][19]. However, these ingredients have not been jointly realized in any system thus far. To provide a tangible framework, we discuss realization of these key elements in the context of quantum Hall physics, and show when these ingredients come together they can construct a basic building block for creating FQH states.The FQH states are commonly studied in 2-dimensional electron gases, a fermionic condensed matter system [8, 9]. However, many of the recent advancem...

One of the key applications of quantum information is simulating nature. Fermions are ubiquitous in nature, appearing in condensed matter systems, chemistry and high energy physics. However, universally simulating their interactions is arguably one of the largest challenges, because of the difficulties arising from anticommutativity. Here we use digital methods to construct the required arbitrary interactions, and perform quantum simulation of up to four fermionic modes with a superconducting quantum circuit. We employ in excess of 300 quantum logic gates, and reach fidelities that are consistent with a simple model of uncorrelated errors. The presented approach is in principle scalable to a larger number of modes, and arbitrary spatial dimensions.

The discovery of topological phases in condensed matter systems has changed the modern conception of phases of matter [1, 2]. The global nature of topological ordering makes these phases robust and hence promising for applications [3]. However, the non-locality of this ordering makes direct experimental studies an outstanding challenge, even in the simplest model topological systems, and interactions among the constituent particles adds to this challenge. Here we demonstrate a novel dynamical method [4] to explore topological phases in both interacting and noninteracting systems, by employing the exquisite control afforded by state-of-the-art superconducting quantum circuits. We utilize this method to experimentally explore the well-known Haldane model of topological phase transitions [5] by directly measuring the topological invariants of the system. We construct the topological phase diagram of this model and visualize the microscopic evolution of states across the phase transition, tasks whose experimental realizations have remained elusive [6, 7]. Furthermore, we developed a new qubit architecture [8, 9] that allows simultaneous control over every term in a two-qubit Hamiltonian, with which we extend our studies to an interacting Hamiltonian and discover the emergence of an interaction-induced topological phase. Our implementation, involving the measurement of both global and local textures of quantum systems, is close to the original idea of quantum simulation as envisioned by R. Feynman [10], where a controllable quantum system is used to investigate otherwise inaccessible quantum phenomena. This approach demonstrates the potential of superconducting qubits for quantum simulation [11, 12] and establishes a powerful platform for the study of topological phases in quantum systems.Since the first observations of topological ordering in quantum Hall systems in the 1980s [1, 2], experimental studies of topological phases have been primarily limited to indirect measurements. The non-local nature of topological ordering renders local probes ineffective, and when global probes, such as transport, are used, interpretations [13] are required to infer topological properties from the measurements. Topological phases are charac- Figure 1. Dynamical measurement of Berry curvature and Ch. In this schematic drawing, brown arrows represent the ground states (adiabatic limit) for given points on a closed manifold S (green enclosure) in the parameter space, and the blue arrows are the measured states during a non-adiabatic passage. According to (2), the Berry curvature B can be calculated from the deviation from adiabaticity. Integrating B over S gives the Chern number Ch, which corresponds to the total number of degeneracies enclosed.terized by topological invariants, such as the first Chern number Ch, whose discrete jumps indicate transitions between different topologically ordered phases [14, 15]. For a quantum system, Ch is defined as the integral over a closed manifold S in the parameter space of the Hamiltonian as...

Superconducting qubits are an attractive platform for quantum computing since they have demonstrated high-fidelity quantum gates and extensibility to modest system sizes. Nonetheless, an outstanding challenge is stabilizing their energy-relaxation times, which can fluctuate unpredictably in frequency and time. Here, we use qubits as spectral and temporal probes of individual two-level-system defects to provide direct evidence that they are responsible for the largest fluctuations. This research lays the foundation for stabilizing qubit performance through calibration, design, and fabrication.

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Quantum algorithms offer a dramatic speedup for computational problems in material science and chemistry. However, any near-term realizations of these algorithms will need to be optimized to fit within the finite resources offered by existing noisy hardware. Here, taking advantage of the adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a threefold reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an imaginary swap-like (iSWAP-like) gate to attain an arbitrary swap angle, θ, and a controlled-phase gate that generates an arbitrary conditional phase, ϕ. Using one of each of these gates, we can perform an arbitrary two-qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic simulation (fSim) gate set. We benchmark the fidelity of the iSWAP-like and controlled-phase gate families as well as 525 other fSim gates spread evenly across the entire fSimðθ; ϕÞ parameter space, achieving a purity-limited average two-qubit Pauli error of 3.8 × 10 −3 per fSim gate.