Harnessing techniques from analog signal processing, we establish a new path for large-scale quantum computation.

We describe and implement a family of entangling gates activated by radio-frequency flux modulation applied to a tunable transmon that is statically coupled to a neighboring transmon. The effect of this modulation is the resonant exchange of photons directly between levels of the two-transmon system, obviating the need for mediating qubits or resonator modes and allowing for the full utilization of all qubits in a scalable architecture. The resonance condition is selective in both the frequency and amplitude of modulation and thus alleviates frequency crowding. We demonstrate the use of three such resonances to produce entangling gates that enable universal quantum computation: one iSWAP gate and two distinct controlled Z gates. We report interleaved randomized benchmarking results indicating gate error rates of 6% for the iSWAP (duration 135ns) and 9% for the controlled Z gates (durations 175 ns and 270 ns), limited largely by qubit coherence.A central challenge in building a scalable quantum computer with superconducting qubits is the execution of high-fidelity, two-qubit gates within an architecture containing many resonant elements. As more elements are added, or as the multiplicity of couplings between elements is increased, the frequency space of the design becomes crowded and device performance suffers. In architectures composed of transmon qubits [1], there are two main approaches to implementing two-qubit gates. The first utilizes fixed-frequency qubits with static couplings where the two-qubit operations are activated by applying transverse microwave drives [2][3][4][5][6][7][8]. While fixedfrequency qubits generally have long coherence times, this architecture requires satisfying stringent constraints on qubit frequencies and anharmonicities [5,6,8] which requires some tunability to scale to many qubits [9]. The second approach relies on frequency-tunable transmons, and two-qubit gates are activated by tuning qubits into and out of resonance with a particular transition [10][11][12][13][14][15][16]. However, tunability comes at the cost of additional decoherence channels, thus significantly limiting coherence times [17]. In this approach the delivery of shaped unbalanced control signals poses a challenge [15]. Such gates are furthermore sensitive to frequency crowdingavoiding unwanted crossings with neighboring qubit energy levels during gate operations limits the flexibility and connectivity of the architecture.An alternative to these approaches is to modulate a circuit's couplings or energy levels at a frequency corresponding to the detuning between particular energy levels of interest [18][19][20][21][22][23][24][25][26]. This enables an entangling gate between a qubit and a single resonator [21,22], a qubit and many resonator modes [26], two transmon qubits coupled by a tunable mediating qubit [16,25], or two tunable transmons coupled to a mediating resonator [23,24].Building on these earlier results, we implement two entangling gates, iSWAP and controlled Z (CZ), between a flux-tunable transmon an...

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The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moiré bands for twisted bilayer graphene (TBG) at small twist angles. We derive a generalized continuum model for TBG near any commensurate twist angle, which is characterized by a complex inter-layer hopping at commensurate AA stackings (rather than the real hopping in the BM model), a real inter-layer hopping at commensurate AB/BA stackings, and a global energy shift. The complex phase of the AA stacking hopping and the twist angle together define a single angle parameter φ0. We compute the model parameters for the first six distinct commensurate TBG configurations, among which the 38.2 • configuration may be within experimentally observable energy scales. We identify the first magic angle for any φ0 at a condition similar to that of the BM model. At this angle, the lowest two moiré bands at charge neutrality become flat (except in the vicinity of the ΓM point) and retain fragile topology, but lose particle-hole symmetry. We further identify a hyper-magic manifold in the parameter space at φ0 = ±π/2, where seven or more moiré bands around charge neutrality become flat simultaneously. The lowest two moiré flat bands in the hyper-magic manifold have fragile (trivial) topology when close to (far from) the chiral limit with zero AA hopping.

We present a framework for modeling superconducting circuits that integrates classical microwave analysis with circuit quantization. Our framework enables the calculation of the lossy eigenmodes of superconducting circuits, and we demonstrate the method by analyzing several circuits relevant to multiplexed, Purcell filtered transmon readout architectures. We show that the transmon relaxation times obtained by our method agree with the established approximation T1 ≈ C/Re[Y (iωq)] away from environmental resonances and do not vanish on resonance. We also show that the hybridization of the modes in the readout circuit is highly sensitive to the bandwidth of the Purcell filter.