Superconducting metamaterial transmission lines implemented with lumped circuit elements can exhibit left-handed dispersion, where the group and phase velocity have opposite sign, ina frequency range relevant for superconducting artificial atoms. Forming such a metamaterial transmission line into a ring and coupling it to qubits at different points around the ring results in a multimode bus resonator with a compact footprint. Using flux-tunable qubits, we characterize and theoretically model the variation in the coupling strength between the two qubits and each of the ring resonator modes. Although the qubits have negligible direct coupling between them, their interactions with the multimode ring resonator result in both a transverse exchange coupling and a higher order ZZ interaction between the qubits. As we vary the detuning between the qubits and their frequency relative to the ring resonator modes, we observe significant variations in both of these inter-qubit interactions, including zero crossings and changes of sign. The ability to modulate interaction terms such as the ZZ scale between zero and large values for small changes in qubit frequency provides a promising pathway for implementing entangling gates in a system capable of hosting many qubits.
Stabilizer operations are at the heart of quantum error correction and are typically implemented in software-controlled entangling gates and measurements of groups of qubits. Alternatively,qubits can be designed so that the Hamiltonian corresponds directly to a stabilizer for protecting quantum information. We demonstrate such a hardware implementation of stabilizers in a superconducting circuit composed of chains of π-periodic Josephson elements. With local on-chip flux- and charge-biasing, we observe a softening of the energy band dispersion with respect to flux that is exponential in the number of frustrated plaquette elements, in close agreement with our numerical modeling.
Quantum error correction can preserve quantum information in the presence of local errors; however, errors that are correlated across a qubit array are fatal. For superconducting qubits,high-energy particle impacts due to background radioactivity or cosmic ray muons produce bursts of energetic phonons that travel throughout the substrate and create excitations out of the superconducting ground state, known as quasiparticles, which poison all qubits on the chip. Here we use thick normal metal reservoirs on the back side of the chip to promote rapid downconversion of phonons to sufficiently low energies where they can no longer poison qubits. We introduce a pump-probe scheme involving controlled injection of pair-breaking phonons into the qubit chips. We examine quasiparticle poisoning on chips with and without backside metallization and demonstrate a reduction in the flux of pair-breaking phonons by more than a factor of 20. In addition, we use a Ramsey interferometer scheme to simultaneously monitor quasiparticle parity on three qubits for each chip and observe a two-order of magnitude reduction in correlated poisoning due to ambient radiation. Our approach reduces correlated errors due to background radiation below the level necessary for fault-tolerant operation of a multiqubit array.
We describe an approach to the high-fidelity measurement of a superconducting qubit using an on-chip microwave photon counter. The protocol relies on the transient response of a dispersivelycoupled measurement resonator to map the state of the qubit to „bright“ and „dark“ cavity pointer states that are characterized by a large differential photon occupation. Following this mapping, we photodetect the resonator using the Josephson Photomultipler (JPM), which transitions between classically distinguishable flux states when cavity photon occupation exceeds a certain threshold. Our technique provides access to the binary outcome of projective quantum measurement at the millikelvin stage without the need for quantum-limited preamplification and thresholding at room temperature. We achieve raw single-shot measurement fidelity in excess of 98% across multiple samples using this approach in total measurement times under 500 ns. In addition, we show that the backaction and crosstalk associated with our measurement protocol can be mitigated by exploiting the intrinsic damping of the JPM itself.
Metamaterial resonant structures made from arrays of superconducting lumped circuit elements can exhibit microwave mode spectra with left-handed dispersion, resulting in a high densityof modes in the same frequency range where superconducting qubits are typically operated, as well as a bandgap at lower frequencies that extends down to dc. Using this novel regime for multi-mode circuit quantum electrodynamics, we have performed a series of measurements of such a superconducting metamaterial resonator coupled to a flux-tunable transmon qubit. Through microwave measurements of the metamaterial, we have observed the coupling of the qubit to each of the modes that it passes through. Using a separate readout resonator, we have probed the qubit dispersively and characterized the qubit energy relaxation as a function of frequency, which is strongly affected by the Purcell effect in the presence of the dense mode spectrum. Additionally, we have investigated the ac Stark shift of the qubit as the photon number in the various metamaterial modes is varied. The ability to tailor the dense mode spectrum through the choice of circuit parameters and manipulate the photonic state of the metamaterial through interactions with qubits makes this a promising platform for analog quantum simulation and quantum memories.
Mitigating crosstalk errors, whether classical or quantum mechanical, is critically important for achieving high-fidelity entangling gates in multi-qubit circuits. For weakly anharmonicsuperconducting qubits, unwanted ZZ interactions can be suppressed by combining qubits with opposite anharmonicity. We present experimental measurements and theoretical modeling of two-qubit gate error for gates based on the cross resonance interaction between a capacitively shunted flux qubit and a transmon and demonstrate the elimination of the ZZ interaction.
We have used Ramsey tomography to characterize charge noise in a weakly charge-sensitive superconducting qubit. We find a charge noise that scales with frequency as 1/fα over 5 decadeswith α=1.93 and a magnitude Sq(1Hz)=2.9×10−4 e2/Hz. The noise exponent and magnitude of the low-frequency noise are much larger than those seen in prior work on single electron transistors, yet are consistent with reports of frequency noise in other superconducting qubits. Moreover, we observe frequent large-amplitude jumps in offset charge exceeding 0.1e; these large discrete charge jumps are incompatible with a picture of localized dipole-like two-level fluctuators. The data reveal an unexpected dependence of charge noise on device scale and suggest models involving either charge drift or fluctuating patch potentials.
Cross-resonance interactions are a promising way to implement all-microwave two-qubit gates with fixed-frequency qubits. In this work, we study the dependence of the cross-resonanceinteraction rate on qubit-qubit detuning and compare with a model that includes the higher levels of a transmon system. To carry out this study we employ two transmon qubits–one fixed frequency and the other flux tunable–to allow us to vary the detuning between qubits. We find that the interaction closely follows a three-level model of the transmon, thus confirming the presence of an optimal regime for cross-resonance gates.
Superconducting metamaterials are a promising resource for quantum information science. In the context of circuit QED, they provide a means to engineer on-chip, novel dispersion relationsand a band structure that could ultimately be utilized for generating complex entangled states of quantum circuitry, for quantum reservoir engineering, and as an element for quantum simulation architectures. Here we report on the development and measurement at millikelvin temperatures of a particular type of circuit metamaterial resonator composed of planar superconducting lumped-element reactances in the form of a discrete left-handed transmission line (LHTL). We discuss the details of the design, fabrication, and circuit properties of this system. As well, we provide an extensive characterization of the dense mode spectrum in these metamaterial resonators, which we conducted using both microwave transmission measurements and laser scanning microscopy (LSM). Results are observed to be in good quantitative agreement with numerical simulations and also an analytical model based upon current-voltage relationships for a discrete transmission line. In particular, we demonstrate that the metamaterial mode frequencies, spatial profiles of current and charge densities, and damping due to external loading can be readily modeled and understood, making this system a promising tool for future use in quantum circuit applications and for studies of complex quantum systems.
Fast, high-fidelity measurement is a key ingredient for quantum error correction. Conventional approaches to the measurement of superconducting qubits, involving linear amplificationof a microwave probe tone followed by heterodyne detection at room temperature, do not scale well to large system sizes. Here we introduce an alternative approach to measurement based on a microwave photon counter. We demonstrate raw single-shot measurement fidelity of 92%. Moreover, we exploit the intrinsic damping of the counter to extract the energy released by the measurement process, allowing repeated high-fidelity quantum non-demolition measurements. Crucially, our scheme provides access to the classical outcome of projective quantum measurement at the millikelvin stage. In a future system, counter-based measurement could form the basis for a scalable quantum-to-classical interface.