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Ternary quantum information processing in superconducting devices poses a promising alternative to its more popular binary counterpart through larger, more connected computational spaces and proposed advantages in quantum simulation and error correction. Although generally operated as qubits, transmons have readily addressable higher levels, making them natural candidates for operation as quantum three-level systems (qutrits). Recent works in transmon devices have realized high fidelity single qutrit operation. Nonetheless, effectively engineering a high-fidelity two-qutrit entanglement remains a central challenge for realizing qutrit processing in a transmon device. In this work, we apply the differential AC Stark shift to implement a flexible, microwave-activated, and dynamic cross-Kerr entanglement between two fixed-frequency transmon qutrits, expanding on work performed for the Z Z interaction with transmon qubits. We then use this interaction to engineer efficient, high-fidelity qutrit CZ † and CZ gates, with estimated process fidelities of 97.3(1)% and 95.2(3)% respectively, a significant step forward for operating qutrits on a multi-transmon device. Qutrits, or quantum three-level systems, can provide advantages over qubits in certain quantum information applications, and high-fidelity single-qutrit gates have been demonstrated. Goss et al. realize high-fidelity entangling gates between two superconducting qutrits that are universal for ternary computation.

The development of noisy intermediate-scale quantum devices has extended the scope of executable quantum circuits with high-fidelity single- and two-qubit gates. Equipping these devices with three-qubit gates will enable the realization of more complex quantum algorithms and efficient quantum error correction protocols with reduced circuit depth. Several three-qubit gates have been implemented for superconducting qubits, but their use in gate synthesis has been limited owing to their low fidelity. Here, using fixed-frequency superconducting qubits, we demonstrate a high-fidelity i Toffoli gate based on two-qubit interactions, the so-called cross-resonance effect. As with the Toffoli gate, this three-qubit gate can be used to perform universal quantum computation. The i Toffoli gate is implemented by simultaneously applying microwave pulses to a linear chain of three qubits, revealing a process fidelity as high as 98.26(2)%. Moreover, we numerically show that our gate scheme can produce additional three-qubit gates that provide more efficient gate synthesis than the Toffoli and i Toffoli gates. Our work not only brings a high-fidelity i Toffoli gate to current superconducting quantum processors but also opens a pathway for developing multi-qubit gates based on two-qubit interactions. The efficiency of running quantum algorithms can be improved by expanding the hardware operations that a quantum computer can perform. A high-fidelity three-qubit i Toffoli gate has now been demonstrated using superconducting qubits.

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error that has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomized benchmarking and related protocols are not sensitive to the full impact of coherent errors and therefore do not reliably predict the global performance of quantum algorithms, leaving us unprepared to validate the accuracy of future large-scale quantum computations. Randomized compiling is a protocol designed to overcome these performance limitations by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of algorithmic performance from error rates measured via cycle benchmarking. In this work, we demonstrate significant performance gains under randomized compiling for the four-qubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. Additionally, we accurately predict algorithm performance using experimentally measured error rates. Our results demonstrate that randomized compiling can be utilized to leverage and predict the capabilities of modern-day noisy quantum processors, paving the way forward for scalable quantum computing.

In microwave quantum optics, dissipation usually corresponds to quantum jumps, where photons are lost one by one. Here we demonstrate a new approach to dissipation engineering. By coupling a high impedance microwave resonator to a tunnel junction, we use the photoassisted tunneling of quasiparticles as a tunable dissipative process. We are able to adjust the minimum number of lost photons per tunneling event to be one, two or more, through a dc voltage. Consequently, different Fock states of the resonator experience different loss processes. Causality then implies that each state experiences a different energy (Lamb) shift, as confirmed experimentally. This photoassisted tunneling process is analogous to a photoelectric effect, which requires a quantum description of light to be quantitatively understood. This work opens up new possibilities for quantum state manipulation in superconducting circuits, which do not rely on the Josephson effect. Quantum bath engineering in the context of circuit quantum electrodynamics typically relies on single-photon losses. Aiello et al. demonstrate an approach for engineering higher-order photon losses in a microwave resonator coupled to a tunnel junction, which may be utilized in quantum information applications.

The original version of this Article contained an error in the second sentence of the Acknowledgements, which incorrectly read: ‘This work was supported by the Quantum Testbed Program of the Advanced Scientific Computing Research for Basic Energy Sciences program, Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231’. The correct version states ‘the Quantum Testbed Program of the Advanced Scientific Computing Research Division’ in place of ‘the Quantum Testbed Program of the Advanced Scientific Computing Research for Basic Energy Sciences program’. This has been corrected in both the PDF and HTML versions of the Article.

The leakage of quantum information out of the two computational states of a qubit into other energy states represents a major challenge for quantum error correction. During the operation of an error-corrected algorithm, leakage builds over time and spreads through multi-qubit interactions. This leads to correlated errors that degrade the exponential suppression of the logical error with scale, thus challenging the feasibility of quantum error correction as a path towards fault-tolerant quantum computation. Here, we demonstrate a distance-3 surface code and distance-21 bit-flip code on a quantum processor for which leakage is removed from all qubits in each cycle. This shortens the lifetime of leakage and curtails its ability to spread and induce correlated errors. We report a tenfold reduction in the steady-state leakage population of the data qubits encoding the logical state and an average leakage population of less than 1 × 10−3 throughout the entire device. Our leakage removal process efficiently returns the system back to the computational basis. Adding it to a code circuit would prevent leakage from inducing correlated error across cycles. With this demonstration that leakage can be contained, we have resolved a key challenge for practical quantum error correction at scale.Physical realizations of qubits are often vulnerable to leakage errors, where the system ends up outside the basis used to store quantum information. A leakage removal protocol can suppress the impact of leakage on quantum error-correcting codes.

We have designed honeycomb lattices for microwave photons with a frequency imbalance between the two sites in the unit cell. This imbalance is the equivalent of a mass term that breaks the lattice inversion symmetry. At the interface between two lattices with opposite imbalance, we observe topological valley edge states. By imaging the spatial dependence of the modes along the interface, we obtain their dispersion relation that we compare to the predictions of an ab initio tight-binding model describing our microwave photonic lattices.

We have realized different honeycomb lattices for microwave photons in the 4 to 8 GHz band using superconducting spiral resonators. Each lattice comprises a few hundred sites. Two designs have been studied, one leading to two bands touching at the Dirac points and one where a gap opens at the Dirac points. Using a scanning laser technique to image the eigenmodes of this new type of photonic lattices, we are able to reconstruct their band structure. The measured bands are in excellent agreement with ab initio models that combine numerical simulations of the electromagnetic properties of the spiral resonator and analytical calculations.

We demonstrate a new approach to dissipation engineering in microwave quantum optics. For a single mode, dissipation usually corresponds to quantum jumps, where photons are lost one by one. Here, we are able to tune the minimal number of lost photons per jump to be two (or more) with a simple dc voltage. As a consequence, different quantum states experience different dissipation. Causality implies that the states must also experience different energy shifts. Our measurements of these Lamb shifts are in good agreement with the predictions of the Kramers-Kronig relations for single quantum states in a regime of highly non-linear bath coupling. This work opens new possibilities for quantum state manipulation in circuit QED, without relying on the Josephson effect.