The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resultingtime dynamics in numerical simulations, a very small integration time step is required, which can severely impact the simulation run-time. Here, we introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical integrators. This solver, which we name Dysolve, efficiently captures the effect of the highly oscillatory terms in the system Hamiltonian, significantly reducing the simulation’s run time as well as its sensitivity to the time-step size. Furthermore, this solver provides the exact derivative of the time-evolution operator with respect to the drive amplitudes. This key feature allows for optimal control in the limit of strong drives and goes beyond common pulse-optimization approaches that rely on rotating-wave approximations. As an illustration of our method, we show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
Superconducting circuits are a strong contender for realizing quantum computing systems, and are also successfully used to study quantum optics and hybrid quantum systems. However,their cryogenic operation temperatures and the current lack of coherence-preserving microwave-to-optical conversion solutions have hindered the realization of superconducting quantum networks either spanning different cryogenics systems or larger distances. Here, we report the successful operation of a cryogenic waveguide coherently linking transmon qubits located in two dilution refrigerators separated by a physical distance of five meters. We transfer qubit states and generate entanglement on-demand with average transfer and target state fidelities of 85.8 % and 79.5 %, respectively, between the two nodes of this elementary network. Cryogenic microwave links do provide an opportunity to scale up systems for quantum computing and create local area quantum communication networks over length scales of at least tens of meters.
Detecting traveling photons is an essential primitive for many quantum information processing tasks. We introduce a single-photon detector design operating in the microwave domain,based on a weakly nonlinear metamaterial where the nonlinearity is provided by a large number of Josephson junctions. The combination of weak nonlinearity and large spatial extent circumvents well-known obstacles limiting approaches based on a localized Kerr medium. Using numerical many-body simulations we show that the single-photon detection fidelity increases with the length of the metamaterial to approach one at experimentally realistic lengths. A remarkable feature of the detector is that the metamaterial approach allows for a large detection bandwidth. In stark contrast to conventional photon detectors operating in the optical domain, the photon is not destroyed by the detection and the photon wavepacket is minimally disturbed. The detector design we introduce offers new possibilities for quantum information processing, quantum optics and metrology in the microwave frequency domain.
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereofis the quantum approximate optimization algorithm (QAOA), an approach to solve combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) systems. Gaining computational power from QAOA critically relies on the mitigation of errors during the execution of the algorithm, which for coherence-limited operations is achievable by reducing the gate count. Here, we demonstrate an improvement of up to a factor of 3 in algorithmic performance as measured by the success probability, by implementing a continuous hardware-efficient gate set using superconducting quantum circuits. This gate set allows us to perform the phase separation step in QAOA with a single physical gate for each pair of qubits instead of decomposing it into two CZ-gates and single-qubit gates. With this reduced number of physical gates, which scales with the number of layers employed in the algorithm, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances mapped onto three and seven qubits, using up to a total of 399 operations and up to 9 layers. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.
We introduce an efficient tensor network toolbox to compute the low-energy excitations of large-scale superconducting quantum circuits up to a desired accuracy. We benchmark this algorithmon the fluxonium qubit, a superconducting quantum circuit based on a Josephson junction array with over a hundred junctions. As an example of the possibilities offered by this numerical tool, we compute the pure-dephasing coherence time of the fluxonium qubit due to charge noise and coherent quantum phase slips, taking into account the array degrees of freedom corresponding to a Hilbert space as large as 15180. Our algorithm is applicable to the wide variety of circuit-QED systems and may be a useful tool for scaling up superconducting-qubit technologies.
Encoding a qubit in logical quantum states with wavefunctions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing.Using a circuit-quantum-electrodynamics architecture, we experimentally realize a superconducting 0−π qubit, which hosts protected states suitable for quantum-information processing. Multi-tone spectroscopy measurements reveal the energy level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. We find that the parity symmetry of the qubit results in charge-insensitive levels connecting the protected states, allowing for logical operations. The measured relaxation (1.6 ms) and dephasing times (25 μs) demonstrate that our implementation of the 0−π circuit not only broadens the family of superconducting qubits, but also represents a promising candidate for the building block of a fault-tolerant quantum processor.
We have developed and characterized a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noise, and dephasingfrom flux noise. The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, thus forming a superconducting loop. Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a cosϕ/2 Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference. In this regime, the logical-state wavefunctions reside in disjoint regions of phase space, thereby ensuring the protection against energy decay. By switching the protection on, we observed a ten-fold increase of the decay time, reaching up to 100μs. Though the qubit is sensitive to charge noise, the sensitivity is much reduced in comparison with the charge qubit, and the charge-noise-induced dephasing time of the current device exceeds 1μs. Implementation of the full dephasing protection can be achieved in the next-generation devices by combining several cosϕ/2 Josephson elements in a small array.
The code capacity threshold for error correction using qubits which exhibit asymmetric or biased noise channels is known to be much higher than with qubits without such structured noise.However, it is unclear how much this improvement persists when realistic circuit level noise is taken into account. This is because implementations of gates which do not commute with the dominant error un-bias the noise channel. In particular, a native bias-preserving controlled-NOT (CX) gate, which is an essential ingredient of stabilizer codes, is not possible in strictly two-level systems. Here we overcome the challenge of implementing a bias-preserving CX gate by using stabilized cat qubits in driven nonlinear oscillators. The physical noise channel of this qubit is biased towards phase-flips, which increase linearly with the size of the cat, while bit-flips are exponentially suppressed with cat size. Remarkably, the error channel of this native CX gate between two such cat qubits is also dominated by phase-flips, while bit-flips remain exponentially suppressed. This CX gate relies on the topological phase that arises from the rotation of the cat qubit in phase space. The availability of bias-preserving CX gates opens a path towards fault-tolerant codes tailored to biased-noise cat qubits with high threshold and low overhead. As an example, we analyze a scheme for concatenated error correction using cat qubits. We find that the availability of CX gates with moderately sized cat qubits, having mean photon number <10, improves a rigorous lower bound on the fault-tolerance threshold by a factor of two and decreases the overhead in logical Clifford operations by a factor of 5. We expect these estimates to improve significantly with further optimization and with direct use of other codes such as topological codes tailored to biased noise.[/expand]
Heralding techniques are useful in quantum communication to circumvent losses without resorting to error correction schemes or quantum repeaters. Such techniques are realized, for example,by monitoring for photon loss at the receiving end of the quantum link while not disturbing the transmitted quantum state. We describe and experimentally benchmark a scheme that incorporates error detection in a quantum channel connecting two transmon qubits using traveling microwave photons. This is achieved by encoding the quantum information as a time-bin superposition of a single photon, which simultaneously realizes high communication rates and high fidelities. The presented scheme is straightforward to implement in circuit QED and is fully microwave-controlled, making it an interesting candidate for future modular quantum computing architectures.
Kitaev’s 0-π qubit encodes quantum information in two protected, near-degenerate states of a superconducting quantum circuit. In a recent work, we have shown that the coherencetimes of a realistic 0-π device can surpass that of today’s best superconducting qubits [Groszkowski et al., New Journal of Physics 20 043053 (2018)]. Here we address controllability of the 0-π qubit. Specifically, we investigate the potential for dispersive control and readout, and introduce a new, fast and high-fidelity single-qubit gate that can interpolate smoothly between logical X and Z. We characterize the action of this gate using a multi-level treatment of the device, and analyze the impact of circuit element disorder and deviations in control and circuit parameters from their optimal values. Furthermore, we propose a cooling scheme to decrease the photon shot-noise dephasing rate, which we previously found to limit the coherence times of 0-π devices within reach of current experiments. Using this approach, we predict coherence time enhancements between one and three orders of magnitude, depending on parameter regime.