Delay lines capable of storing quantum information are crucial for advancing quantum repeaters and hardware efficient quantum computers. Traditionally, they are physically realizedas extended systems that support wave propagation, such as waveguides. But such delay lines typically provide limited control over the propagating fields. Here, we introduce a parametrically addressed delay line (PADL) for microwave photons that provides a high level of control over the dynamics of stored pulses, enabling us to arbitrarily delay or even swap pulses. By parametrically driving a three-waving mixing superconducting circuit element that is weakly hybridized with an ensemble of resonators, we engineer a spectral response that simulates that of a physical delay line, while providing fast control over the delay line’s properties and granting access to its internal modes. We illustrate the main features of the PADL, operating on pulses with energies on the order of a single photon, through a series of experiments, which include choosing which photon echo to emit, translating pulses in time, and swapping two pulses. We also measure the noise added to the delay line from our parametric interactions and find that the added noise is much less than one photon.
Superconducting quantum circuits are a promising hardware platform for realizing a fault-tolerant quantum computer. Accelerating progress in this field of research demands general approachesand computational tools to analyze and design more complex superconducting circuits. We develop a framework to systematically construct a superconducting quantum circuit’s quantized Hamiltonian from its physical description. As is often the case with quantum descriptions of multicoordinate systems, the complexity rises rapidly with the number of variables. Therefore, we introduce a set of coordinate transformations with which we can find bases to diagonalize the Hamiltonian efficiently. Furthermore, we broaden our framework’s scope to calculate the circuit’s key properties required for optimizing and discovering novel qubits. We implement the methods described in this work in an open-source Python package SQcircuit. In this manuscript, we introduce the reader to the SQcircuit environment and functionality. We show through a series of examples how to analyze a number of interesting quantum circuits and obtain features such as the spectrum, coherence times, transition matrix elements, coupling operators, and the phase coordinate representation of eigenfunctions.
We can encode a qubit in the energy levels of a quantum system. Relaxation and other dissipation processes lead to decay of the fidelity of this stored information. Is it possible topreserve the quantum information for a longer time by introducing additional drives and dissipation? The existence of autonomous quantum error correcting codes answers this question in the positive. Nonetheless, discovering these codes for a real physical system, i.e., finding the encoding and the associated driving fields and bath couplings, remains a challenge that has required intuition and inspiration to overcome. In this work, we develop and demonstrate a computational approach based on adjoint optimization for discovering autonomous quantum error correcting codes given a description of a physical system. We implement an optimizer that searches for a logical subspace and control parameters to better preserve quantum information. We demonstrate our method on a system of a harmonic oscillator coupled to a lossy qubit, and find that varying the Hamiltonian distance in Fock space — a proxy for the control hardware complexity — leads to discovery of different and new error correcting schemes. We discover what we call the 3‾√ code, realizable with a Hamiltonian distance d=2, and propose a hardware-efficient implementation based on superconducting circuits.
We present a comprehensive architectural analysis for a fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware,we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated near-term physical parameters for electro-acoustic systems, we perform a detailed error analysis of measurements and gates, including CNOT and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, we devise a new magic-state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1,000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits which are intractable for classical supercomputers. Hardware with 32,000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.
We investigate the performance of microwave-frequency phononic crystal resonators fabricated on thin-film lithium niobate for integration with superconducting quantum circuits. Fordifferent design geometries at millikelvin temperatures, we achieve mechanical internal quality factors Qi above 105−106 at high microwave drive power, corresponding to 5×106 phonons inside the resonator. By sweeping the defect size of resonators with identical mirror cell designs, we are able to indirectly observe signatures of the complete phononic bandgap via the resonators‘ internal quality factors. Examination of quality factors‘ temperature dependence shows how superconducting and two-level system (TLS) loss channels impact device performance. Finally, we observe an anomalous low-temperature frequency shift consistent with resonant TLS decay and find that material choice can help to mitigate these losses.
Quantum networks are likely to have a profound impact on the way we compute and communicate in the future. In order to wire together superconducting quantum processors over kilometer-scaledistances, we need transducers that can generate entanglement between the microwave and optical domains with high fidelity. We present an integrated electro-optic transducer that combines low-loss lithium niobate photonics with superconducting microwave resonators on a sapphire substrate. Our triply-resonant device operates in a dilution refrigerator and converts microwave photons to optical photons with an on-chip efficiency of 6.6×10−6 and a conversion bandwidth of 20 MHz. We discuss design trade-offs in this device, including strategies to manage acoustic loss, and outline ways to increase the conversion efficiency in the future.
The evenly-spaced modes of an electromagnetic resonator are coupled to each other by appropriate time-modulation, leading to dynamics analogous to those of particles hopping betweendifferent sites of a lattice. This substitution of a real spatial dimension of a lattice with a „synthetic'“ dimension in frequency space greatly reduces the hardware complexity of an analog quantum simulator. Complex control and read-out of a highly multi-moded structure can thus be accomplished with very few physical control lines. We demonstrate this concept with microwave photons in a superconducting transmission line resonator by modulating the system parameters at frequencies near the resonator’s free spectral range and observing propagation of photon wavepackets in time domain. The linear propagation dynamics are equivalent to a tight-binding model, which we probe by measuring scattering parameters between frequency sites. We extract an approximate tight-binding dispersion relation for the synthetic lattice and initialize photon wavepackets with well-defined quasimomenta and group velocities. As an example application of this platform in simulating a physical system, we demonstrate Bloch oscillations associated with a particle in a periodic potential and subject to a constant external field. The simulated field strongly affects the photon dynamics despite photons having zero charge. Our observation of photon dynamics along a synthetic frequency dimension generalizes immediately to topological photonics and single-photon power levels, and expands the range of physical systems addressable by quantum simulation.
We analyze the quantum information processing capability of a superconducting transmon circuit used to mediate interactions between quantum information stored in a collection of phononiccrystal cavity resonators. Having only a single processing element to be controlled externally makes this approach significantly less hardware-intensive than traditional architectures with individual control of each qubit. Moreover, when compared with the commonly considered alternative approach using coplanar waveguide or 3d cavity microwave resonators for storage, the nanomechanical resonators offer both very long lifetime and small size — two conflicting requirements for microwave resonators. A detailed gate error analysis leads to an optimal value for the qubit-resonator coupling rate as a function of the number of mechanical resonators in the system. For a given set of system parameters, a specific amount of coupling and number of resonators is found to optimize the quantum volume, an approximate measure for the computational capacity of a system. We see this volume is higher in the proposed hybrid nanomechanical architecture than in the competing on-chip electromagnetic approach.
Superconducting microwave circuits form a versatile platform for storing and manipulating quantum information. A major challenge to further scalability is to find approaches for connectingthese systems over long distances and at high rates. One approach is to convert the quantum state of a microwave circuit to optical photons that can be transmitted over kilometers at room temperature with little loss. Many proposals for electro-optic conversion between microwave and optics use optical driving of a weak three-wave mixing nonlinearity to convert the frequency of an excitation. Residual absorption of this optical pump leads to heating, which is problematic at cryogenic temperatures. Here we propose an alternative approach where a nonlinear superconducting circuit is driven to interconvert between microwave-frequency and millimeter-wave-frequency (300 GHz) photons. To understand the potential for quantum conversion between microwave and mm-wave photons, we consider the driven four-wave mixing quantum dynamics of nonlinear circuits. In contrast to the linear dynamics of the driven three-wave mixing converters, the proposed four-wave mixing converter has nonlinear decoherence channels that lead to a more complex parameter space of couplings and pump powers that we map out. We consider physical realizations of such converter circuits by deriving theoretically the upper bound on the maximum obtainable nonlinear coupling between any two modes in a lossless circuit, and synthesizing an optimal circuit based on realistic materials that saturates this bound. Our proposed circuit dissipates less than 10−9 times the energy of current electro-optic converters per qubit. Finally, we outline the quantum link budget for optical, microwave, and mm-wave connections, showing that our approach is viable for realizing interconnected quantum processors for intracity or quantum datacenter environments.