Dual-rail encoding with superconducting cavities.

The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computation. To this end, we introduce the circuit-Quantum Electrodynamics (QED) dual-rail qubit in which our physical qubit is encoded in the single-photon subspace, [Formula: see text], of two superconducting microwave cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are in general much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers unique capabilities. Using just one additional transmon ancilla per dual-rail qubit, we describe how to perform a gate-based set of universal operations that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors in the cavities and the transmon can be detected and converted to erasure errors in all operations, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit exhibits a favorable hierarchy of error rates and is expected to perform well below the relevant QEC thresholds with today's coherence times.

Entanglement of bosonic modes through an engineered exchange interaction.

Quantum computation presents a powerful new paradigm for information processing. A robust universal quantum computer can be realized with any well controlled quantum system, but a successful platform will ultimately require the combination of highly coherent, error-correctable quantum elements with at least one entangling operation between them1,2. Quantum information stored in a continuous-variable system-for example, a harmonic oscillator-can take advantage of hardware-efficient quantum error correction protocols that encode information in the large available Hilbert space of each element3-5. However, such encoded states typically have no controllable direct couplings, making deterministic entangling operations between them particularly challenging. Here we develop an efficient implementation of the exponential-SWAP operation6 and present its experimental realization between bosonic qubits stored in two superconducting microwave cavities. This engineered operation is analogous to the exchange interaction between discrete spin systems, but acts within any encoded subspace of the continuous-variable modes. Based on a control rotation, the operation produces a coherent superposition of identity and SWAP operations between arbitrary states of two harmonic oscillator modes and can be used to enact a deterministic entangling gate within quantum error correction codes. These results provide a valuable building block for universal quantum computation using bosonic modes.

Erasure Detection of a Dual-Rail Qubit Encoded in a Double-Post Superconducting Cavity.

Qubits with predominantly erasure errors present distinctive advantages for quantum error correction (QEC) and fault-tolerant quantum computing. Logical qubits based on dual-rail encoding that exploit erasure detection have been recently proposed in superconducting circuit architectures, with either coupled transmons or cavities. Here, we implement a dual-rail qubit encoded in a compact, double-post superconducting cavity. Using an auxiliary transmon, we perform erasure detection on the dual-rail subspace. We characterize the behavior of the code space by a novel method to perform joint-Wigner tomography. This is based on modifying the cross-Kerr interaction between the cavity modes and the transmon. We measure an erasure rate of 3.981±0.003 (ms)^{-1} and a residual, postselected dephasing error rate up to 0.17 (ms)^{-1} within the code space. This strong hierarchy of error rates, together with the compact and hardware-efficient nature of this novel architecture, holds promise in realizing QEC schemes with enhanced thresholds and improved scaling.

Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator.

Quantum states of mechanical motion can be important resources for quantum information, metrology and studies of fundamental physics. Recent demonstrations of superconducting qubits coupled to acoustic resonators have opened up the possibility of performing quantum operations on macroscale motional modes1-3, which can act as long-lived quantum memories or transducers. In addition, they can potentially be used to test decoherence mechanisms in macroscale objects and other modifications to standard quantum theory4,5. Many of these applications call for the ability to create and characterize complex quantum states, such as states with a well defined phonon number, also known as phonon Fock states. Such capabilities require fast quantum operations and long coherence times of the mechanical mode. Here we demonstrate the controlled generation of multi-phonon Fock states in a macroscale bulk acoustic-wave resonator. We also perform Wigner tomography and state reconstruction to highlight the quantum nature of the prepared states6. These demonstrations are made possible by the long coherence times of our acoustic resonator and our ability to selectively couple a superconducting qubit to individual phonon modes. Our work shows that circuit quantum acoustodynamics7 enables sophisticated quantum control of macroscale mechanical objects and opens up the possibility of using acoustic modes as quantum resources.

Path-Independent Quantum Gates with Noisy Ancilla.

Ancilla systems are often indispensable to universal control of a nearly isolated quantum system. However, ancilla systems are typically more vulnerable to environmental noise, which limits the performance of such ancilla-assisted quantum control. To address this challenge of ancilla-induced decoherence, we propose a general framework that integrates quantum control and quantum error correction, so that we can achieve robust quantum gates resilient to ancilla noise. We introduce the path independence criterion for fault-tolerant quantum gates against ancilla errors. As an example, a path-independent gate is provided for superconducting circuits with a hardware-efficient design.

Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles.

Owing to the low-loss propagation of electromagnetic signals in superconductors, Josephson junctions constitute ideal building blocks for quantum memories, amplifiers, detectors and high-speed processing units, operating over a wide band of microwave frequencies. Nevertheless, although transport in superconducting wires is perfectly lossless for direct current, transport of radio-frequency signals can be dissipative in the presence of quasiparticle excitations above the superconducting gap. Moreover, the exact mechanism of this dissipation in Josephson junctions has never been fully resolved experimentally. In particular, Josephson's key theoretical prediction that quasiparticle dissipation should vanish in transport through a junction when the phase difference across the junction is π (ref. 2) has never been observed. This subtle effect can be understood as resulting from the destructive interference of two separate dissipative channels involving electron-like and hole-like quasiparticles. Here we report the experimental observation of this quantum coherent suppression of quasiparticle dissipation across a Josephson junction. As the average phase bias across the junction is swept through π, we measure an increase of more than one order of magnitude in the energy relaxation time of a superconducting artificial atom. This striking suppression of dissipation, despite the presence of lossy quasiparticle excitations above the superconducting gap, provides a powerful tool for minimizing decoherence in quantum electronic systems and could be directly exploited in quantum information experiments with superconducting quantum bits.

Hardware-Efficient Quantum Random Access Memory with Hybrid Quantum Acoustic Systems.

Hybrid quantum systems in which acoustic resonators couple to superconducting qubits are promising quantum information platforms. High quality factors and small mode volumes make acoustic modes ideal quantum memories, while the qubit-phonon coupling enables the initialization and manipulation of quantum states. We present a scheme for quantum computing with multimode quantum acoustic systems, and based on this scheme, propose a hardware-efficient implementation of a quantum random access memory (QRAM). Quantum information is stored in high-Q phonon modes, and couplings between modes are engineered by applying off-resonant drives to a transmon qubit. In comparison to existing proposals that involve directly exciting the qubit, this scheme can offer a substantial improvement in gate fidelity for long-lived acoustic modes. We show how these engineered phonon-phonon couplings can be used to access data in superposition according to the state of designated address modes-implementing a QRAM on a single chip.

Holonomic Quantum Control with Continuous Variable Systems.

Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second gate consists of "colliding" two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems that support tunable nonlinearities, such as trapped ions and circuit QED.

Cavity State Manipulation Using Photon-Number Selective Phase Gates.

The large available Hilbert space and high coherence of cavity resonators make these systems an interesting resource for storing encoded quantum bits. To perform a quantum gate on this encoded information, however, complex nonlinear operations must be applied to the many levels of the oscillator simultaneously. In this work, we introduce the selective number-dependent arbitrary phase (snap) gate, which imparts a different phase to each Fock-state component using an off-resonantly coupled qubit. We show that the snap gate allows control over the quantum phases by correcting the unwanted phase evolution due to the Kerr effect. Furthermore, by combining the snap gate with oscillator displacements, we create a one-photon Fock state with high fidelity. Using just these two controls, one can construct arbitrary unitary operations, offering a scalable route to performing logical manipulations on oscillator-encoded qubits.

Surpassing millisecond coherence in on chip superconducting quantum memories by optimizing materials and circuit design.

The performance of superconducting quantum circuits for quantum computing has advanced tremendously in recent decades; however, a comprehensive understanding of relaxation mechanisms does not yet exist. In this work, we utilize a multimode approach to characterizing energy losses in superconducting quantum circuits, with the goals of predicting device performance and improving coherence through materials, process, and circuit design optimization. Using this approach, we measure significant reductions in surface and bulk dielectric losses by employing a tantalum-based materials platform and annealed sapphire substrates. With this knowledge we predict the relaxation times of aluminum- and tantalum-based transmon qubits, and find that they are consistent with experimental results. We additionally optimize device geometry to maximize coherence within a coaxial tunnel architecture, and realize on-chip quantum memories with single-photon Ramsey times of 2.0 - 2.7 ms, limited by their energy relaxation times of 1.0 - 1.4 ms. These results demonstrate an advancement towards a more modular and compact coaxial circuit architecture for bosonic qubits with reproducibly high coherence.

Hardware-efficient autonomous quantum memory protection.

We propose to encode a quantum bit of information in a superposition of coherent states of an oscillator, with four different phases. Our encoding in a single cavity mode, together with a protection protocol, significantly reduces the error rate due to photon loss. This protection is ensured by an efficient quantum error correction scheme employing the nonlinearity provided by a single physical qubit coupled to the cavity. We describe in detail how to implement these operations in a circuit quantum electrodynamics system. This proposal directly addresses the task of building a hardware-efficient quantum memory and can lead to important shortcuts in quantum computing architectures.

High-fidelity parametric beamsplitting with a parity-protected converter.

Fast, high-fidelity operations between microwave resonators are an important tool for bosonic quantum computation and simulation with superconducting circuits. An attractive approach for implementing these operations is to couple these resonators via a nonlinear converter and actuate parametric processes with RF drives. It can be challenging to make these processes simultaneously fast and high fidelity, since this requires introducing strong drives without activating parasitic processes or introducing additional decoherence channels. We show that in addition to a careful management of drive frequencies and the spectrum of environmental noise, leveraging the inbuilt symmetries of the converter Hamiltonian can suppress unwanted nonlinear interactions, preventing converter-induced decoherence. We demonstrate these principles using a differentially-driven DC-SQUID as our converter, coupled to two high-Q microwave cavities. Using this architecture, we engineer a highly-coherent beamsplitter and fast (~100 ns) swaps between the cavities, limited primarily by their intrinsic single-photon loss. We characterize this beamsplitter in the cavities' joint single-photon subspace, and show that we can detect and post-select photon loss events to achieve a beamsplitter gate fidelity exceeding 99.98%, which to our knowledge far surpasses the current state of the art.

Quantum control of bosonic modes with superconducting circuits.

Bosonic modes have wide applications in various quantum technologies, such as optical photons for quantum communication, magnons in spin ensembles for quantum information storage and mechanical modes for reversible microwave-to-optical quantum transduction. There is emerging interest in utilizing bosonic modes for quantum information processing, with circuit quantum electrodynamics (circuit QED) as one of the leading architectures. Quantum information can be encoded into subspaces of a bosonic superconducting cavity mode with long coherence time. However, standard Gaussian operations (e.g., beam splitting and two-mode squeezing) are insufficient for universal quantum computing. The major challenge is to introduce additional nonlinear control beyond Gaussian operations without adding significant bosonic loss or decoherence. Here we review recent advances in universal control of a single bosonic code with superconducting circuits, including unitary control, quantum feedback control, driven-dissipative control and holonomic dissipative control. Various approaches to entangling different bosonic modes are also discussed.

Storage of multiple coherent microwave excitations in an electron spin ensemble.

Strong coupling between a microwave photon and electron spins, which could enable a long-lived quantum memory element for superconducting qubits, is possible using a large ensemble of spins. This represents an inefficient use of resources unless multiple photons, or qubits, can be orthogonally stored and retrieved. Here we employ holographic techniques to realize a coherent memory using a pulsed magnetic field gradient and demonstrate the storage and retrieval of up to 100 weak 10 GHz coherent excitations in collective states of an electron spin ensemble. We further show that such collective excitations in the electron spin can then be stored in nuclear spin states, which offer coherence times in excess of seconds.

Quantum acoustics with superconducting qubits.

Mechanical objects have important practical applications in the fields of quantum information and metrology as quantum memories or transducers for measuring and connecting different types of quantum systems. The field of electromechanics is in pursuit of a robust and highly coherent device that couples motion to nonlinear quantum objects such as superconducting qubits. Here, we experimentally demonstrate a high-frequency bulk acoustic wave resonator that is strongly coupled to a superconducting qubit using piezoelectric transduction with a cooperativity of 260. We measure qubit and mechanical coherence times on the order of 10 microseconds. Our device requires only simple fabrication methods and provides controllable access to a multitude of phonon modes. We demonstrate quantum control and measurement on gigahertz phonons at the single-quantum level.

Implementing a universal gate set on a logical qubit encoded in an oscillator.

A logical qubit is a two-dimensional subspace of a higher dimensional system, chosen such that it is possible to detect and correct the occurrence of certain errors. Manipulation of the encoded information generally requires arbitrary and precise control over the entire system. Whether based on multiple physical qubits or larger dimensional modes such as oscillators, the individual elements in realistic devices will always have residual interactions, which must be accounted for when designing logical operations. Here we demonstrate a holistic control strategy which exploits accurate knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system. We use this approach to realize high-fidelity (98.5%, inferred), decoherence-limited operations on a logical qubit encoded in a superconducting cavity resonator using four-component cat states. Our results show the power of applying numerical techniques to control linear oscillators and pave the way for utilizing their large Hilbert space as a resource in quantum information processing.A logical qubit is a two-dimensional subspace of a higher dimensional system, whose manipulation requires precise control over the whole system. Here the authors demonstrate a control strategy which exploits precise knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system.