Session F39: Microwave Photonics with Superconducting Circuits II

Microwave activated two-photon transition for remote entanglement of superconducting circuits

Building a large scale quantum computing platform or network will most probably require to entangle distant systems that do not interact directly. This can be done by performing entangling gates between standing information carriers, used as memories or local computationnal resources, and flying ones, acting as quantum buses. In this talk, we report the realization of such gates between superconducting circuits and traveling microwave photons based on microwave activated two-photon transitions. We have implemented this protocol in a superconducting circuit architecture. Temporal and, to some extent, frequential shaping of the traveling wavepacket have been applied. We demonstrate both an entangling gate corresponding to the emission of a shaped photon conditionned on the excitation of a circuit and a swap gate corresponding to the absorption of this photon by a distant circuit. Combining both, we remotely entangle two transmon qubits with a Bell state fidelity of 73 %, limited by losses in the transmission line and decoherence of each qubit.   

Deterministic Quantum State Transfer and Generation of Remote Entanglement using Microwave Photons

Sharing information coherently between nodes of a quantum network is at the foundation of distributed quantum information processing. In this scheme, the computation is divided into subroutines and performed on several smaller quantum registers connected by classical and quantum channels. A direct quantum channel, which connects nodes deterministically rather than probabilistically, is advantageous for fault-tolerant quantum computation because it reduces the threshold requirements and can achieve larger entanglement rates. Here, we implement deterministic state transfer and entanglement protocols between two superconducting qubits [1] fabricated on separate chips [2] and connected by about one meter of coaxial cable with well characterized loss [3]. Superconducting circuits constitute a universal node capable of sending, receiving, storing, and processing quantum information. Our implementation is based on an all-microwave cavity-assisted Raman process which entangles or transfers the qubit state of a transmon-type artificial atom with a time-symmetric itinerant single photon [4]. We transfer qubit states at a rate of 50 kHz using the emitted photons which are absorbed at the receiving node with a probability of 98\% achieving a transfer process fidelity of 80\%. We also prepare on demand remote entanglement with a fidelity as high as 79\%. Our results are in excellent agreement with a numerical simulations based on a master equation description of the system. Deterministic state transfer protocols have the potential to be used as a backbone of surface code quantum error correction across different nodes of a cryogenic network to realize large scale fault-tolerant quantum computation. It is also interesting to consider augmenting the methods presented in this work by quantum-non-demolition detection of single photons [5].\newline\newline [1] P. Kurpiers et al., arXiv:1712.08593 (2017)\newline [2] T. Walter et al., Phys. Rev. Applied 7, 054020 (2017)\newline [3] P. Kurpiers et al., EPJ Quantum Technology 4, 8 (2017)\newline [4] M. Pechal et al., Phys. Rev. X 4, 041010 (2014)\newline [5] J.-C. Besse et al., arXiv:1711.11569 (2017)   

Distilling Entanglement Between Remote Superconducting Qubits

The ability to generate entanglement between qubits connected by a lossy channel is an important primitive for large scale quantum information processing. Entanglement distillation allows one to counter this imperfection by consolidating the entanglement between several weakly entangled qubit pairs into a single strongly entangled qubit pair. We present an experiment where we can generate remote entanglement between two nodes, each containing a pair of superconducting transmon qubits, with matching dispersive shifts to their respective cavities. By performing local half-parity measurements, we can detect photon loss in the channel connecting the nodes, and herald the creation of a Bell state with enhanced fidelity. We discuss experimental progress towards the implementation of this protocol.   

Remote communication between two superconducting qubit modules 1

We extend the random access quantum processor module [1] to allow photonic communication between two distant modules. Each module comprises of 8-bit multimode resonators and a flux-tunable transmon. The sideband interaction induced by the transmon flux modulation achieves both the universal operations on each quantum processor and the photonic communication between two modules. Entanglement between two distant modules can be created by a transfer process heralded to photon loss during the transmission. Our implementation opens a clear path towards modular architecture of quantum information processing with superconducting qubits.

1. Random access quantum information processors. R. K. Naik, N. Leung, S. Chakram, P. Groszkowski, Y. Lu, N. Earnest, D. C. McKay, Jens Koch, D. I. Schuster, arXiv:1705.00579   

Remote communication between two superconducting qubit modules 2

We report our experimental progress towards implementing a heralding protocol for the transfer of an arbitrary qubit state between two distant superconducting qubits. We employ sideband interactions induced by parametric flux modulation for the preparation of locally entangled qubit-photon states, as well as for their transfer that generates entanglement between two distant superconducting qubits. As an useful application, we demonstrate how Bell states can be created between the two remote qubits via this technique. Through encoding a qubit state with two flying microwave photons, photon loss error can be heralded by the measurement of the receiving qubit, without the need of using ancillary qubits. This simple and efficient communication protocol provides a promising approach for realizing a scalable quantum network processor using the quantum computation modules as building blocks.   

Deterministic Generation of Remote Entanglement using Shaped Single Photons in Circuit Quantum Electrodynamics

Sharing information coherently in a quantum network is the foundation of quantum communication and distributed quantum information processing. Here, we discuss our progress toward implementing a deterministic quantum state transfer and remote entanglement protocol in a circuit QED architecture. We embed a superconducting transmon-type three level system in a transmission line resonator at two spatially separated nodes. We generate an itinerant shaped microwave photon based on a microwave drive induced second-order process [1] and transmit it via a coaxial line [2]. Emitting and absorbing the single photon with high fidelity ideally achieves coherent qubit state transfer or remote entanglement generation. Our experiments, therefore, suggest a path toward realizing all-microwave quantum networks based on deterministic interactions between individual nodes.
[1] M. Pechal et al., Phys. Rev. X 4, 041010 (2014)
[2] P.Kurpiers et al.,EPJ Quantum Technology 4, 8 (2017)   

Detailed analysis of spontaneous emission of an atom in front of a mirror

The spontaneous emission rate of a two-level atom is proportional to the local density of states of the electromagnetic modes of the environment close to its transition frequency.
In Ref. [1], this was experimentally demonstrated for a 1D environment using a transmon qubit placed in a coplanar waveguide at a distance from its shorted end. The short acts as a mirror and thus modifies the local density of states. Here, we analyse in detail the atom dynamics when the distance is such that the density of states at the transition frequency is vanishing. We find that this indeed corresponds to a dark state of the system and discuss how this dark state is approached. We also discuss the emission dynamics as a function of the coupling strength and distance between the atom and the mirror.

[1] Probing the quantum vacuum with an artificial atom in front of a mirror, I.-C. Hoi et al., Nature Physics 11, 10451049 (2015)
  

Deterministic Generation of a Traveling Cat State with a Kerr Parametric Oscillator

Quantum computation with a network of Kerr parametric oscillators, or KPOs for short, has been proposed for the standard gate model [1,2] and adiabatic optimization [3]. Such a new machine is expected to be implemented with superconducting circuits [4,5]. A remarkable feature of a KPO is the ability to generate a Schödinger cat state deterministically via quantum adiabatic evolution. However, the cat state inside the KPO seems difficult to observe because of the large Kerr effect. Here we theoretically propose a method to release the cat state from the KPO without a tunable output coupler. As a result, a traveling cat state can be generated deterministically with a KPO and observed, e.g., by homodyne detection. We will also propose a superconducting-circuit implementation of the traveling-cat generator.
[1] H. Goto, Phys. Rev. A 93, 050301(R) (2016).
[2] S. Puri, S. Boutin and A. Blais, npj Quantum Information 3, 18 (2017).
[3]H. Goto, Sci. Rep. 6, 21686 (2016).
[4] S. E. Nigg, N. Lörch and R. P. Tiwari, Sci. Adv. 3, e1602273 (2017).
[5] S. Puri, C. K. Andersen, A. L. Grimsmo and A. Blais, Nat. Commun. 8, 15785 (2017).   

Full Kerr Cancellation in an Inductively-Shunted Josephson Ring Modulator

Quantum-limited amplification plays a vital role in efficient quantum measurement. For superconducting qubits, such amplification can be achieved through parametrically driven three-wave mixing in the Josephson Ring Modulator (JRM). However, we have shown that Kerr nonlinearities in and between the JRM’s modes limit the device’s saturation power and jeopardize frequency matching conditions for multiply parametric driven modes of operation. We present a JRM shunted with linear inductors [1] which, for a range of parameters, cancels all the Kerr terms at a certain flux bias point while retaining three-wave mixing terms. The stability of this special bias point depends crucially on the ratio of shunt inductance to Josephson junction inductance as well as stray inductance in the JRM ring itself. We present both self- and cross-Kerr measurements showing simultaneous cancellation as well as the absence of fourth-order behaviors in the amplifier’s response to large signal powers. This device, in addition to enhanced saturation power is expected to be an excellent candidate for multiply-driven parametric devices.
[1] N. Roch et al, PRL 108, 147701 (2012)   

Drive-enhanced Superradiance in Circuit QED

We recently analyzed theoretically how two-photon driving of a cavity could be used to exponentially enhance the light-matter coupling in a cavity QED system, allowing a weak coupling system to exhibit features of ultra-strong coupling [1]. Here, we extend this idea to a system where an ensemble of two-level systems couple weakly to a cavity. We discuss how the superradiant phase transition manifests itself in this system, and how it is sensitive to the structure of the input noise driving the cavity. We discuss potential implementations using superconducting circuits, where simple flux-pumping provides the necessary driving. Our scheme allows for a tuneable analog quantum simulation of the open-system Dicke model. [1] C. Leroux, L. C. G. Govia, and A. A. Clerk, arXiv:1709.09091.