Quantum-limited Parametric Amplification with Josephson Circuits in the Regime of Pump Depletion

  1. Ananda Roy,
  2. and Michel Devoret
Linear parametric amplification is a key operation in information processing. Our interest here is quantum-limited parametric amplification, i.e., amplification of quantum signals while
adding the minimum amount of noise allowed by quantum mechanics, which is essential for any viable implementation of quantum information processing. We describe parametric amplifiers based on the dispersive nonlinearity of Josephson junctions driven with appropriate tones playing the role of pumps. We discuss two defining characteristics in the architecture of these amplifiers: the number of modes occupied by the signal, idler and pump waves and the number of independent ports through which these waves enter into the circuit. We discuss scattering properties of these amplifiers. This is followed by computations of the dynamic range and phase-space distributions of the fluctuations of the modes of the amplifiers.

Concurrent Remote Entanglement with Quantum Error Correction

  1. Ananda Roy,
  2. A. Douglas Stone,
  3. and Liang Jiang
Remote entanglement of distant, non-interacting quantum entities is a key primitive for quantum information processing. We present a new protocol to remotely entangle two stationary
qubits by first entangling them with propagating ancilla qubits and then performing a joint two-qubit measurement on the ancillas. Subsequently, single-qubit measurements are performed on each of the ancillas. We describe two continuous variable implementations of the protocol using propagating microwave modes. The first implementation uses propagating Schro┬Ędinger cat-states as the flying ancilla qubits, a joint-photon-number-modulo-2 measurement of the propagating modes for the two-qubit measurement and homodyne detections as the final single-qubit measurements. The presence of inefficiencies in realistic quantum systems limit the success-rate of generating high fidelity Bell-states. This motivates us to propose a second continuous variable implementation, where we use quantum error correction to suppress the decoherence due to photon loss to first order. To that end, we encode the ancilla qubits in superpositions of Schr\“odinger cat states of a given photon-number-parity, use a joint-photon-number-modulo-4 measurement as the two-qubit measurement and homodyne detections as the final single-qubit measurements. We demonstrate the resilience of our quantum-error-correcting remote entanglement scheme to imperfections. Further, we describe a modification of our error-correcting scheme by incorporating additional individual photon-number-modulo-2 measurements of the ancilla modes to improve the success-rate of generating high-fidelity Bell-states. Our protocols can be straightforwardly implemented in state-of-the-art superconducting circuit-QED systems.

Introduction to Quantum-limited Parametric Amplification of Quantum Signals with Josephson Circuits

  1. Michel Devoret,
  2. and Ananda Roy
This short and opinionated review starts with a concept of quantum signals at microwave frequencies and focuses on the principle of linear parametric amplification. The amplification
process arises from the dispersive nonlinearity of Josephson junctions driven with appropriate tones. We discuss two defining characteristics of these amplifiers: the number of modes receiving the signal, idler and pump waves and the number of independent ports through which these waves enter into the circuit.

Remote Entanglement by Coherent Multiplication of Concurrent Quantum Signals

  1. Ananda Roy,
  2. Liang Jiang,
  3. A. Douglas Stone,
  4. and Michel Devoret
Concurrent remote entanglement of distant, non-interacting quantum entities is a crucial function for quantum information processing. In contrast with the existing protocols which employ
addition of signals to generate entanglement between two remote qubits, the protocol we present is based on multiplication of signals. This protocol can be straightforwardly implemented by a novel Josephson junction mixing circuit. Our scheme would be able to generate provable entanglement even in presence of practical imperfections: finite quantum efficiency of detectors and undesired photon loss in current state-of-the-art devices.

Continuous Generation and Stabilization of Mesoscopic Field Superposition States in a Quantum Circuit

  1. Ananda Roy,
  2. Zaki Leghtas,
  3. A. Douglas Stone,
  4. Michel Devoret,
  5. and Mazyar Mirrahimi
While dissipation is widely considered as being harmful for quantum coherence, it can, when properly engineered, lead to the stabilization of non-trivial pure quantum states. We propose
a scheme for continuous generation and stabilization of Schr\“{o}dinger cat states in a cavity using dissipation engineering. We first generate non-classical photon states with definite parity by means of a two-photon drive and dissipation, and then stabilize these transient states against single-photon decay. The single-photon stabilization is autonomous, and is implemented through a second engineered bath, which exploits the photon number dependent frequency-splitting due to Kerr interactions in the strongly dispersive regime of circuit QED. Starting with the Hamiltonian of the baths plus cavity, we derive an effective model of only the cavity photon states along with analytic expressions for relevant physical quantities, such as the stabilization rate. The deterministic generation of such cat states is one of the key ingredients in performing universal quantum computation.

Asymmetric frequency conversion in nonlinear systems driven by a biharmonic pump

  1. Archana Kamal,
  2. Ananda Roy,
  3. John Clarke,
  4. and Michel H. Devoret
A novel mechanism of asymmetric frequency conversion is investigated in nonlinear dispersive devices driven parametrically with a biharmonic pump. When the relative phase between the
first and second harmonics combined in a two-tone pump is appropriately tuned, nonreciprocal frequency conversion, either upward or downward, can occur. Full directionality and efficiency of the conversion process is possible, provided that the distribution of pump power over the harmonics is set correctly. While this asymmetric conversion effect is generic, we describe its practical realization in a model system consisting of a current-biased, resistively-shunted Josephson junction. Here, the multiharmonic Josephson oscillations, generated internally from the static current bias, provide the pump drive.