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.

A CNOT gate between multiphoton qubits encoded in two cavities

  1. Serge Rosenblum,
  2. Yvonne Gao,
  3. Philip Reinhold,
  4. Chen Wang,
  5. Christopher Axline,
  6. Luigi Frunzio,
  7. Steven Girvin,
  8. Liang Jiang,
  9. Mazyar Mirrahimi,
  10. Michel Devoret,
  11. and Robert Schoelkopf
Entangling gates between qubits are a crucial component for performing algorithms in quantum computers. However, any quantum algorithm will ultimately have to operate on error-protected
logical qubits, which are effective qubits encoded in a high-dimensional Hilbert space. A common approach is to encode logical qubits in collective states of multiple two-level systems, but algorithms operating on multiple logical qubits are highly complex and have not yet been demonstrated. Here, we experimentally realize a controlled NOT (CNOT) gate between two multiphoton qubits in two microwave cavities. In this approach, we encode a qubit in the large Hilbert space of a single cavity mode, rather than in multiple two-level systems. We couple two such encoded qubits together through a transmon, which is driven with an RF pump to apply the CNOT gate within 190 ns. This is two orders of magnitude shorter than the decoherence time of any part of the system, enabling high-fidelity operations comparable to state-of-the-art gates between two-level systems. These results are an important step towards universal algorithms on error-corrected logical qubits.

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.

Josephson directional amplifier for quantum measurement of superconducting circuits

  1. Baleegh Abdo,
  2. Katrina Sliwa,
  3. S. Shankar,
  4. Michael Hatridge,
  5. Luigi Frunzio,
  6. Robert Schoelkopf,
  7. and Michel Devoret
We have realized a microwave quantum-limited amplifier that is directional and can therefore function without the front circulator needed in many quantum measurements. The amplification
takes place in only one direction between the input and output ports. Directionality is achieved by multi-pump parametric amplification combined with wave interference. We have verified the device noise performances by using it to readout a superconducting qubit and observed quantum jumps. With an improved version of this device, qubit and preamplifer could be integrated on the same chip.

Directional amplification with a Josephson circuit

  1. Baleegh Abdo,
  2. Katrina Sliwa,
  3. Luigi Frunzio,
  4. and Michel Devoret
Non-reciprocal devices, which have different transmission coefficients for propagating waves in opposite directions, are crucial components in many low noise quantum measurements. In
most schemes, magneto-optical effects provide the necessary non-reciprocity. In contrast, the proof-of-principle device presented here, consists of two on-chip coupled Josephson parametric converters (JPCs), which achieves directionality by exploiting the non-reciprocal phase response of the JPC in the trans-gain mode. The non-reciprocity of the device is controlled in-situ by varying the amplitude and phase difference of two independent microwave pump tones feeding the system. At the desired working point and for a signal frequency of 8.453 GHz, the device achieves a forward power gain of 15 dB within a dynamical bandwidth of 9 MHz, a reverse gain of -6 dB and suppression of the reflected signal by 8 dB. We also find that the amplifier adds a noise equivalent to less than one and a half photons at the signal frequency (referred to the input). It can process up to 3 photons at the signal frequency per inverse dynamical bandwidth. With a directional amplifier operating along the principles of this device, qubit and readout preamplifier could be integrated on the same chip.

Gain, directionality and noise in microwave SQUID amplifiers: Input-output approach

  1. Archana Kamal,
  2. John Clarke,
  3. and Michel Devoret
We present a new theoretical framework to analyze microwave amplifiers based on the dc SQUID. Our analysis applies input-output theory generalized for Josephson junction devices biased
in the running state. Using this approach we express the high frequency dynamics of the SQUID as a scattering between the participating modes. This enables us to elucidate the inherently nonreciprocal nature of gain as a function of bias current and input frequency. This method can, in principle, accommodate an arbitrary number of Josephson harmonics generated in the running state of the junction. We report detailed calculations taking into account the first few harmonics that provide simple semi-quantitative results showing a degradation of gain, directionality and noise of the device as a function of increasing signal frequency. We also discuss the fundamental limits on device performance and applications of this formalism to real devices.

Black-box superconducting circuit quantization

  1. Simon E. Nigg,
  2. Hanhee Paik,
  3. Brian Vlastakis,
  4. Gerhard Kirchmair,
  5. Shyam Shankar,
  6. Luigi Frunzio,
  7. Michel Devoret,
  8. Robert Schoelkopf,
  9. and Steven Girvin
We present a semi-classical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions
coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multi-mode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D-transmon system, and quantitative agreement with measurements is found.