arXiv:1409.0510 · Physical Review Letters

Prediction and Retrodiction for a Continuously Monitored Superconducting Qubit

D. Tan, Steven J. Weber, Irfan A. Siddiqi, Klaus Mølmer, Kater W. Murch

Published Mar 5, 2015• 105 citations

Abstract

The quantum state of a superconducting transmon qubit inside a three-dimensional cavity is monitored by transmission of a microwave field through the cavity. The information inferred from the measurement record is incorporated in a density matrix ρ_{t}, which is conditioned on probe results until t, and in an auxiliary matrix E_{t}, which is conditioned on probe results obtained after t. Here, we obtain these matrices from experimental data and we illustrate their application to predict and retrodict the outcome of weak and strong qubit measurements.

DOI: 10.1103/physrevlett.114.090403

Related papers

Weak Measurement and Quantum Smoothing of a Superconducting Qubit

Dian Tan

In quantum mechanics, the measurement outcome of an observable in a quantum system is intrinsically random, yielding a probability distribution. The state of the quantum system can be described by a density matrix (t), which depends on the information accumulated until time t, and represents our knowledge about the system. The density matrix (t) gives probabilities for the outcomes of measurements at time t. Further probing of the quantum system allows us to refine our prediction in hindsight. In this thesis, we experimentally examine a quantum smoothing theory in a superconducting qubit by introducing an auxiliary matrix E(t) which is conditioned on information obtained from time t to a final time T. With the complete information before and after time t, the pair of matrices [(t), E(t)] can be used to make smoothed predictions for the measurement outcome at time t. We apply the quantum smoothing theory in the case of continuous weak measurement unveiling the retrodicted quantum trajectories and weak values. In the case of strong projective measurement, while the density matrix (t) with only diagonal elements in a given basis |n> may be treated as a classical mixture, we demonstrate a failure of this classical mixture description in determining the smoothed probabilities for the measurement outcome at time t with both diagonal (t) and diagonal E(t). We study the correlations between quantum states and weak measurement signals and examine aspects of the time symmetry of continuous quantum measurement. We also extend our study of quantum smoothing theory to the case of resonance fluorescence of a superconducting qubit with homodyne measurement and observe some interesting effects such as the modification of the excited state probabilities, weak values, and evolution of the predicted and retrodicted trajectories.

Jan 1, 20170 citations

Homodyne monitoring of postselected decay

D. Tan, Neda Foroozani, Mahdi Naghiloo +3 more

We use homodyne detection to monitor the radiative decay of a superconducting qubit. According to the classical theory of conditional probabilities, the excited-state population differs from an exponential decay law if it is conditioned upon a later projective qubit measurement. Quantum trajectory theory accounts for the expectation values of general observables, and we use experimental data to show how a homodyne detection signal is conditioned upon both the initial state and the finally projected state of a decaying qubit. We observe, in particular, how anomalous weak values occur in continuous weak measurement for certain pre- and postselected states. Subject to homodyne detection, the density matrix evolves in a stochastic manner, but it is restricted to a specific surface in the Bloch sphere. We show that a similar restriction applies to the information associated with the postselection, and thus bounds the predictions of the theory.

arXiv:1705.04287Physical Review AAug 3, 201725 citations

Prediction, Retrodiction, and Smoothing for a Continuously Monitored Superconducting qubit

Kater W. Murch

Bulletin of the American Physical SocietyMar 3, 20150 citations

Quantum trajectories of superconducting qubits

Steven J. Weber, Kater W. Murch, Mollie E. Schwartz +2 more

In this review, we discuss recent experiments that investigate how the quantum sate of a superconducting qubit evolves during measurement. We provide a pedagogical overview of the measurement process, when the qubit is dispersively coupled to a microwave frequency cavity, and the qubit state is encoded in the phase of a microwave tone that probes the cavity. A continuous measurement record is used to reconstruct the individual quantum trajectories of the qubit state, and quantum state tomography is performed to verify that the state has been tracked accurately. Furthermore, we discuss ensembles of trajectories, time-symmetric evolution, two-qubit trajectories, and potential applications in measurement-based quantum error correction.

arXiv:1506.08165Comptes Rendus PhysiqueAug 1, 201628 citations

Quantum teleportation with continuous measurements

Eliška Greplová, Klaus Mølmer, Christian Kraglund Andersen

We propose a scheme for quantum teleportation between two qubits, coupled sequentially to a cavity field. An implementation of the scheme is analyzed with superconducting qubits and a transmission line resonator, where measurements are restricted to continuous probing of the field leaking from the resonator rather than instantaneous projective Bell state measurement. We show that the past quantum state formalism S. Gammelmark, B. Julsgaard, and K. M\o{}lmer, Phys. Rev. Lett. 111, 160401 (2013) can be successfully applied to estimate what would have been the most likely Bell measurement outcome conditioned on our continuous signal record. This information determines which local operation on the target qubit yields the optimal teleportation fidelity. Our results emphasize the significance of applying a detailed analysis of quantum measurements in feedforward protocols in nonideal leaky quantum systems.

arXiv:1608.01814Physical Review AOct 21, 201612 citations

Quantum Jumps and Measurement Backaction in a Superconducting Qubit

D. H. Slichter

Real-time monitoring of a quantum state provides powerful tools for studying the backaction of quantum measurement and performing quantum feedback. Historically, this monitoring capability has been the exclusive province of atomic and optical physics. This thesis describes the implementation of the first such high-fidelity readout scheme in a solid state circuit, a superconducting quantum bit (qubit) coupled to a microwave cavity in the circuit quantum electrodynamics (circuit QED) architecture. The qubit-state-dependent resonance frequency of the cavity is probed with a microwave drive tone, and the resulting signal amplified using a fast, ultralow-noise superconducting parametric amplifier. This arrangement enables the observation of quantum jumps between the qubit states in real time. The ability to monitor the qubit continuously with high fidelity and resolve quantum jumps can be used to investigate the backaction of the measurement process on the qubit. This thesis examines the quantum Zeno effect--where strong measurement inhibits the evolution of a quantum system-- as well as the transition to non-ideal measurement with increasing measurement strength in the circuit QED architecture, a phenomenon shown to be due to the upconversion of low-frequency dephasing noise. These data allow probes of ``universal'' flux noise in previously inaccessible frequency ranges. The work presented here opens the door for quantum feedback and error correction in solid-state quantum systems using continuous weak measurement.

Jan 1, 201110 citations