Observing single quantum trajectories of a superconducting quantum bit

Abstract

The length of time that a quantum system can exist in a superposition state is determined by how strongly it interacts with its environment. This interaction entangles the quantum state with the inherent fluctuations of the environment. If these fluctuations are not measured, the environment can be viewed as a source of noise, causing random evolution of the quantum system from an initially pure state into a statistical mixture--a process known as decoherence. However, by accurately measuring the environment in real time, the quantum system can be maintained in a pure state and its time evolution described by a 'quantum trajectory' determined by the measurement outcome. Here we use weak measurements to monitor a microwave cavity containing a superconducting quantum bit (qubit), and track the individual quantum trajectories of the system. In this set-up, the environment is dominated by the fluctuations of a single electromagnetic mode of the cavity. Using a near-quantum-limited parametric amplifier, we selectively measure either the phase or the amplitude of the cavity field, and thereby confine trajectories to either the equator or a meridian of the Bloch sphere. We perform quantum state tomography at discrete times along the trajectory to verify that we have faithfully tracked the state of the quantum system as it diffuses on the surface of the Bloch sphere. Our results demonstrate that decoherence can be mitigated by environmental monitoring, and validate the foundation of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new means of implementing 'quantum steering'--the harnessing of action at a distance to manipulate quantum states through measurement.

Quantum dynamics of simultaneously measured non-commuting observables

“…To mitigate these effects, we actively feedback to stabilize the Rabi frequency to within 10 kHz and suppress leakage of the local oscillator used to generate the sidebands to the 10 −4 photon level. Because a single SQM commutes with itself at all times, the integral of the signal fully specifies the amount of projection onto an eigenstate 18 . We perform tomographic state validation on subsets of the data post-selected according to this integrated signal.…”

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

“…Following the path of Yurke's et al work in the late 1980s [1][2][3], several designs of Josephson junction-based parametric amplifiers (JPAs) have been introduced [4][5][6][7][8][9][10][11]. In addition to high-fidelity superconducting qubit readout leading to the observation of quantum jumps [12,13], this new generation of near quantumlimited amplifiers have opened up new experimental possibilities such as the creation and tomography of squeezed microwave light [14][15][16], and detailed weak measurement experiments [17][18][19]. JPAs are now ubiquitous in current superconducting circuit experiments, and applications in other research communities are growing [20][21][22][23].…”

“…The properties of JPAs as a source of squeezed light are therefore intimately related to their noise properties as a phase-sensitive amplifier. While JPAs are usually modeled as quantum-limited amplifiers, and thus perfect squeezers, experimental results indicate that nonidealities limits both the achievable level of squeezing [28][29][30] and the measurement quantum efficiency [17,29,31,32].…”

Heisenberg scaling with weak measurement: a quantum state discrimination point of view

“…See Refs. [11,12] for recent experiments using this interaction. This name "light shift" is related to a Hamiltonian of the form…”

“…Notably, this example is a variation of the original weak value amplification scenario [1], but using a different parameter regime that more commonly appears in cavity and circuit QED [11,12]. Even though the coherent state used in their example is typically considered to be a classical quantity that does not provide quantum resources, the authors showed the surprising result that the Fisher information about the coupling parameter seemed to scale at the optimal Heisenberg limit as the average number of photons was increased, rather than at the standard quantum limit that one would typically expect.…”