We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. In particular, we focus on the case when the qubit Hamiltonian and the qubit's operator being probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and because the measurement data is mixed with a detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the state of the qubit can be extracted. It turns out that the measurement basis is stochastically determined every time the experiment is repeated. We analyze in detail the probability distributions that govern the choice of measurement bases. We also analyze the information acquisition rate and show that it is largely unaffected by the apparent conflict between the measurement and intrinsic qubit dynamics. We discuss the relation between our analysis and the stochastic master equation that describes the evolution of the qubit's state under the influence of measurement and decoherence. In particular, we write down a stochastic equation that encompasses the usual stochastic master equation for the evolution of the qubit's density matrix and additionally contains the measurement information that can be extracted from the observed signal.
In two-qubit gates activated by microwave pulses, by turning pulse on or off, the state of qubits are swapped between entangled or idle modes. In either mode, the presence of stray couplings makes qubits accumulate coherent phase error. However, the error rates in the two modes differ because qubits carry different stray coupling strengths in each mode; therefore, eliminating stray coupling from one mode does not remove it from the other. We propose to combine such a gate with a tunable coupler and show that both idle and entangled qubits can become free from stray couplings. This significantl…
How Time Works in Quantum Systems: Overview of time ordering and time correlation in weakly perturbed atomic collisions and in strongly perturbed qubits
Flux-tunable qubits are a useful resource for superconducting quantum processors. They can be used to perform cPhase gates, facilitate fast reset protocols, avoid qubit-frequency collisions in large processors, and enable certain fast readout schemes. However, flux-tunable qubits suffer from a trade-off between their tunability range and sensitivity to flux noise. Optimizing this trade-off is particularly important for enabling fast, high-fidelity, all-microwave cross-resonance gates in large, high-coherence processors. This is mainly because cross-resonance gates set stringent conditions on t…
Superconducting cavities with high quality factors play an essential role in circuit quantum electrodynamics and quantum computing. In measurements of the the intrinsic loss rates of high frequency modes, it can be challenging to design an appropriate coupling to the measurement circuit in such a way that the resulting signal is sufficiently strong but also that this coupling does not lead to unwanted loading circuit, obscuring the intrinsic internal loss rates. Here, we propose and demonstrate a spectroscopic probe of high-Q resonators based on the phenomena of electromagnetically-induced tra…
We propose a quantum state readout mechanism of a weakly coupled qubit in dispersive regime. The hybrid system consists of ferromagnetic insulator and a superconducting qubit in a microwave cavity. The enhancement of the measurement sensitivity is achieved by exerting torque on the ferromagnetic insulator magnetization, which compensates the damping of the system leading to an exceptional point. The proposed machanism allows to measure the qubit state either via the transmission of the cavity or the FMR signal of the magnetic material.
For some cavity-quantum-electrodynamics systems, such as a single electron spin coupled to a passive cavity, it is challenging to reach the strong-coupling regime. In such a weak-coupling regime, the conventional dispersive readout technique cannot be used to resolve the quantum states of the spin. Here we propose an improved dispersive readout method to measure the quantum states of a weakly coupled qubit by harnessing either one or two auxiliary cavities linearly coupled to the passive cavity containing the qubit. With appropriate parameters in both cases, the system excluding the qubit can …
The dispersive coupling between a qubit and a cavity mode is widely used for performing non-destructive readout of the qubit state. In this approach, it is typically required that the dispersive strong coupling regime is achieved. Here we show that the use of an auxiliary cavity mode reduces by orders of magnitude the required value of the dispersive coupling, for a given decay rate of the cavity mode. The analysis is performed within the input-output formalism, in terms of the photon scattering matrix elements and of the signal-to-noise ratio. We derive simple analytical expressions for the o…
Quantum non Markovianity and quantum Darwinism are two phenomena linked by a common theme: the flux of quantum information between a quantum system and the quantum environment it interacts with. In this work, making use of a quantum collision model, a formalism initiated by Sudarshan and his school, we will analyse the efficiency with which the information about a single qubit gained by a quantum harmonic oscillator, acting as a meter, is transferred to a bosonic environment. We will show how, in some regimes, such quantum information flux is inefficient, leading to the simultaneous emergence …
We consider the implementation of two-qubit gates when the physical systems used to realize the qubits possess additional quantum states in the accessible energy range. We use optimal control theory to determine the maximum achievable gate speed for two-qubit gates in the qubit subspace of the many-level Hilbert space, and we analyze the effect of the additional quantum states on the gate speed. We identify two competing mechanisms. On one hand, higher energy levels are generally more strongly coupled to each other. Under suitable conditions, this stronger coupling can be utilized to make two-…
A while loop tests a termination condition on every iteration. On a quantum computer, such measurements perturb the evolution of the algorithm. We define a while loop primitive using weak measurements, offering a trade-off between the perturbation caused and the amount of information gained per iteration. This trade-off is adjusted with a parameter set by the programmer. We provide sufficient conditions that let us determine, with arbitrarily high probability, a worst-case estimate of the number of iterations the loop will run for. As an example, we solve Grover's search problem using a while …
Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the maximum measurement strength and thus the achievable readout speed and fidelity. We address this problem here and provide a plausible mechanism for drive-power dependence of relaxation rates. To this end we introduce a two-parameter perturbative expansion in qubit anharmonicity and the drive amplitude through a unitary transformation technique introduced in Part I. This approach naturally reveals number non-conservi…
The dynamics of a weakly anharmonic superconducting qubit in a complex electromagnetic environment is generally well-described by an effective multimode Kerr Hamiltonian at sufficiently weak excitation. This Hamiltonian can be embedded in a master equation with losses determined by the details of the electromagnetic environment. Recent experiments indicate, however, that when a superconducting circuit is driven with microwave signals the observed relaxation rates appear to be substantially different from expectations based on the electromagnetic environment of the qubit alone. This issue is a …
The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space probabilities. We prove that this POVM is achieved by collectively measuring the spin projection of an ensemble of qubits weakly and isotropically. We apply this in the context of optimal tomography of pure qubits. We show numerically that through a sequence of weak measurements of random directions of the collective spin component, sampled discretely or in a continu…
Weak measurements of a superconducting qubit produce noisy voltage signals that are weakly correlated with the qubit state. To recover individual quantum trajectories from these noisy signals, traditional methods require slow qubit dynamics and substantial prior information in the form of calibration experiments. Monitoring rapid qubit dynamics, e.g. during quantum gates, requires more complicated methods with increased demand for prior information. Here, we experimentally demonstrate an alternative method for accurately tracking rapidly driven superconducting qubit trajectories that uses a Lo…
We investigate the open dynamics of a probe qubit weakly interacting with distinct qubit environments bearing quantum information. We show that the proposed dissipative model yields a binary classification of the reservoir qubits' quantum information in the steady state in the Bloch qubit parameter space, depending on the coupling rates. To describe the dissipation model dynamics, we have adopted the collision model, in which the input information parameters of the reservoir qubits are easily determined. We develop a generalized classification rule based on the results of the micromaser-like m…
The long coherence time of a single nitrogen vacancy (NV) center spin in diamond is a crucial advantage for implementing quantum information processing. However, the realization of strong coupling between single NV spins is challenging. Here we propose a method to greatly enchance the interaction between two single NV spins in diamond which are only weakly coupled to an electromechanical cavity. Owing to the presence of a critical point for the linearized electromechanical subsystem, the coupling between a single NV spin and the high-frequency polariton (formed by the mechanical and cavity mod…
We study the influence of a thermal environment on a non-adiabatic spin-flip driving protocol of spin-orbit qubits. The driving protocol operates by moving the qubit, trapped in a harmonic potential, along a nanowire in the presence of a time-dependent spin-orbit interaction. We consider the harmonic degrees of freedom to be weakly coupled to a thermal bath. We find an analytical expression for the Floquet states and derive the Lindblad equation for a strongly non-adiabatically driven qubit. The Lindblad equation corrects the dynamics of an isolated qubit with Lamb shift terms and a dissipativ…
Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
University of Cologne（科隆大学）；University of Geneva（日内瓦大学）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
