Quantum measurements are described as instantaneous projections in textbooks. They can be stretched out in time using weak measurements, whereby one can observe the evolution of a quantum state as it heads towards one of the eigenstates of the measured operator. This evolution can be understood as a continuous nonlinear stochastic process, generating an ensemble of quantum trajectories, consisting of noisy fluctuations on top of geodesics that attract the quantum state towards the measured operator eigenstates. The rate of evolution is specific to each system-apparatus pair, and the Born rule constraint requires the magnitudes of the noise and the attraction to be precisely related. We experimentally observe the entire quantum trajectory distribution for weak measurements of a superconducting qubit in circuit QED architecture, quantify it, and demonstrate that it agrees very well with the predictions of a single-parameter white-noise stochastic process. This characterisation of quantum trajectories is a powerful clue to unraveling the dynamics of quantum measurement, beyond the conventional axiomatic quantum theory.
Superconducting quantum technologies require qubit systems whose properties meet several often conflicting requirements, such as long coherence times and high anharmonicity. Here, we provide an engineering framework based on a generalized superconducting qubit model in the flux regime, which abstracts multiple circuit design parameters and thereby supports design optimization across multiple qubit properties. We experimentally investigate a special parameter regime which has both high anharmonicity ($\sim\!1$GHz) and long quantum coherence times ($T_1\!=\!40\!-\!80\,\mathrm{μs}$ and $T_\mathrm…
This interpretation establishes a completely classical ontology -- only the classical trajectory in configuration space -- and interprets the wave function as describing incomplete information (in form of a probability flow) about this trajectory. This combines basic ideas of de Broglie-Bohm theory and Nelsonian stochastics about the trajectory with a Bayesian interpretation of the wave function. Various objections are considered and discussed. In particular a regularity principle for the zeros of the wave function allows to meet the Wallstrom objection.
We study the synchronization of a superconducting qubit to an external optical field via a mechanical resonator in a hybrid optoelectromechanical system. The quantum trajectory method is employed to investigate synchronization. The bistability in one of the qubit polarization vectors, where the qubit rotates about the polarization vector, is observed for a single quantum trajectory run. The rotation in one of the stable states is synced with the external optical drive. When the number of trajectories is significantly increased, the qubit no longer displays bistability. However, synchronization…
With a counter-diabatic field supplemented to the reference control field, the `shortcut to adiabaticiy' (STA) protocol is implemented in a superconducting phase qubit. The Berry phase measured in a short time scale is in good agreement with the theoretical result acquired from an adiabatic loop. The trajectory of a qubit vector is extracted, verifying the Berry phase alternatively by the integrated solid angle. The classical noise is introduced to the amplitude or phase of the total control field. In the statistics of the Berry phase, the mean with either noise is almost equal to that without…
In a `shortcut-to-adiabaticity' (STA) protocol, the counter-diabatic Hamiltonian, which suppresses the non-adiabatic transition of a reference `adiabatic' trajectory, induces a quantum uncertainty of the work cost in the framework of quantum thermodynamics. Following a theory derived recently [Funo et al 2017 Phys. Rev. Lett. 118 100602], we perform an experimental measurement of the STA work statistics in a high-quality superconducting Xmon qubit. Through the frozen-Hamiltonian and frozen-population techniques, we experimentally realize the two-point measurement of the work distribution for g…
Based on a `shortcut-to-adiabaticity' (STA) scheme, we theoretically design and experimentally realize a set of high-fidelity single-qubit quantum gates in a superconducting Xmon qubit system. Through a precise microwave control, the qubit is driven to follow a fast `adiabatic' trajectory with the assistance of a counter-diabatic field and the correction of derivative removal by adiabatic gates. The experimental measurements of quantum process tomography and interleaved randomized benchmarking show that the process fidelities of our STA quantum gates are higher than 94.9% and the gate fideliti…
Due to the low error tolerance of a qubit, detecting and correcting errors on it is essential for fault-tolerant quantum computing. Surface code (SC) associated with its decoding algorithm is one of the most promising quantum error correction (QEC) methods. % One of the challenges of QEC is its high complexity and computational demand. QEC needs to be very power-efficient since the power budget is limited inside of a dilution refrigerator for superconducting qubits by which one of the most successful quantum computers (QCs) is built. In this paper, we propose an online-QEC algorithm and its ha…
We employ the quantum jump trajectory approach to construct a systematic framework to study the thermodynamics at the trajectory level in a nonequilibrium open quantum system under discrete feedback control. Within this framework, we derive quantum versions of the generalized Jarzynski equalities, which are demonstrated in an isolated pseudospin system and a coherently driven two-level open quantum system. Due to quantum coherence and measurement backaction, a fundamental distinction from the classical generalized Jarzynski equalities emerges in the quantum versions, which is characterized by …
Quantum state on Bloch sphere for superconducting charge qubit, phase qubit and flux qubit for all time in absence of external drive is stable to initial state. By driving the qubits, approximation of charge and flux Hamiltonian lead to quantum state rotation in Bloch sphere around an axis completely differ from rotation vector of exact Hamiltonian. The trajectory of quantum state for phase qubit for approximated and exact Hamiltonian is the same but the expectation of quantum observable has considerable errors as two other qubits. microwave drive control is designed for approximated Hamiltoni…
We apply quantum trajectory techniques to analyze a realistic set-up of a superconducting qubit coupled to a heat bath formed by a resistor, a system that yields explicit expressions of the relevant transition rates to be used in the analysis. We discuss the main characteristics of the jump trajectories and relate them to the expected outcomes ("clicks") of a fluorescence measurement using the resistor as a nanocalorimeter. As the main practical outcome we present a model that predicts the time-domain response of a realistic calorimeter subject to single microwave photons, incorporating the in…
The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the `shortcut to adiabaticity' (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting …
Delivering on the revolutionary promise of a universal quantum computer will require processors with millions of quantum bits (qubits). In superconducting quantum processors, each qubit is individually addressed with microwave signal lines that connect room temperature electronics to the cryogenic environment of the quantum circuit. The complexity and heat load associated with the multiple coaxial lines per qubit limits the possible size of a processor to a few thousand qubits. Here we introduce a photonic link employing an optical fiber to guide modulated laser light from room temperature to …
The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantum-limited readout. The inductance is either set by tailoring the metal-oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local current-biased flux lines. JJs based on superconducto…
