Quantum non-demolition measurement of a superconducting two-level system

Lupaşcu, Adrian; Saito, Shiro; Picot, Thomas; Groot, P. C. de; Harmans, C.J.P.M.; Mooij, J. E.

doi:10.1038/nphys509

Cited by 255 publications

(261 citation statements)

References 24 publications

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“…The randomness of quantum mechanics then arises merely from a randomness in the initial points of the set of trajectories. During a measurement process, the single 14 Visiting is good, but home is better 15 We need pluralism, there cannot be two opinions on that 16 In order to distinguish two concepts often used in the literature, we use the word "reduction" as meaning the transformation of the initial state of S + A into the final reduced state associated with one or another single run of the measurement, as specified in § 1.1.2, although the same word is often used in the literature to designate what we call "truncation" (decay of off-diagonal elements of the density matrix) initial bundle of trajectories, associated with |ψ , is split into separate bundles, each of which is associated with a wave function |s i . While this interpretation accounts for the bifurcation and for the uniqueness of the outcome of each run of a measurement process, it is not widely accepted [18,19,24,35,89].…”

Section: Mikhail Gorbachevmentioning

confidence: 99%

“…Moreover, rather than considering cases where quantum interference terms (the infamous "Schrödinger cat problem" [8,13,39]) vanish owing to decoherence processes [40], experimentalists have become able to control these very interferences [41], which are essential to describe the physics of quantum superpositions of macroscopic states and to explore the new possibilities offered by quantum information [22,42]. Examples include left and right going currents in superconducting circuits [15,43,44,45], macroscopic atomic ensembles [41] and entangled mechanical oscillators [46].…”

Section: General Features Of Quantum Measurementsmentioning

confidence: 99%

“…Indeed, the matrix element (5.11) is a sum of exponentials involving the eigenfrequencies 15) where m q are the eigenvalues ofm. The number Q of these eigenfrequencies is large as an exponential of the number N of microscopic degrees of freedom of the pointer, for instance Q = 2 N for (6.13).…”

Section: Armenian Proverbmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: Mikhail Gorbachevmentioning

confidence: 99%

Section: General Features Of Quantum Measurementsmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…Coupling between superconducting flux qubits and superconducting resonator has been demonstrated experimentally [42][43][44][45][46]. Here consider a coplanar waveguide resonator inductively coupled to the flux qubits in the TFIM.…”

Section: Discussionmentioning

confidence: 99%

Superconducting circuit probe for analog quantum simulators

You

Tian

2015

Phys. Rev. A

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Analog quantum simulators can be used to study quantum correlation in novel many-body systems by emulating the Hamiltonian of these systems. One essential question in quantum simulation is to probe the properties of an emulated many-body system. Here we present a circuit QED scheme for probing such properties by measuring the spectrum of a superconducting resonator coupled to a quantum simulator. We first study a general framework of this approach, and show that the spectrum of the resonator is directly related to the correlation function of the coupling operator between the resonator and the simulator. We then apply this scheme to a simulator of the transverse field Ising model implemented with superconducting qubits, where the resonance peaks in the resonator spectrum correspond to the frequencies of the elementary excitations. The effects of resonator damping, qubit decoherence, and resonator backaction are also discussed. This setup can be used to probe a broad range of many-body models.

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“…Recent developments of such detection schemes, using an oscillator as the pointer, have led to vast improvements [28,29,30,31,32,33,34] over previous measurement protocols.…”

Section: Introductionmentioning

confidence: 99%

Quantum nondemolition-like fast measurement scheme for a superconducting qubit

2008

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We present a measurement protocol for a flux qubit coupled to a dc-Superconducting QUantum Interference Device (SQUID), representative of any two-state system with a controllable coupling to an harmonic oscillator quadrature, which consists of two steps. First, the qubit state is imprinted onto the SQUID via a very short and strong interaction. We show that at the end of this step the qubit dephases completely, although the perturbation of the measured qubit observable during this step is weak. In the second step, information about the qubit is extracted by measuring the SQUID. This step can have arbitrarily long duration, since it no longer induces qubit errors.

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Quantum non-demolition measurement of a superconducting two-level system

Abstract: In quantum mechanics, the process of measurement is a subtle interplay between extraction of information and disturbance of the state of the quantum system. A

Cited by 255 publications

References 24 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

Superconducting circuit probe for analog quantum simulators

Quantum nondemolition-like fast measurement scheme for a superconducting qubit

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