Quantum Back-Action of an Individual Variable-Strength Measurement

Hatridge, Michael; Shankar, Shyam; Mirrahimi, Mazyar; Schackert, Flavius; Geerlings, K.; Brecht, T.; Sliwa, K.M.; Abdo, Baleegh; Frunzio, Luigi; Girvin, S. M.; Schoelkopf, Robert; Devoret, Michel

doi:10.1126/science.1226897

Cited by 265 publications

(333 citation statements)

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“…This results in a qubit-state dependent shift of the cavity mode frequency. By applying a microwave tone to a single cavity mode, one can infer the qubit state from the phase of the reflected signal 16 ; this readout scheme has been used extensively with superconducting qubits for quantum information processing, and also to perform weak measurements 17 and track quantum trajectories of a single qubit 18 . In our configuration, each cavity mode constitutes a measurement channel which extracts the projection of the qubit spin along the σ z axis of the Bloch sphere.…”

mentioning

confidence: 99%

Quantum dynamics of simultaneously measured non-commuting observables

Hacohen-Gourgy

Martin

Flurin

et al. 2016

Nature

143

181

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In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, whereas for non-commuting observables such as position and momentum Heisenbergs uncertainty principle limits the intrinsic precision of a state.Although theoretical work 1 has demonstrated that it should be possible to perform simultaneous non-commuting measurements and has revealed the limits on measurement outcomes, only recently 2,3 has the dynamics of the quantum state been discussed. To realize this unexplored regime, we simultaneously apply two continuous quantum non-demolition probes of non-commuting observables to a superconducting qubit. We implement multiple readout channels by coupling the qubit to multiple modes of a cavity. To control the measurement observables, we implement a single quadrature measurement by driving the qubit and applying cavity sidebands with a relative phase that sets the observable. Here, we use this approach to show that the uncertainty principle governs the dynamics of the wavefunction by enforcing a lower bound on the measurement-induced disturbance. Consequently, as we transition from measuring identical to measuring non-commuting observables, the dynamics make a smooth transition from standard wavefunction collapse to localized persistent diffusion and then to isotropic persistent diffusion. Although the evolution of the state differs markedly from that of a conventional measurement, information about both non-commuting observables is extracted by keeping track of the time ordering of the measurement record, enabling quantum state tomography without alternating measurements. Our work creates novel capabilities for quantum control, including rapid state purification 4 , adaptive measurement 5,6 , measurement-based state steering and continuous quantum error correction 7 . As physical systems often interact continuously with their environment via non-commuting degrees of freedom, our work offers a way 8,9 to * shayhh@berkeley.edushayhh@berkeley.edu study how notions of contemporary quantum foundations 10-14 arise in such settings.In this work, we implement two high quantum efficiency readouts of the angular momenta about two different axes of an artificial spin-1/2 system and observe in real-time the resulting dynamics. Importantly, our measurements are designed to be individually quantum non-demolition, which ensures that the back-action arises only from the competition between incompatible observables.Our experiment utilizes a single superconducting transmon qubit coupled dispersively to a multimode waveguide cavity 15 . This results in a qubit-state dependent shift of the cavity mode frequency. By applying a microwave tone to a single cavity mode, one can infer the qubit state from the phase of the reflected signal 16 ; this readout scheme has been used extensively with superconducting qubits for quantum information processing, and also to perform weak measurements 17 and track quantum trajectories of a single qubit 18 . In our configuration, each cavity mode constitutes a measure...

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mentioning

confidence: 99%

Quantum dynamics of simultaneously measured non-commuting observables

Hacohen-Gourgy

Martin

Flurin

et al. 2016

Nature

143

181

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“…The joint-readout of the qubits used for tomography, was implemented with high-fidelity singleshot measurements 35 , by pulsing the cavity input for 500 ns using the source f GG c (msmt) (Agilent N5183) set at ω gg c (see Fig. ED1).…”

Section: Joint-readout Implementation With Jpcmentioning

confidence: 99%

Autonomously stabilized entanglement between two superconducting quantum bits

Shankar¹,

Hatridge²,

Leghtas³

et al. 2013

Nature

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327

344

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Quantum error-correction codes would protect an arbitrary state of a multi-qubit register against decoherence-induced errors 1 , but their implementation is an outstanding challenge for the development of large-scale quantum computers. A first step is to stabilize a nonequilibrium state of a simple quantum system such as a qubit or a cavity mode in the presence of decoherence. Several groups have recently accomplished this goal using measurementbased feedback schemes [2][3][4][5] . A next step is to prepare and stabilize a state of a composite system [6][7][8] . Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved by an autonomous feedback scheme which combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have recently been used for qubit reset 9 and the stabilization of a single qubit state 10 , as well as for creating 11 and stabilizing 6 states of multipartite quantum systems. Unlike conventional, measurement-based schemes, an autonomous approach counter-intuitively uses engineered dissipation to fight decoherence [12][13][14][15] , obviating the need 1 arXiv:1307.4349v3 [quant-ph] 23 Oct 2013 for a complicated external feedback loop to correct errors, simplifying implementation. Instead the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building-block state for quantum information processing. Such autonomous schemes, broadly applicable to a variety of physical systems as demonstrated by a concurrent publication with trapped ion qubits 16 , will be an essential tool for the implementation of quantum-error correction.Here we implement a proposal 17 , tailored to the circuit Quantum Electrodynamics (cQED) architecture 18 , for stabilizing entanglement between two superconducting transmon qubits 19 . The qubits are dispersively coupled to an open cavity which acts as the dissipative reservoir. The cavity in our implementation is furthermore engineered to preferentially decay into a 50 Ω transmission line that we can monitor on demand. We show, using two-qubit quantum state tomography and high-fidelity single-shot readout, that the steady-state of the system reaches the target Bell state with a fidelity of 67 %, well above the 50 % threshold that witnesses entanglement. As discussed in Ref. 17, the fidelity can be further improved by monitoring the cavity output and performing conditional tomography when the output indicates that the two qubits are in the Bell state. We implemented this protocol via post-selection and demonstrated that the fidelity increased to ∼ 77 %.Our cQED setup, outlined schematically in Fig. 1a, consists of two individually addressable qubits, Alice and Bob, coupled dispersively to a three-dimensional (3D) rectangular copper cavity.The setup is described by...

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“…The limiting case of n m → 0 is approached when the measurement record is dominated by back-actioninduced fluctuations. This occurs when the measurement nears unit efficiency [265], i.e., when the measurement rate, Γ meas = 1/16n imp , approaches the effective thermal decoherence rate, Γ tot = (n m,th + n m,BA )Γ m ≥ Γ meas . To meet this condition for a typical mechanical oscillator a linear position sensor must achieve an imprecision far (∼ n m,th times) below the natural scale set by the standard quantum limit (SQL, see section 2.3) (n imp = n m,BA = 1/4), while maintaining back-action near the uncertainty limit: 4 √ n m,BA n imp ≥ 1.…”

Section: Heisenberg-uncertainty-limited Measurementmentioning

confidence: 99%

“…This penalty would appear to prohibit ground-state cooling, as it entails substantially heating the oscillator to achieve the necessary imprecision. Remarkably, however, feedback counteracts back-action [265,293], so that a phonon occupancy of n m ≈ 2 n imp (n m,BA + n m,th ) − 1/2 < 1 (eq. (3.1.11)) can still be achieved.…”

Section: Heisenberg-uncertainty-limited Measurementmentioning

confidence: 99%

“…In a quantum mechanical description of such "real-time" feedback control [263,264], the burden of timescale is shifted to the measurement: the measurement must be strong enough to track the quantum fluctuations of the system under control, while simultaneously being weak enough to not impart excess back-action [265]. Spectacular applications of such measurementbased feedback, for example to stabilize microwave Fock states [266,267] and persistent Rabi oscillations of an artificial atom [268], have been limited to well isolated quantum systems.…”

Section: Measurement-based Control At the Thermal Decoherence Ratementioning

confidence: 99%

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Quantum Limits on Measurement and Control of a Mechanical Oscillator

Sudhir

2018

Springer Theses

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PAR Vivishek SUDHIR JOSEPH CONRAD, Heart of DarknessExperimental physics demands a certain degree of manual dexterity, the patience to tolerate the mundane, and an inexhaustible supply of optimism. Tobias hired me to work on an immensely sophisticated experiment despite any proof of my possessing these qualities; I am indebted to him for the belief he has placed in me. I would also like to acknowledge his dedication to fostering an environment where the pursuit of science is unencumbered by other worldly concerns. Stefan, Ewold and Samuel bore the brunt of a theorist trying to perform delicate experiments; the stern, yet encouraging, stewardship of this trio ensured that I enjoyed the culture shock. Dal Wilson was more than a colleague and a post-doc; his pragmatic approach to physics provided the ideal counter-point in our attempts to forge a deeper understanding of things ranging from vibration isolation to the subtleties of quantum mechanics. Without the patient efforts of Amir, Ryan and Hendrik in designing, fabricating, and testing of devices, none of the results reported here would have been possible. I hope I have been able to bequeath a better vision of the future of our experiment to Sergey. Conversations with Alexey, Daniel and Nathan have enabled me to vicariously learn how to measure microwave "photons". John Jost once taught me how to decorate a Christmas tree; since then he has imparted some wisdom on frequency metrology, and some on atomic physics. Together with Dal, Victor and Caroline have probably spent the most time with me outside the lab; it was fun to exercise an air of social normalcy with this bunch. Christophe has been an amazing sparring partner on every subject capable of being brought under scientific scrutiny.The personal space required for the pursuit of science comes through the sacrifice of many people. My family back home in India -parents, sister, grand-parents -have had to patiently wait for the brief interludes when I go home. No words can do justice to this and the very many other pleasures they have surrendered over the years for my sake. Before physics attracted me, I was charmed by someone else; I am lucky to have married her. Long time friends, mentorsAjith and Subeesh -have played pivotal roles in my being able to engage in physics; I hope to repay this enormous debt, some day.It was a privilege to have learnt from a few great teachers during my formative years. Their vision of an indelible unity in nature continues to motivate my study of physics. vii AbstractThe precision measurement of position has a long-standing tradition in physics. Cavendish's verification of the universal law of gravitation using a torsion pendulum, Perrin's confirmation of the atomic hypothesis via the precise measurement of the Brownian motion, and, the verification of the mechanical effect of electromagnetic radiation, all belong to this classical heritage. Quantum mechanics posits that the measurement of position results in an uncertain momentum; an idea developed to full maturity within the ...

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Quantum Back-Action of an Individual Variable-Strength Measurement

Cited by 265 publications

References 30 publications

Quantum dynamics of simultaneously measured non-commuting observables

Quantum dynamics of simultaneously measured non-commuting observables

Autonomously stabilized entanglement between two superconducting quantum bits

Quantum Limits on Measurement and Control of a Mechanical Oscillator

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