Superconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, ... more Superconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, are a leading platform for emerging quantum technologies. Increasing circuit complexity further requires efficient methods for the calculation and optimization of the spectrum, nonlinear interactions, and dissipation in multi-mode distributed quantum circuits. Here we present a method based on the energy-participation ratio (EPR) of a dissipative or nonlinear element in an electromagnetic mode. The EPR, a number between zero and one, quantifies how much of the mode energy is stored in each element. The EPRs obey universal constraints and are calculated from one electromagnetic-eigenmode simulation. They lead directly to the system quantum Hamiltonian and dissipative parameters. The method provides an intuitive and simple-to-use tool to quantize multi-junction circuits. We experimentally tested this method on a variety of Josephson circuits and demonstrated agreement within several percents for nonlinear couplings and modal Hamiltonian parameters, spanning five orders of magnitude in energy, across a dozen samples.
While dissipation is widely considered as being harmful for quantum coherence, it can, when prope... more While dissipation is widely considered as being harmful for quantum coherence, it can, when properly engineered, lead to the stabilization of non-trivial pure quantum states. We propose a scheme for continuous generation and stabilization of Schrödinger cat states in a cavity using dissipation engineering. We first generate non-classical photon states with definite parity by means of a twophoton drive and dissipation, and then stabilize these transient states against single-photon decay. The single-photon stabilization is autonomous, and is implemented through a second engineered bath, which exploits the photon number dependent frequency-splitting due to Kerr interactions in the strongly dispersive regime of circuit QED. Starting with the Hamiltonian of the baths plus cavity, we derive an effective model of only the cavity photon states along with analytic expressions for relevant physical quantities, such as the stabilization rate. The deterministic generation of such cat states is one of the key ingredients in performing universal quantum computation.
Accurate and precise detection of multi-qubit entanglement is key for the experimental developmen... more Accurate and precise detection of multi-qubit entanglement is key for the experimental development of quantum computation. Traditionally, non-classical correlations between entangled qubits are measured by counting coincidences between single-shot readouts of individual qubits. We report entanglement metrology using a single detection channel with direct access to ensemble-averaged correlations between two superconducting qubits. Following validation and calibration of this joint readout, we demonstrate full quantum tomography on both separable and highly-entangled twoqubit states produced on demand. Using a subset of the measurements required for full tomography, we perform entanglement metrology with ∼95% accuracy and ∼98% precision despite ∼10% fidelity of single measurements. For the highly entangled states, measured Clauser-Horne-Shimony-Holt operators reach a maximum value of 2.61 ± 0.04, and entanglement witnesses give a lower bound of ∼88% on concurrence. In its present form, this detector will be able to resolve future improvements in the production of two-qubit entanglement and is immediately extendable to 3 or 4 qubits. L(R) z is the single-qubit Pauli z operator [25] on the left (right) qubit). A schematic of the experimental setup [26] is shown in Fig. 1A.
Josephson junction parametric amplifiers are playing a crucial role in the readout chain in super... more Josephson junction parametric amplifiers are playing a crucial role in the readout chain in superconducting quantum information experiments. However, their integration with current 3D cavity implementations poses the problem of transitioning between waveguide, coax cables and planar circuits. Moreover, Josephson amplifiers require auxiliary microwave components, like directional couplers and/or hybrids, that are sources of spurious losses and impedance mismatches that limit measurement efficiency and amplifier tunability. We have developed a wireless architecture for these parametric amplifiers that eliminates superfluous microwave components and interconnects. This greatly simplifies their assembly and integration into experiments. We present an experimental realization of such a device operating in the 9 − 11 GHz band with about 100 MHz of amplitude gain-bandwidth product, on par with devices mounted in conventional sample holders. The simpler impedance environment presented to the amplifier also results in increased amplifier tunability.
We show that a quantum-limited phase-preserving amplifier can act as a which-path information era... more We show that a quantum-limited phase-preserving amplifier can act as a which-path information eraser when followed by heterodyne detection. This 'beam splitter with gain' implements a continuous joint measurement on the signal sources. As an application, we propose heralded concurrent remote entanglement generation between two qubits coupled dispersively to separate cavities. Dissimilar qubit-cavity pairs can be made indistinguishable by simple engineering of the cavity driving fields providing further experimental flexibility and the prospect for scalability. Additionally, we find an analytic solution for the stochastic master equation-a quantum filter-yielding a thorough physical understanding of the nonlinear measurement process leading to an entangled state of the qubits. We determine the concurrence of the entangled states and analyze its dependence on losses and measurement inefficiencies.
Engineered quantum systems allow us to observe phenomena that are not easily accessible naturally... more Engineered quantum systems allow us to observe phenomena that are not easily accessible naturally. The LEGO®-like nature of superconducting circuits makes them particularly suited for building and coupling artificial atoms. Here, we introduce an artificial molecule, composed of two strongly coupled fluxonium atoms, which possesses a tunable magnetic moment. Using an applied external flux, one can tune the molecule between two regimes: one in which the ground-excited state manifold has a magnetic dipole moment and one in which the ground-excited state manifold has only a magnetic quadrupole moment. By varying the applied external flux, we find the coherence of the molecule to be limited by local flux noise. The ability to engineer and control artificial molecules paves the way for building more complex circuits for quantum simulation and protected qubits.
The Schrodinger's cat thought experiment highlights the counterintuitive concept of entanglement ... more The Schrodinger's cat thought experiment highlights the counterintuitive concept of entanglement in macroscopically distinguishable systems. The hallmark of entanglement is the detection of strong correlations between systems, most starkly demonstrated by the violation of a Bell inequality. No violation of a Bell inequality has been observed for a system entangled with a superposition of coherent states, known as a cat state. Here we use the Clauser-Horne-Shimony-Holt formulation of a Bell test to characterize entanglement between an artificial atom and a cat state, or a Bell-cat. Using superconducting circuits with high-fidelity measurements and real-time feedback, we detect correlations that surpass the classical maximum of the Bell inequality. We investigate the influence of decoherence with states up to 16 photons in size and characterize the system by introducing joint Wigner tomography. Such techniques demonstrate that information stored in superpositions of coherent states can be extracted efficiently, a crucial requirement for quantum computing with resonators.
We present a quantum-limited Josephson-junction-based 3-wave-mixing parametric amplifier, the SNA... more We present a quantum-limited Josephson-junction-based 3-wave-mixing parametric amplifier, the SNAIL Parametric Amplifier (SPA), which uses an array of SNAILs (Superconducting Nonlinear Asymmetric Inductive eLements) as the source of tunable nonlinearity. We show how to engineer the nonlinearity over multiple orders of magnitude by varying the physical design of the device. As a function of design parameters, we systematically explore two important amplifier nonidealities that limit dynamic range: the phenomena of gain compression and intermodulation distortion, whose minimization are crucial for high-fidelity multi-qubit readout. Through a comparison with firstprinciples theory across multiple devices, we demonstrate how to optimize both the nonlinearity and the input-output port coupling of these SNAIL-based parametric amplifiers to achieve higher saturation power, without sacrificing any other desirable characteristics. The method elaborated in our work can be extended to improve all forms of parametrically induced mixing that can be employed for quantum information applications.
Large-scale quantum information processing networks will most probably require the entanglement o... more Large-scale quantum information processing networks will most probably require the entanglement of distant systems that do not interact directly. This can be done by performing entangling gates between standing information carriers, used as memories or local computational resources, and flying ones, acting as quantum buses. We report the deterministic entanglement of two remote transmon qubits by Raman stimulated emission and absorption of a traveling photon wavepacket. We achieve a Bell state fidelity of 73%, well explained by losses in the transmission line and decoherence of each qubit.
Amplifiers are crucial in every experiment carrying out a very sensitive measurement. However, th... more Amplifiers are crucial in every experiment carrying out a very sensitive measurement. However, they always degrade the information by adding noise. Quantum mechanics puts a limit on how small this degradation can be. Theoretically, the minimum noise energy added by a phase preserving am
A quantum system driven by a weak deterministic force while under strong continuous energy measur... more A quantum system driven by a weak deterministic force while under strong continuous energy measurement exhibits quantum jumps between its energy levels (Nagourney et al., 1986, Sauter et al., 1986, Bergquist et al., 1986). This celebrated phenomenon is emblematic of the special nature of randomness in quantum physics. The times at which the jumps occur are reputed to be fundamentally unpredictable. However, certain classical phenomena, like tsunamis, while unpredictable in the long term, may possess a degree of predictability in the short term, and in some cases it may be possible to prevent a disaster by detecting an advance warning signal. Can there be, despite the indeterminism of quantum physics, a possibility to know if a quantum jump is about to occur or not? In this dissertation, we answer this question affirmatively by experimentally demonstrating that the completed jump from the ground to an excited state of a superconducting artificial atom can be tracked, as it follows its predictable "flight," by monitoring the population of an auxiliary level coupled to the ground state. Furthermore, the experimental results demonstrate that the jump when completed is continuous, coherent, and deterministic. Exploiting these features, we catch and reverse a quantum jump mid-flight, thus deterministically preventing its completion. This real-time Contents Contents iv List of Figures vi List of Tables viii
We present the experimental discovery of multiple simultaneous degeneracies in the spectrum of a ... more We present the experimental discovery of multiple simultaneous degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing, in combination with the Kerr interaction creates an effective static two-well potential in the frame rotating at half the frequency of the sinusoidal driving force. Remarkably, these degeneracies can be turned on-and-off on demand, and their number is tunable. We find that when the detuning ∆ between the frequency of the oscillator and characteristic frequency of the drive equals an even multiple of the Kerr coefficient K, ∆/K = 2m, the oscillator displays m + 1 exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. The degeneracies stem from the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime creating a super-protected cat qubit in the ground state manifold of our oscillator. Our results demonstrate the relationship between degeneracies and noise protection in quantum systems.
We derive the static effective Lindbladian beyond the rotating wave approximation (RWA) for a dri... more We derive the static effective Lindbladian beyond the rotating wave approximation (RWA) for a driven nonlinear oscillator coupled to a bath of harmonic oscillators. The associated dissipative effects may explain orders of magnitude differences between the predictions of the ordinary RWA model and results from recent superconducting circuits experiments on the Kerr-cat qubit. The higher-order dissipators found in our calculations have important consequences for quantum errorcorrection protocols and parametric processses.
By applying a microwave drive to a specially designed Josephson circuit, we have realized an elem... more By applying a microwave drive to a specially designed Josephson circuit, we have realized an elementary quantum optics model, the squeezed Kerr oscillator. This model displays, as the squeezing amplitude is increased, a cross-over from a single ground state regime to a doubly-degenerate ground state regime. In the latter case, the ground state manifold is spanned by Schrödinger-cat states, i.e. quantum superpositions of coherent states with opposite phases. For the first time, having resolved up to the tenth excited state in a spectroscopic experiment, we confirm that the proposed emergent static effective Hamiltonian correctly describes the system, despite its driven character. We also find that the lifetime of the coherent state components of the cat states increases in steps as a function of the squeezing amplitude. We interpret the staircase pattern as resulting from pairwise level kissing in the excited state spectrum. Considering the Kerr-cat qubit encoded in this ground state manifold, we achieve for the first time quantum nondemolition readout fidelities greater than 99%, and enhancement of the phase-flip lifetime by more than two orders of magnitude, while retaining universal quantum control. Our experiment illustrates the crucial role of parametric drive Hamiltonian engineering for hardware-efficient quantum computation.
The 'Schrödinger's cat' thought experiment highlights the counterintuitive facet of quantum theor... more The 'Schrödinger's cat' thought experiment highlights the counterintuitive facet of quantum theory that entanglement can exist between microscopic and macroscopic systems, producing a superposition of distinguishable states like the fictitious cat that is both alive and dead. The hallmark of entanglement is the detection of strong correlations between systems, for example by the violation of Bell's inequality [1]. Using the CHSH variant [2] of the Bell test, this violation has been observed with photons [3, 4], atoms [5, 6], solid state spins [7], and artificial atoms in superconducting circuits [8]. For larger, more distinguishable states, the conflict between quantum predictions and our classical expectations is typically resolved due to the rapid onset of decoherence. To investigate this reconciliation, one can employ a superposition of coherent states in an oscillator, known as a cat state [9]. In contrast to discrete systems, one can continuously vary the size of the prepared cat state and therefore its dependence on decoherence. No violation of Bell's inequality has yet been observed for a system entangled with a cat state. Here we demonstrate and quantify entanglement between an artificial atom and a cat state in a cavity, which we call a 'Bell-cat' state. We use a circuit QED [10] architecture, highfidelity measurements, and real-time feedback control to violate Bell's inequality [2] without post-selection or corrections for measurement inefficiencies. Furthermore, we investigate the influence of decoherence by continuously varying the size of created Bell-cat states and characterize the entangled system by joint Wigner tomography. These techniques provide a toolset for quantum information processing with entangled qubits and resonators [11]. While recent results have demonstrated a high level of control of such systems [12, 13, 14], this experiment demonstrates that information can be extracted efficiently and with high fidelity, a crucial requirement for quantum computing with resonators [15].
Superconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, ... more Superconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, are a leading platform for emerging quantum technologies. Increasing circuit complexity further requires efficient methods for the calculation and optimization of the spectrum, nonlinear interactions, and dissipation in multi-mode distributed quantum circuits. Here we present a method based on the energy-participation ratio (EPR) of a dissipative or nonlinear element in an electromagnetic mode. The EPR, a number between zero and one, quantifies how much of the mode energy is stored in each element. The EPRs obey universal constraints and are calculated from one electromagnetic-eigenmode simulation. They lead directly to the system quantum Hamiltonian and dissipative parameters. The method provides an intuitive and simple-to-use tool to quantize multi-junction circuits. We experimentally tested this method on a variety of Josephson circuits and demonstrated agreement within several percents for nonlinear couplings and modal Hamiltonian parameters, spanning five orders of magnitude in energy, across a dozen samples.
While dissipation is widely considered as being harmful for quantum coherence, it can, when prope... more While dissipation is widely considered as being harmful for quantum coherence, it can, when properly engineered, lead to the stabilization of non-trivial pure quantum states. We propose a scheme for continuous generation and stabilization of Schrödinger cat states in a cavity using dissipation engineering. We first generate non-classical photon states with definite parity by means of a twophoton drive and dissipation, and then stabilize these transient states against single-photon decay. The single-photon stabilization is autonomous, and is implemented through a second engineered bath, which exploits the photon number dependent frequency-splitting due to Kerr interactions in the strongly dispersive regime of circuit QED. Starting with the Hamiltonian of the baths plus cavity, we derive an effective model of only the cavity photon states along with analytic expressions for relevant physical quantities, such as the stabilization rate. The deterministic generation of such cat states is one of the key ingredients in performing universal quantum computation.
Accurate and precise detection of multi-qubit entanglement is key for the experimental developmen... more Accurate and precise detection of multi-qubit entanglement is key for the experimental development of quantum computation. Traditionally, non-classical correlations between entangled qubits are measured by counting coincidences between single-shot readouts of individual qubits. We report entanglement metrology using a single detection channel with direct access to ensemble-averaged correlations between two superconducting qubits. Following validation and calibration of this joint readout, we demonstrate full quantum tomography on both separable and highly-entangled twoqubit states produced on demand. Using a subset of the measurements required for full tomography, we perform entanglement metrology with ∼95% accuracy and ∼98% precision despite ∼10% fidelity of single measurements. For the highly entangled states, measured Clauser-Horne-Shimony-Holt operators reach a maximum value of 2.61 ± 0.04, and entanglement witnesses give a lower bound of ∼88% on concurrence. In its present form, this detector will be able to resolve future improvements in the production of two-qubit entanglement and is immediately extendable to 3 or 4 qubits. L(R) z is the single-qubit Pauli z operator [25] on the left (right) qubit). A schematic of the experimental setup [26] is shown in Fig. 1A.
Josephson junction parametric amplifiers are playing a crucial role in the readout chain in super... more Josephson junction parametric amplifiers are playing a crucial role in the readout chain in superconducting quantum information experiments. However, their integration with current 3D cavity implementations poses the problem of transitioning between waveguide, coax cables and planar circuits. Moreover, Josephson amplifiers require auxiliary microwave components, like directional couplers and/or hybrids, that are sources of spurious losses and impedance mismatches that limit measurement efficiency and amplifier tunability. We have developed a wireless architecture for these parametric amplifiers that eliminates superfluous microwave components and interconnects. This greatly simplifies their assembly and integration into experiments. We present an experimental realization of such a device operating in the 9 − 11 GHz band with about 100 MHz of amplitude gain-bandwidth product, on par with devices mounted in conventional sample holders. The simpler impedance environment presented to the amplifier also results in increased amplifier tunability.
We show that a quantum-limited phase-preserving amplifier can act as a which-path information era... more We show that a quantum-limited phase-preserving amplifier can act as a which-path information eraser when followed by heterodyne detection. This 'beam splitter with gain' implements a continuous joint measurement on the signal sources. As an application, we propose heralded concurrent remote entanglement generation between two qubits coupled dispersively to separate cavities. Dissimilar qubit-cavity pairs can be made indistinguishable by simple engineering of the cavity driving fields providing further experimental flexibility and the prospect for scalability. Additionally, we find an analytic solution for the stochastic master equation-a quantum filter-yielding a thorough physical understanding of the nonlinear measurement process leading to an entangled state of the qubits. We determine the concurrence of the entangled states and analyze its dependence on losses and measurement inefficiencies.
Engineered quantum systems allow us to observe phenomena that are not easily accessible naturally... more Engineered quantum systems allow us to observe phenomena that are not easily accessible naturally. The LEGO®-like nature of superconducting circuits makes them particularly suited for building and coupling artificial atoms. Here, we introduce an artificial molecule, composed of two strongly coupled fluxonium atoms, which possesses a tunable magnetic moment. Using an applied external flux, one can tune the molecule between two regimes: one in which the ground-excited state manifold has a magnetic dipole moment and one in which the ground-excited state manifold has only a magnetic quadrupole moment. By varying the applied external flux, we find the coherence of the molecule to be limited by local flux noise. The ability to engineer and control artificial molecules paves the way for building more complex circuits for quantum simulation and protected qubits.
The Schrodinger's cat thought experiment highlights the counterintuitive concept of entanglement ... more The Schrodinger's cat thought experiment highlights the counterintuitive concept of entanglement in macroscopically distinguishable systems. The hallmark of entanglement is the detection of strong correlations between systems, most starkly demonstrated by the violation of a Bell inequality. No violation of a Bell inequality has been observed for a system entangled with a superposition of coherent states, known as a cat state. Here we use the Clauser-Horne-Shimony-Holt formulation of a Bell test to characterize entanglement between an artificial atom and a cat state, or a Bell-cat. Using superconducting circuits with high-fidelity measurements and real-time feedback, we detect correlations that surpass the classical maximum of the Bell inequality. We investigate the influence of decoherence with states up to 16 photons in size and characterize the system by introducing joint Wigner tomography. Such techniques demonstrate that information stored in superpositions of coherent states can be extracted efficiently, a crucial requirement for quantum computing with resonators.
We present a quantum-limited Josephson-junction-based 3-wave-mixing parametric amplifier, the SNA... more We present a quantum-limited Josephson-junction-based 3-wave-mixing parametric amplifier, the SNAIL Parametric Amplifier (SPA), which uses an array of SNAILs (Superconducting Nonlinear Asymmetric Inductive eLements) as the source of tunable nonlinearity. We show how to engineer the nonlinearity over multiple orders of magnitude by varying the physical design of the device. As a function of design parameters, we systematically explore two important amplifier nonidealities that limit dynamic range: the phenomena of gain compression and intermodulation distortion, whose minimization are crucial for high-fidelity multi-qubit readout. Through a comparison with firstprinciples theory across multiple devices, we demonstrate how to optimize both the nonlinearity and the input-output port coupling of these SNAIL-based parametric amplifiers to achieve higher saturation power, without sacrificing any other desirable characteristics. The method elaborated in our work can be extended to improve all forms of parametrically induced mixing that can be employed for quantum information applications.
Large-scale quantum information processing networks will most probably require the entanglement o... more Large-scale quantum information processing networks will most probably require the entanglement of distant systems that do not interact directly. This can be done by performing entangling gates between standing information carriers, used as memories or local computational resources, and flying ones, acting as quantum buses. We report the deterministic entanglement of two remote transmon qubits by Raman stimulated emission and absorption of a traveling photon wavepacket. We achieve a Bell state fidelity of 73%, well explained by losses in the transmission line and decoherence of each qubit.
Amplifiers are crucial in every experiment carrying out a very sensitive measurement. However, th... more Amplifiers are crucial in every experiment carrying out a very sensitive measurement. However, they always degrade the information by adding noise. Quantum mechanics puts a limit on how small this degradation can be. Theoretically, the minimum noise energy added by a phase preserving am
A quantum system driven by a weak deterministic force while under strong continuous energy measur... more A quantum system driven by a weak deterministic force while under strong continuous energy measurement exhibits quantum jumps between its energy levels (Nagourney et al., 1986, Sauter et al., 1986, Bergquist et al., 1986). This celebrated phenomenon is emblematic of the special nature of randomness in quantum physics. The times at which the jumps occur are reputed to be fundamentally unpredictable. However, certain classical phenomena, like tsunamis, while unpredictable in the long term, may possess a degree of predictability in the short term, and in some cases it may be possible to prevent a disaster by detecting an advance warning signal. Can there be, despite the indeterminism of quantum physics, a possibility to know if a quantum jump is about to occur or not? In this dissertation, we answer this question affirmatively by experimentally demonstrating that the completed jump from the ground to an excited state of a superconducting artificial atom can be tracked, as it follows its predictable "flight," by monitoring the population of an auxiliary level coupled to the ground state. Furthermore, the experimental results demonstrate that the jump when completed is continuous, coherent, and deterministic. Exploiting these features, we catch and reverse a quantum jump mid-flight, thus deterministically preventing its completion. This real-time Contents Contents iv List of Figures vi List of Tables viii
We present the experimental discovery of multiple simultaneous degeneracies in the spectrum of a ... more We present the experimental discovery of multiple simultaneous degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing, in combination with the Kerr interaction creates an effective static two-well potential in the frame rotating at half the frequency of the sinusoidal driving force. Remarkably, these degeneracies can be turned on-and-off on demand, and their number is tunable. We find that when the detuning ∆ between the frequency of the oscillator and characteristic frequency of the drive equals an even multiple of the Kerr coefficient K, ∆/K = 2m, the oscillator displays m + 1 exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. The degeneracies stem from the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime creating a super-protected cat qubit in the ground state manifold of our oscillator. Our results demonstrate the relationship between degeneracies and noise protection in quantum systems.
We derive the static effective Lindbladian beyond the rotating wave approximation (RWA) for a dri... more We derive the static effective Lindbladian beyond the rotating wave approximation (RWA) for a driven nonlinear oscillator coupled to a bath of harmonic oscillators. The associated dissipative effects may explain orders of magnitude differences between the predictions of the ordinary RWA model and results from recent superconducting circuits experiments on the Kerr-cat qubit. The higher-order dissipators found in our calculations have important consequences for quantum errorcorrection protocols and parametric processses.
By applying a microwave drive to a specially designed Josephson circuit, we have realized an elem... more By applying a microwave drive to a specially designed Josephson circuit, we have realized an elementary quantum optics model, the squeezed Kerr oscillator. This model displays, as the squeezing amplitude is increased, a cross-over from a single ground state regime to a doubly-degenerate ground state regime. In the latter case, the ground state manifold is spanned by Schrödinger-cat states, i.e. quantum superpositions of coherent states with opposite phases. For the first time, having resolved up to the tenth excited state in a spectroscopic experiment, we confirm that the proposed emergent static effective Hamiltonian correctly describes the system, despite its driven character. We also find that the lifetime of the coherent state components of the cat states increases in steps as a function of the squeezing amplitude. We interpret the staircase pattern as resulting from pairwise level kissing in the excited state spectrum. Considering the Kerr-cat qubit encoded in this ground state manifold, we achieve for the first time quantum nondemolition readout fidelities greater than 99%, and enhancement of the phase-flip lifetime by more than two orders of magnitude, while retaining universal quantum control. Our experiment illustrates the crucial role of parametric drive Hamiltonian engineering for hardware-efficient quantum computation.
The 'Schrödinger's cat' thought experiment highlights the counterintuitive facet of quantum theor... more The 'Schrödinger's cat' thought experiment highlights the counterintuitive facet of quantum theory that entanglement can exist between microscopic and macroscopic systems, producing a superposition of distinguishable states like the fictitious cat that is both alive and dead. The hallmark of entanglement is the detection of strong correlations between systems, for example by the violation of Bell's inequality [1]. Using the CHSH variant [2] of the Bell test, this violation has been observed with photons [3, 4], atoms [5, 6], solid state spins [7], and artificial atoms in superconducting circuits [8]. For larger, more distinguishable states, the conflict between quantum predictions and our classical expectations is typically resolved due to the rapid onset of decoherence. To investigate this reconciliation, one can employ a superposition of coherent states in an oscillator, known as a cat state [9]. In contrast to discrete systems, one can continuously vary the size of the prepared cat state and therefore its dependence on decoherence. No violation of Bell's inequality has yet been observed for a system entangled with a cat state. Here we demonstrate and quantify entanglement between an artificial atom and a cat state in a cavity, which we call a 'Bell-cat' state. We use a circuit QED [10] architecture, highfidelity measurements, and real-time feedback control to violate Bell's inequality [2] without post-selection or corrections for measurement inefficiencies. Furthermore, we investigate the influence of decoherence by continuously varying the size of created Bell-cat states and characterize the entangled system by joint Wigner tomography. These techniques provide a toolset for quantum information processing with entangled qubits and resonators [11]. While recent results have demonstrated a high level of control of such systems [12, 13, 14], this experiment demonstrates that information can be extracted efficiently and with high fidelity, a crucial requirement for quantum computing with resonators [15].
Uploads
Papers by Michel Devoret