Autonomously stabilized entanglement between two superconducting quantum bits

Abstract

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...

Quantum Nondemolition Measurement of a Quantum Squeezed State Beyond the 3 dB Limit

“…Therefore, it is, in principle, impossible to have a steady state where the mechanical motion is squeezed below one half of the zero-point level using only parametric driving. These limitations may be overcome by combining continuous quantum measurement and feedback [9][10][11][12], but it would substantially increase the experimental complexity.Another method to generate a robust quantum state is quantum reservoir engineering [13], which has been used to generate quantum squeezed states and entanglement with trapped ions [14,15] and superconducting qubits [16]. It can also be applied to an optomechanical system to generate strong steady-state squeezing without quantumlimited measurement and feedback [17].…”

“…Another method to generate a robust quantum state is quantum reservoir engineering [13], which has been used to generate quantum squeezed states and entanglement with trapped ions [14,15] and superconducting qubits [16]. It can also be applied to an optomechanical system to generate strong steady-state squeezing without quantumlimited measurement and feedback [17].…”

Stabilizing Entanglement via Symmetry-Selective Bath Engineering in Superconducting Qubits

“…The engineered symmetries in our system distinguish it from the two-qubit bath engineering experiment in Ref. [13], where cooling to |S is achieved by utilizing far-detuned qubits in a single cavity; stabilizing entanglement in this system required six microwave drives, and only |S was accessible. In our implementation, the resonant construction of the photonic lattice imprints itself onto the effective qubit Hamiltonian and lifts the degeneracy in the single-excitation subspace.…”

“…An alternate approach, quantum bath engineering [8][9][10][11], explicitly utilizes this coupling in conjunction with microwave drives, to modify the dissipative environment and dynamically cool to a desired quantum state. Bath engineering in superconducting qubits has resulted in the stabilization of a single qubit on the Bloch sphere [12], a Bell-state of two qubits housed in the same cavity [13], many-body states [14], and a variety of non-classical resonator states [15,16]. Additionally, theoretical proposals have been put forward for dissipative error correction [17][18][19] and ultimately a universal quantum computation [20,21].…”

Single-Photon-Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-Number States

“…QRE does not require an external feedback with calculation since the Hamiltonian interactions are designed a priori to determine the final state avoiding uncertainty induced by the quantum-classical interface. In addition, QRE is less susceptible to experimental noise [14] and in some cases thrives in a noisy environment [15].QRE has been demonstrated in macroscopic atomic ensembles [16], trapped atomic systems [17], and superconducting circuits [18][19][20]. Circuit quantum electrodynamics (cQED) systems are an attractive platform for QRE due to the experimental freedom to design strong interactions between superconducting qubits and microwave cavities [21].…”