On-demand maximally entangled states with a parity meter and continuous feedback

Abstract

Generating on-demand maximally entangled states is one of the corner stones for quantum information processing. Parity measurements can serve to create Bell states and have been implemented via an electronic Mach-Zehnder interferometer among others. However, the entanglement generation is necessarily harmed by measurement induced dephasing processes in one of the two parity subspace. In this work, we propose two different schemes of continuous feedback for a parity measurement. They enable us to avoid both the measurement-induced dephasing process and the experimentally unavoidable dephasing, e.g. due to fluctuations of the gate voltages controlling the initialization of the qubits. We show that we can generate maximally entangled steady states in both parity subspaces. Importantly, the measurement scheme we propose is valid for implementation of parity measurements with feedback loops in various solid-state environments. I. MOTIVATIONThe generation, the control and the read-out of pairs of entangled qubits serve as stepping stones towards the implementation of quantum information protocols. While the readout of individual qubits is typically associated with the irreversible destruction of the given coherent state, it has been shown that a joint measurement of two qubits can serve as an effective mechanism to generate entanglement between two measured qubits initially in a product state, [1][2][3][4][5][6][7][8][9][10][11][12] and may be used for error correction schemes.13,14 This measurement-based creation of entanglement is achieved by operating the detector as a parity meter. The corresponding observable in the computational basis of the qubits readsP =σ 1 z ⊗σ 2 z , where σ i z are the Pauli matrices for the qubits i = 1, 2. The parity operator P has two eigenvalues, ±1, corresponding to the even subspace spanned by the states {|↑↑ , |↓↓ }, and to the odd subspace spanned by {|↑↓ , |↓↑ }. Measuring the parity causes the two-qubit state to collapse onto a superposition of even or odd states and, in particular onto the maximally entangled states or Bell states in an ideal situation, |ΨParity measurements have been proposed in various solid-state systems that serve as potential architectures for quantum computing. In circuit quantum electrodynamics (QED), generation of entanglement through a parity measurement has been very recently achieved in 3D circuit QED 15,16 as well as in 2D Circuit QED 17 , an architecture suitable for surface coding. Also quantum transport-based measurements can equally well act as parity measurements: both the quantum point contact (QPC) 4,6 and the electronic Mach-Zehnder interferometer (MZI) 9 have been investigated as parity meters for two double-quantum dots (DDs) chargeOn-demand generation of steady maximally-entangled states via a parity measurement with feedback Generating on-demand maximally entangled states is one of the key corner stones for quantum information processing. Parity measurements can serve to create Bell states and have been implemented via an electronic Mac...

Always-On Quantum Error Tracking with Continuous Parity Measurements

“…A possible route to perform QEC without the overhead of ancilla qubits is to directly monitor the error syndromes continuously in time [22,23]. With this variation, the code subspaces for the error syndromes are directly coupled to a continuous readout device [24][25][26][27][28][29][30], avoiding the need for periodic entangling gates and additional ancilla measurements. This idea of continuous quantum error correction was proposed in Ref.…”

Quantum Trajectories and Their Statistics for Remotely Entangled Quantum Bits

“…Since we expect most of the off-diagonal terms to damp quickly, we only consider five relevant density matrix elements: 44 , and x 5 ≡ jρ 23 j [52]. In order to compare the Bayesian prediction to the true density matrix, we perform conditional tomography [12,53] to experimentally reconstruct the full experimental mapping V t ↦ ρðV t ; tÞ.…”

“…In solid-state systems, such as superconducting qubit transitions in the microwave regime, there has been tremendous interest in continuously generating bipartite [3][4][5][6]39] and multipartite [2,40,41] entangled states, using weak measurements that slowly interact with the qubits, in such a way that enables the resolution of the dynamical aspects of the entangling backaction. Analog feedback control can naturally be applied in the weak continuousmeasurement regimes [42][43][44], and digital feedbackgenerated entanglement has already been demonstrated [45]. Joint measurement is uniquely useful as a means to generate entanglement between remote qubits [12,[46][47][48][49][50], for which no local coupling exists and therefore no unitary means of generating entanglement are available.…”

Generation and stabilization of Bell states via repeated projective measurements on a driven ancilla qubit

“…In this context, different schemes have been proposed [23][24][25][26][27][28]55] and implemented [29][30][31] which rely on the use of a parity meter on the collective state of two qubits. The introduction of a feedback control based on the readout of a continuous weak measurement of parity provides further means to entangle bipartite systems [32][33][34][35]. A parity meter of the state of two qubits, α and β, discriminates if they are in an even or odd parity collective state, associated to the two eigenvalues 1 and −1 of the parity operator An advantage of the class of schemes based on parity measurements is that they do not require direct interaction between the qubits, a feature that makes them suitable for linear optics setups, e.g., the scheme for quantum computing discussed in Ref [36].…”