Theory of remote entanglement via quantum-limited phase-preserving amplification

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.Comment: Main text (11 pages, 5 figures), updated to the published versio

New class of quantum error-correcting codes for a bosonic mode

We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite superposition of Fock states weighted with binomial coefficients. The binomial codes can exactly correct errors that are polynomial up to a specific degree in bosonic creation and annihilation operators, including amplitude damping and displacement noise as well as boson addition and dephasing errors. For realistic continuous-time dissipative evolution, the codes can perform approximate quantum error correction to any given order in the timestep between error detection measurements. We present an explicit approximate quantum error recovery operation based on projective measurements and unitary operations. The binomial codes are tailored for detecting boson loss and gain errors by means of measurements of the generalized number parity. We discuss optimization of the binomial codes and demonstrate that by relaxing the parity structure, codes with even lower unrecoverable error rates can be achieved. The binomial codes are related to existing two-mode bosonic codes but offer the advantage of requiring only a single bosonic mode to correct amplitude damping as well as the ability to correct other errors. Our codes are similar in spirit to 'cat codes' based on superpositions of the coherent states, but offer several advantages such as smaller mean number, exact rather than approximate orthonormality of the code words, and an explicit unitary operation for repumping energy into the bosonic mode. The binomial quantum codes are realizable with current superconducting circuit technology and they should prove useful in other quantum technologies, including bosonic quantum memories, photonic quantum communication, and optical-to-microwave up- and down-conversion.Comment: Published versio

Stark effect and generalized Bloch-Siegert shift in a strongly driven two-level system

A superconducting qubit was driven in an ultrastrong fashion by an oscillatory microwave field, which was created by coupling via the nonlinear Josephson energy. The observed Stark shifts of the `atomic' levels are so pronounced that corrections even beyond the lowest-order Bloch-Siegert shift are needed to properly explain the measurements. The quasienergies of the dressed two-level system were probed by resonant absorption via a cavity, and the results are in agreement with a calculation based on the Floquet approach.Comment: 4+ page

Multimode physics of the unimon circuit

We consider a superconducting half-wavelength resonator that is grounded at its both ends and contains a single Josephson junction. Previously this circuit was considered as a unimon qubit in the single-mode approximation where dc-phase-biasing the junction to $\pi$ leads to increased anharmonicity and 99.9% experimentally observed single-qubit gate fidelity. Inspired by the promising first experimental results, we develop here a theoretical and numerical model for the detailed understanding of the multimode physics of the unimon circuit. To this end, first, we consider the high-frequency modes of the unimon circuit and find that even though these modes are at their ground state, they imply a significant renormalization to the Josephson energy. We introduce an efficient method how the relevant modes can be fully taken into account and show that unexcited high-lying modes lead to corrections in the qubit energy and anharmonicity. Interestingly, provided that the junction is offset from the middle of the circuit, we find strong cross-Kerr coupling strengths between a few low-lying modes. This observation paves the way for the utilization of the multimode structure, for example, as several qubits embedded into a single unimon circuit

Non-Hermitian topological quantum states in a reservoir-engineered transmon chain

Dissipation in open systems enriches the possible symmetries of the Hamiltonians beyond the Hermitian framework, allowing the possibility of novel non-Hermitian topological phases which exhibit long-living end states that are protected against disorder. So far, non-Hermitian topology has been explored in settings where probing genuine quantum effects has been challenging. We theoretically show that a non-Hermitian topological quantum phase can be realized in a reservoir-engineered transmon chain. The spatial modulation of dissipation is obtained by coupling each transmon to a quantum circuit refrigerator, allowing in situ tuning of dissipation strength in a wide range. By solving the many-body Lindblad master equation using a combination of the density matrix renormalization group and Prosen-Seligman third quantization approaches, we show that the topological end modes and the associated phase transition are visible in simple reflection measurements with experimentally realistic parameters. Finally, we demonstrate that genuine quantum effects are observable in this system via robust and slowly decaying long-range quantum entanglement of the topological end modes, which can be generated passively starting from a locally excited transmon.publishedVersionPeer reviewe