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The implementation of holonomic quantum computation on superconducting quantum circuits is challenging due to the general requirement of controllable complicated coupling between multilevel systems. Here we solve this problem by proposing a scalable circuit QED lattice with simple realization of a universal set of nonadiabatic holonomic quantum gates. Compared with the existing proposals, we can achieve both the single and two logical qubit gates in an tunable and all-resonant way through a hybrid transmon-transmission-line encoding of the logical qubits in the decoherence-free subspaces. This distinct advantage thus leads to quantum gates with very fast speeds and consequently very high fidelities. Therefore, our scheme paves a promising way towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.Comment: v2: thoroughly rewritten version with major revission; v3: Accepted by PRA; V4: Published versio

Quantum sensing exploits fundamental features of quantum system to achieve highly efficient measurement of physical quantities. Here, we propose a strategy to realize a single-qubit pseudo-Hermitian sensor from a dilated two-qubit Hermitian system. The pseudo-Hermitian sensor exhibits divergent susceptibility in dynamical evolution that does not necessarily involve exceptional point. We demonstrate its potential advantages to overcome noises that cannot be averaged out by repetitive measurements. The proposal is feasible with the state-of-art experimental capability in a variety of qubit systems, and represents a step towards the application of non-Hermitian physics in quantum sensing.Introduction.-Non-Hermitian Hamiltonians usually have complex energy eigenvalues and do not conserve probabilities, thus presumably only serve as phenomenological descriptions of open quantum system [1,2]. Remarkably, a non-Hermitian Hamiltonian H with an exact PT -symmetry [3-5] and more general pseudo-Hermiticity (i.e. ηH = H † η with a Hermitian invertible linear operator η) [6-9] can have real spectrum. The discovery has opened a new avenue to intriguing non-Hermitian physics in both classical and quantum systems [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In particular, the concepts of exceptional point [25][26][27] and PT -phase transition [28,29] lead to important experimental observations such as single-mode lasers [30, 31], non-reciprocal light transport [32, 33], non-Hermitian topological light steering [34], asymmetric mode switching [35] and topological energy transfer [36] when encircling an exceptional point.Among a number of important applications, enhancing the sensitivity of energy splitting detection by using exceptional points attracts increasingly intensive theoretical interest [37][38][39][40][41][42]. The unique feature of exceptional point based sensing is the divergent eigenvalue susceptibility arising from the square-root frequency topology around exceptional points [27]. Exceptional point based sensing has been demonstrated in PT -symmetric linear coupled-mode optic systems, with potential applications for single-particle detection [43,44] and optical gyroscope [45]. Nevertheless, the singular behavior of the energy splitting is counteracted by the eigenstate coalescence [46][47][48]. Quantum sensing based on non-Hermitian qubit system without involving exceptional points and its potential advantages remain largely unexplored.In this work, we propose a novel strategy to harness a qubit probe with pseudo-Hermiticity as a resource for quantum sensing by introducing an additional qubit ancilla [49][50][51][52]. The dilated two-qubit Hermitian system, when exposed to a parameter-dependent weak field, reproduces an effective pseudo-Hermitian qubit sensor by postselection, inheriting the influence of the parameter. The eigenstate coalescence without involving exceptional point induces divergent susceptibility in the normalized

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