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There is currently a tremendous interest in developing practical applications of NISQ processors without the overhead required by full error correction. Quantum information processing is especially challenging within the gate model, as algorithms quickly lose fidelity as the problem size and circuit depth grow. This has lead to a number of non-gate-model approaches such as analog quantum simulation and quantum annealing. These approaches come with specific hardware requirements that are typically different than that of a universal gate-based quantum computer. We have previously proposed a non-gate-model approach called the single-excitation subspace (SES) method, which requires a complete graph of superconducting qubits. Like any approach lacking error correction, the SES method is not scalable, but it often leads to algorithms with constant depth, allowing it to outperform the gate model in a wide variety of applications. A challenge of the SES method is that it requires a physical qubit for every basis state in the computers Hilbert space. This imposes large resource costs for algorithms using registers of ancillary qubits, as each ancilla would double the required graph size. Here we show how to circumvent this doubling by leaving the SES and reintroducing a tensor product structure in the computational subspace. Specifically, we implement the tensor product of an SES register holding ``data with one or more ancilla qubits. This enables a hybrid form of quantum computation where fast SES operations are performed on the data, traditional logic gates and measurements are performed on the ancillas, and controlled-unitaries act between. As an application we give an SES implementation of the quantum linear system solver of Harrow, Hassidim, and Lloyd.
We propose a scheme to implement quantum computation in decoherence-free subspace with superconducting devices inside a cavity by unconventional geometric manipulation. Universal single-qubit gates in encoded qubit can be achieved with cavity assiste
Trapped ions (TI) are a leading candidate for building Noisy Intermediate-Scale Quantum (NISQ) hardware. TI qubits have fundamental advantages over other technologies such as superconducting qubits, including high qubit quality, coherence and connect
Crosstalk is a major source of noise in Noisy Intermediate-Scale Quantum (NISQ) systems and is a fundamental challenge for hardware design. When multiple instructions are executed in parallel, crosstalk between the instructions can corrupt the quantu
We use quantum process tomography to characterize a full universal set of all-microwave gates on two superconducting single-frequency single-junction transmon qubits. All extracted gate fidelities, including those for Clifford group generators, singl
We propose a realistic hybrid classical-quantum linear solver to solve systems of linear equations of a specific type, and demonstrate its feasibility using Qiskit on IBM Q systems. This algorithm makes use of quantum random walk that runs in $mathca