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Register a new userTwo-qubit quantum gates for defect qubits in diamond and similar systems
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We propose a fast, scalable all-optical design for arbitrary two-qubit operations for defect qubits in diamond (NV centers) and in silicon carbide, which are promising candidates for room temperature quantum computing. The interaction between qubits is carried out by microcavity photons. The approach uses constructive interference from higher energy excited states activated by optical control. In this approach the cavity mode remains off-resonance with the directly accessible optical transitions used for initialization and readout. All quantum operations are controlled by near-resonant narrow-bandwidth optical pulses. We perform full quantum numerical modeling of the proposed gates and show that high-fidelity operations can be obtained with realistic parameters.
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Universal quantum computation will require qubit technology based on a scalable platform, together with quantum error correction protocols that place strict limits on the maximum infidelities for one- and two-qubit gate operations. While a variety of qubit systems have shown high fidelities at the one-qubit level, superconductor technologies have been the only solid-state qubits manufactured via standard lithographic techniques which have demonstrated two-qubit fidelities near the fault-tolerant threshold. Silicon-based quantum dot qubits are also amenable to large-scale manufacture and can achieve high single-qubit gate fidelities (exceeding 99.9%) using isotopically enriched silicon. However, while two-qubit gates have been demonstrated in silicon, it has not yet been possible to rigorously assess their fidelities using randomized benchmarking, since this requires sequences of significant numbers of qubit operations ($gtrsim 20$) to be completed with non-vanishing fidelity. Here, for qubits encoded on the electron spin states of gate-defined quantum dots, we demonstrate Bell state tomography with fidelities ranging from 80% to 89%, and two-qubit randomized benchmarking with an average Clifford gate fidelity of 94.7% and average Controlled-ROT (CROT) fidelity of 98.0%. These fidelities are found to be limited by the relatively slow gate times employed here compared with the decoherence times $T_2^*$ of the qubits. Silicon qubit designs employing fast gate operations based on high Rabi frequencies, together with advanced pulsing techniques, should therefore enable significantly higher fidelities in the near future.
This paper addresses the question how to implement a desired two-qubit gate U using a given tunable two-qubit entangling interaction H_int. We present a general method which is based on the K_1 A K_2 decomposition of unitary matrices in SU(4) to calculate analytically the smallest number of two-qubit gates U_int [based on H_int] and single-qubit rotations, and the explicit sequence of these operations that are required to implement U. We illustrate our protocol by calculating the implementation of (1) the transformation from standard basis to Bell basis, (2) the CNOT gate, and (3) the quantum Fourier transform for two kinds of interaction - Heisenberg exchange interaction and quantum inductive coupling - and discuss the relevance of our results for solid-state qubits.
We investigate capacitively coupled two-qubit quantum gates based on quantum dots. For exchange-only coded qubits electron spin $S$ and its projection $S_z$ are exact quantum numbers. Capacitive coupling between qubits, as distinct from interqubit exchange, preserves these quantum numbers. We prove, both analytically and numerically, that conservation of the spins of individual qubits has dramatic effect on performance of two-qubit gates. By varying the level splittings of individual qubits, $J_a$ and $J_b$, and the interqubit coupling time $t$, we can find an infinite number of triples $(J_a, J_b, t)$ for which the two-qubit entanglement, in combination with appropriate single-qubit rotations, can produce an exact CNOT gate. This statement is true for practically arbitrary magnitude and form of capacitive interqubit coupling. Our findings promise a large decrease in the number of nonlocal (two-qubit) operations in quantum circuits.
Any single-qubit unitary operation or quantum gate can be considered a rotation. Typical experimental implementations of single-qubit gates involve two or three fixed rotation axes, and up to three rotation steps. Here we show that, if the rotation axes can be tuned arbitrarily in a fixed plane, then two rotation steps are sufficient for implementing a single-qubit gate, and one rotation step is sufficient for implementing a state transformation. The results are relevant for exchange-only logical qubits encoded in three-spin blocks, which are important for universal quantum computation in decoherence free subsystems and subspaces.
Resonant exchange qubits are a promising addition to the family of experimentally implemented encodings of single qubits using semiconductor quantum dots. We have shown previously that it ought to be straightforward to perform a CPHASE gate between two resonant exchange qubits with a single exchange pulse. This approach uses energy gaps to suppress leakage rather than conventional pulse sequences. In this paper we present analysis and simulations of our proposed two-qubit gate subject to charge and Overhauser field noise at levels observed in current experiments. Our main result is that we expect implementations of our two-qubit gate to achieve high fidelities, with errors at the percent level and gate times comparable to single-qubit operations. As such, exchange-coupled resonant exchange qubits remain an attractive approach for quantum computing.
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