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Register a new userImplementing optimal control pulse shaping for improved single-qubit gates
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We employ pulse shaping to abate single-qubit gate errors arising from the weak anharmonicity of transmon superconducting qubits. By applying shaped pulses to both quadratures of rotation, a phase error induced by the presence of higher levels is corrected. Using a derivative of the control on the quadrature channel, we are able to remove the effect of the anharmonic levels for multiple qubits coupled to a microwave resonator. Randomized benchmarking is used to quantify the average error per gate, achieving a minimum of 0.007+/-0.005 using 4 ns-wide pulse.
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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.
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.
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.
Magnetic fluctuations caused by the nuclear spins of a host crystal are often the leading source of decoherence for many types of solid-state spin qubit. In group-IV materials, the spin-bearing nuclei are sufficiently rare that it is possible to identify and control individual host nuclear spins. This work presents the first experimental detection and manipulation of a single $^{29}$Si nuclear spin. The quantum non-demolition (QND) single-shot readout of the spin is demonstrated, and a Hahn echo measurement reveals a coherence time of $T_2 = 6.3(7)$ ms - in excellent agreement with bulk experiments. Atomistic modeling combined with extracted experimental parameters provides possible lattice sites for the $^{29}$Si atom under investigation. These results demonstrate that single $^{29}$Si nuclear spins could serve as a valuable resource in a silicon spin-based quantum computer.
The complete characterisation of the charge transport in a mesoscopic device is provided by the Full Counting Statistics (FCS) $P_t(m)$, describing the amount of charge $Q = me$ transmitted during the time $t$. Although numerous systems have been theoretically characterized by their FCS, the experimental measurement of the distribution function $P_t(m)$ or its moments $langle Q^n rangle$ are rare and often plagued by strong back-action. Here, we present a strategy for the measurement of the FCS, more specifically its characteristic function $chi(lambda)$ and moments $langle Q^n rangle$, by a qubit with a set of different couplings $lambda_j$, $j = 1,dots,k,dots k+p$, $k = lceil n/2 rceil$, $p geq 0$, to the mesoscopic conductor. The scheme involves multiple readings of Ramsey sequences at the different coupling strengths $lambda_j$ and we find the optimal distribution for these couplings $lambda_j$ as well as the optimal distribution $N_j$ of $N = sum N_j$ measurements among the different couplings $lambda_j$. We determine the precision scaling for the moments $langle Q^n rangle$ with the number $N$ of invested resources and show that the standard quantum limit can be approached when many additional couplings $pgg 1$ are included in the measurement scheme.
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