Robust two-qubit gates for exchange-coupled qubits

Abstract

We present composite pulse sequences that perform fault-tolerant two-qubit gate operations on exchange-only quantum-dot spin qubits in various experimentally relevant geometries. We show how to perform dynamically corrected two-qubit gates in exchange-only systems with the leading hyperfine error term canceled. These pulse sequences are constructed to conform to the realistic experimental constraint of strictly non-negative couplings. We establish that our proposed pulse sequences lead to several orders of magnitude improvement in the gate fidelity compared with their uncorrected counterparts. Together with single-qubit dynamically corrected gates, our results enable noise-resistant universal quantum operations with exchange-only qubits.of the square bracket indicates that these three steps are repeated six times to form the entire sequence. An alternative way of performing the permutation is shown in the right diagram of Fig. 2(a). J J J J

Exact CNOT gates with a single nonlocal rotation for quantum-dot qubits

“…If two-qubit coupling is also implemented by exchange, however, the spin quantum numbers of individual qubits will not be conserved, and the system will not generally remain in the coding Hilbert space. Then, to rectify this, one is forced to implement a complicated series of at least 15 nonlocal operations, interspersed with local operations [32,33], all of which take time and can easily lead to errors. By contrast, if the interqubit coupling is mediated only by the Coulomb interaction between electrons in different qubits, the spin quantum numbers of each qubit are conserved by this interaction.…”

“…Depending on the specific shape of two capacitively coupled three-dot qubits and their mutual position, the basic two-qubit configurations may be termed as linear, butterfly, two-corner, and loop geometries [29,31,32]. Details of the geometry mostly determine the interqubit-coupling part H int of the total Hamiltonian H = H 0 + H int , while the Hamiltonian H 0 of individual qubits can always be chosen as…”

“…However, exchange interactions do not conserve S and S Z for the individual qubits, so that, in general, after an interval of exchange coupling, the qubits will no longer be in the coding subspace. In order to rectify this, a proper two-qubit operation requires a sequence of many exchange couplings, interspersed with single-qubit operations [31][32][33], and the total number of operations is very large. Even with high speed and accuracy of individual operations [22][23][24]27], the cost of a long chain of them could be rather high.…”

Entangling distant resonant exchange qubits via circuit quantum electrodynamics

“…14,29,30,32,33,37 The range of exchange-based interactions can be extended via spin chains, 38,39 while that of capacitive interactions can be extended via floating metal gates. 40 In the context of a modular quantum computer architecture, 5,41 these schemes provide potential methods of coupling spatially separated spin qubits within a single module.…”

Approximate exchange-only entangling gates for the three-spin-1/2decoherence-free subsystem

“…Surprisingly this exact spin-independent solution was simpler, in terms of the number of exchange gates and their analytic coefficients, than that of the original spin-dependent solutions. Since then several other spin-independent, exchange-only CNOT gates have been found [17,18].…”