Parallelism for quantum computation with qudits

Abstract

Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the atomic alkalies 87 Rb and 133 Cs. Second, we provide a protocol for implementing parallelized nonlocal two-qudit gates using the assistance of entangled qubit pairs. Because the entangled qubits can be prepared non-deterministically, this offers the possibility of high fidelity two-qudit gates.

Quantum logic gates for superconducting resonator qudits

“…This gate set is sufficient to perform an arbitrary two-qudit unitary operation [38], and by extension to multiple qudits, universal quantum computation [36]. Explicit constructions for circuit synthesis can be found in [39,40]. In the implementation we will present shortly, the rotations will be between neighboring oscillator states j and k = j + 1.…”

Efficient implementation of bipartite nonlocal unitary gates using prior entanglement and classical communication

“…See [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] for other deterministic and probabilistic protocols. We only consider the deterministic case in which the desired unitary is carried out with probability 1; finding efficient protocols that allow for some noise is a challenging problem not addressed here.…”

Orbital Angular Momentum in Quantum Communication and Information

“…There are schemes to perform quantum computation using qunits as the basic logical states [6,[45][46][47][48][49], which would allow the use of fewer physical qunits than qubits to perform the same computation. In quantum computing, the main criterion is efficiency and not security.…”