Multivalued logic gates for quantum computation

We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. 106, 240503 (2011) is detailed and extended to qudits of different dimensions. The topological nature of the phase evolution and its restriction to fractional values are related to both the structure of the projective space of states and entanglement. For maximally entangled states of qudits with the same Hilbert space dimension, the fractional geometric phases are the only ones attainable under local SU(d) operations, an effect that can be experimentally observed through conditional interference.

Section: Discussionmentioning

confidence: 99%

Topological phase structure of entangled qudits

Khoury¹,

Oxman²

2014

“…There seems to be one issue, which, despite notable exceptions (e.g., [1,Footnote 6] and [2]), has not yet been acknowledged widely: the principal irreducibility of quantum information in base n. Define a "nit" as a unit of information equal to the amount of information obtained by learning which of n equally likely events occurred. An n-state particle can be prepared in a single one of n possible states.…”

mentioning

confidence: 99%

Quantum information in basendefined by state partitions

Svozil

2002

We define a "nit" as a radix n measure of quantum information which is based on state partitions associated with the outcomes of n-ary observables and which, for n > 2, is fundamentally irreducible to a binary coding. Properties of this measure for entangled many-particle states are discussed. k particles specify k nits in such a way that k mutually commuting measurements of observables with n possible outcomes are sufficient to determine the information.

“…Particular physical systems exhibit symmetries that constrain and refine the broad picture of unitary evolution presented so far [9,10]. This work focuses on systems in which a limited number of pairs of states can be coupled at any given time.…”

Section: Parallelism In State Synthesis and Unitary Transformatiomentioning

confidence: 99%

“…The controlled gate of item 4 might be decomposed into local gates and the gate of item 3 using standard techniques [8,9,10]. The procedure for realizing ∧ 1 (V ) is as follows.…”

Section: A a Non-local Controlled Unitary Gatementioning

confidence: 99%

Parallelism for quantum computation with qudits

O’Leary

Brennen

Bullock³

2006

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.