15 research outputs found
Entanglement and its Role in Shor's Algorithm
Entanglement has been termed a critical resource for quantum information
processing and is thought to be the reason that certain quantum algorithms,
such as Shor's factoring algorithm, can achieve exponentially better
performance than their classical counterparts. The nature of this resource is
still not fully understood: here we use numerical simulation to investigate how
entanglement between register qubits varies as Shor's algorithm is run on a
quantum computer. The shifting patterns in the entanglement are found to relate
to the choice of basis for the quantum Fourier transform.Comment: 15 pages, 4 eps figures, v1-3 were for conference proceedings (not
included in the end); v4 is improved following referee comments, expanded
explanations and added reference
Using Quantum Computers for Quantum Simulation
Numerical simulation of quantum systems is crucial to further our
understanding of natural phenomena. Many systems of key interest and
importance, in areas such as superconducting materials and quantum chemistry,
are thought to be described by models which we cannot solve with sufficient
accuracy, neither analytically nor numerically with classical computers. Using
a quantum computer to simulate such quantum systems has been viewed as a key
application of quantum computation from the very beginning of the field in the
1980s. Moreover, useful results beyond the reach of classical computation are
expected to be accessible with fewer than a hundred qubits, making quantum
simulation potentially one of the earliest practical applications of quantum
computers. In this paper we survey the theoretical and experimental development
of quantum simulation using quantum computers, from the first ideas to the
intense research efforts currently underway.Comment: 43 pages, 136 references, review article, v2 major revisions in
response to referee comments, v3 significant revisions, identical to
published version apart from format, ArXiv version has table of contents and
references in alphabetical orde
Quantum measurements of atoms using cavity QED
Generalized quantum measurements are an important extension of projective or
von Neumann measurements, in that they can be used to describe any measurement
that can be implemented on a quantum system. We describe how to realize two
non-standard quantum measurements using cavity quantum electrodynamics (QED).
The first measurement optimally and unabmiguously distinguishes between two
non-orthogonal quantum states. The second example is a measurement that
demonstrates superadditive quantum coding gain. The experimental tools used are
single-atom unitary operations effected by Ramsey pulses and two-atom
Tavis-Cummings interactions. We show how the superadditive quantum coding gain
is affected by errors in the field-ionisation detection of atoms, and that even
with rather high levels of experimental imperfections, a reasonable amount of
superadditivity can still be seen. To date, these types of measurement have
only been realized on photons. It would be of great interest to have
realizations using other physical systems. This is for fundamental reasons, but
also since quantum coding gain in general increases with code word length, and
a realization using atoms could be more easily scaled than existing
realizations using photons.Comment: 10 pages, 5 figure
Ancilla-based quantum simulation
We consider simulating the BCS Hamiltonian, a model of low temperature
superconductivity, on a quantum computer. In particular we consider conducting
the simulation on the qubus quantum computer, which uses a continuous variable
ancilla to generate interactions between qubits. We demonstrate an O(N^3)
improvement over previous work conducted on an NMR computer [PRL 89 057904
(2002) & PRL 97 050504 (2006)] for the nearest neighbour and completely general
cases. We then go on to show methods to minimise the number of operations
needed per time step using the qubus in three cases; a completely general case,
a case of exponentially decaying interactions and the case of fixed range
interactions. We make these results controlled on an ancilla qubit so that we
can apply the phase estimation algorithm, and hence show that when N \geq 5,
our qubus simulation requires significantly less operations that a similar
simulation conducted on an NMR computer.Comment: 20 pages, 10 figures: V2 added section on phase estimation and
performing controlled unitaries, V3 corrected minor typo
Approved for External Publication Entanglement and its Role in Shor’s Algorithm
entanglement, Shor's algorithm Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resource is still not fully understood: here we use numerical simulation to investigate how entanglement between register qubits varies as Shor's algorithm is run on a quantum computer. The patterns in the entanglement are found to correlate with the choice of basis for the quantum Fourier transform rather than with any crucially quantum aspect of the algorithm