36 research outputs found
Phase estimation as a quantum nondemolition measurement
The phase estimation algorithm, which is at the heart of a variety of quantum
algorithms, including Shor's factoring algorithm, allows a quantum computer to
accurately determine an eigenvalue of an unitary operator. Quantum
nondemolition measurements are a quantum mechanical procedure, used to overcome
the standard quantum limit when measuring an observable. We show that the phase
estimation algorithm, in both the discrete and continuous variable setting, can
be viewed as a quantum nondemolition measurement.Comment: 4 pages, 2 figures, RevTeX
Measurement of an integral of a classical field with a single quantum particle
A method for measuring an integral of a classical field via local interaction
of a single quantum particle in a superposition of 2^N states is presented. The
method is as efficient as a quantum method with N qubits passing through the
field one at a time and it is exponentially better than any known classical
method that uses N bits passing through the field one at a time. A related
method for searching a string with a quantum particle is proposed.Comment: 3 page
ROM-based computation: quantum versus classical
We introduce a model of computation based on read only memory (ROM), which
allows us to compare the space-efficiency of reversible, error-free classical
computation with reversible, error-free quantum computation. We show that a
ROM-based quantum computer with one writable qubit is universal, whilst two
writable bits are required for a universal classical ROM-based computer. We
also comment on the time-efficiency advantages of quantum computation within
this model.Comment: 12 pages, 3 figures, minor corrections + section 5 substantially
change
Substituting a qubit for an arbitrarily large number of classical bits
We show that a qubit can be used to substitute for an arbitrarily large
number of classical bits. We consider a physical system S interacting locally
with a classical field phi(x) as it travels directly from point A to point B.
The field has the property that its integrated value is an integer multiple of
some constant. The problem is to determine whether the integer is odd or even.
This task can be performed perfectly if S is a qubit. On the otherhand, if S is
a classical system then we show that it must carry an arbitrarily large amount
of classical information. We identify the physical reason for such a huge
quantum advantage, and show that it also implies a large difference between the
size of quantum and classical memories necessary for some computations. We also
present a simple proof that no finite amount of one-way classical communication
can perfectly simulate the effect of quantum entanglement.Comment: 8 pages, LaTeX, no figures. v2: added result on entanglement
simulation with classical communication; v3: minor correction to main proof,
change of title, added referenc
Preparing encoded states in an oscillator
Recently a scheme has been proposed for constructing quantum error-correcting
codes that embed a finite-dimensional code space in the infinite-dimensional
Hilbert space of a system described by continuous quantum variables. One of the
difficult steps in this scheme is the preparation of the encoded states. We
show how these states can be generated by coupling a continuous quantum
variable to a single qubit. An ion trap quantum computer provides a natural
setting for a continuous system coupled to a qubit. We discuss how encoded
states may be generated in an ion trap.Comment: 5 pages, 4 figures, RevTe
Performing joint measurements and transformations on several qubits by operating on a single control qubit
An n-qubit quantum register can in principle be completely controlled by
operating on a single qubit that interacts with the register via an appropriate
fixed interaction. We consider a hypothetical system consisting of n spin-1/2
nuclei that interact with an electron spin via a magnetic interaction. We
describe algorithms that measure non-trivial joint observables on the register
by acting on the control spin only. For large n this is not an efficient model
for universal quantum computation but it can be modified to an efficient one if
one allows n possible positions of the control particle.
This toy model of measurements illustrates in which way specific interactions
between the register and a probe particle support specific types of joint
measurements in the sense that some joint observables can be measured by simple
sequences of operations on the probe particle.Comment: 7 pages, revtex, 3 figure
Fast simulation of a quantum phase transition in an ion-trap realisable unitary map
We demonstrate a method of exploring the quantum critical point of the Ising
universality class using unitary maps that have recently been demonstrated in
ion trap quantum gates. We reverse the idea with which Feynman conceived
quantum computing, and ask whether a realisable simulation corresponds to a
physical system. We proceed to show that a specific simulation (a unitary map)
is physically equivalent to a Hamiltonian that belongs to the same universality
class as the transverse Ising Hamiltonian. We present experimental signatures,
and numerical simulation for these in the six-qubit case.Comment: 12 pages, 6 figure
Improved algorithm for quantum separability and entanglement detection
Determining whether a quantum state is separable or entangled is a problem of
fundamental importance in quantum information science. It has recently been
shown that this problem is NP-hard. There is a highly inefficient `basic
algorithm' for solving the quantum separability problem which follows from the
definition of a separable state. By exploiting specific properties of the set
of separable states, we introduce a new classical algorithm that solves the
problem significantly faster than the `basic algorithm', allowing a feasible
separability test where none previously existed e.g. in 3-by-3-dimensional
systems. Our algorithm also provides a novel tool in the experimental detection
of entanglement.Comment: 4 pages, revtex4, no figure
Implementing the Quantum Random Walk
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the variance on the line, and the mixing time on the circle increase quadratically faster in the quantum versions as compared to the classical versions. Here, we propose a scheme to implement the quantum random walk on a line and on a circle in an ion trap quantum computer. With current ion trap technology, the number of steps that could be experimentally implemented will be relatively small. However, we show how the enhanced features of these walks could be observed experimentally. In the limit of strong decoherence, the quantum random walk tends to the classical random walk. By measuring the degree to which the walk remains `quantum', this algorithm could serve as an important benchmarking protocol for ion trap quantum computers