211 research outputs found
Calculating Unknown Eigenvalues with a Quantum Algorithm
Quantum algorithms are able to solve particular problems exponentially faster
than conventional algorithms, when implemented on a quantum computer. However,
all demonstrations to date have required already knowing the answer to
construct the algorithm. We have implemented the complete quantum phase
estimation algorithm for a single qubit unitary in which the answer is
calculated by the algorithm. We use a new approach to implementing the
controlled-unitary operations that lie at the heart of the majority of quantum
algorithms that is more efficient and does not require the eigenvalues of the
unitary to be known. These results point the way to efficient quantum
simulations and quantum metrology applications in the near term, and to
factoring large numbers in the longer term. This approach is architecture
independent and thus can be used in other physical implementations
Adding control to arbitrary unknown quantum operations
While quantum computers promise significant advantages, the complexity of
quantum algorithms remains a major technological obstacle. We have developed
and demonstrated an architecture-independent technique that simplifies adding
control qubits to arbitrary quantum operations-a requirement in many quantum
algorithms, simulations and metrology. The technique is independent of how the
operation is done, does not require knowledge of what the operation is, and
largely separates the problems of how to implement a quantum operation in the
laboratory and how to add a control. We demonstrate an entanglement-based
version in a photonic system, realizing a range of different two-qubit gates
with high fidelity.Comment: 9 pages, 8 figure
Quantum Simulation of Spin Chains Coupled to Bosonic Modes with Superconducting Circuits
We propose the implementation of a digital quantum simulation of spin chains
coupled to bosonic field modes in superconducting circuits. Gates with high
fidelities allows one to simulate a variety of Ising magnetic pairing
interactions with transverse field, Tavis-Cummings interaction between spins
and a bosonic mode, and a spin model with three-body terms. We analyze the
feasibility of the implementation in realistic circuit quantum electrodynamics
setups, where the interactions are either realized via capacitive couplings or
mediated by microwave resonators.Comment: Chapter in R. S. Anderssen et al. (eds.), Mathematics for Industry 11
(Springer Japan, 2015
Experimental realisation of Shor's quantum factoring algorithm using qubit recycling
Quantum computational algorithms exploit quantum mechanics to solve problems
exponentially faster than the best classical algorithms. Shor's quantum
algorithm for fast number factoring is a key example and the prime motivator in
the international effort to realise a quantum computer. However, due to the
substantial resource requirement, to date, there have been only four
small-scale demonstrations. Here we address this resource demand and
demonstrate a scalable version of Shor's algorithm in which the n qubit control
register is replaced by a single qubit that is recycled n times: the total
number of qubits is one third of that required in the standard protocol.
Encoding the work register in higher-dimensional states, we implement a
two-photon compiled algorithm to factor N=21. The algorithmic output is
distinguishable from noise, in contrast to previous demonstrations. These
results point to larger-scale implementations of Shor's algorithm by harnessing
scalable resource reductions applicable to all physical architectures.Comment: 7 pages, 3 figure
Experimental demonstration of a hyper-entangled ten-qubit Schr\"odinger cat state
Coherent manipulation of an increasing number of qubits for the generation of
entangled states has been an important goal and benchmark in the emerging field
of quantum information science. The multiparticle entangled states serve as
physical resources for measurement-based quantum computing and high-precision
quantum metrology. However, their experimental preparation has proved extremely
challenging. To date, entangled states up to six, eight atoms, or six photonic
qubits have been demonstrated. Here, by exploiting both the photons'
polarization and momentum degrees of freedom, we report the creation of
hyper-entangled six-, eight-, and ten-qubit Schr\"odinger cat states. We
characterize the cat states by evaluating their fidelities and detecting the
presence of genuine multi-partite entanglement. Small modifications of the
experimental setup will allow the generation of various graph states up to ten
qubits. Our method provides a shortcut to expand the effective Hilbert space,
opening up interesting applications such as quantum-enhanced super-resolving
phase measurement, graph-state generation for anyonic simulation and
topological error correction, and novel tests of nonlocality with
hyper-entanglement.Comment: 11 pages, 5 figures, comments welcom
Quantum Simulation of Tunneling in Small Systems
A number of quantum algorithms have been performed on small quantum
computers; these include Shor's prime factorization algorithm, error
correction, Grover's search algorithm and a number of analog and digital
quantum simulations. Because of the number of gates and qubits necessary,
however, digital quantum particle simulations remain untested. A contributing
factor to the system size required is the number of ancillary qubits needed to
implement matrix exponentials of the potential operator. Here, we show that a
set of tunneling problems may be investigated with no ancillary qubits and a
cost of one single-qubit operator per time step for the potential evolution. We
show that physically interesting simulations of tunneling using 2 qubits (i.e.
on 4 lattice point grids) may be performed with 40 single and two-qubit gates.
Approximately 70 to 140 gates are needed to see interesting tunneling dynamics
in three-qubit (8 lattice point) simulations.Comment: 4 pages, 2 figure
Digital Quantum Simulation of the Statistical Mechanics of a Frustrated Magnet
Many interesting problems in physics, chemistry, and computer science are
equivalent to problems of interacting spins. However, most of these problems
require computational resources that are out of reach by classical computers. A
promising solution to overcome this challenge is to exploit the laws of quantum
mechanics to perform simulation. Several "analog" quantum simulations of
interacting spin systems have been realized experimentally. However, relying on
adiabatic techniques, these simulations are limited to preparing ground states
only. Here we report the first experimental results on a "digital" quantum
simulation on thermal states; we simulated a three-spin frustrated magnet, a
building block of spin ice, with an NMR quantum information processor, and we
are able to explore the phase diagram of the system at any simulated
temperature and external field. These results serve as a guide for identifying
the challenges for performing quantum simulation on physical systems at finite
temperatures, and pave the way towards large scale experimental simulations of
open quantum systems in condensed matter physics and chemistry.Comment: 7 pages for the main text plus 6 pages for the supplementary
material
Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
Quantum ground-state problems are computationally hard problems; for general
many-body Hamiltonians, there is no classical or quantum algorithm known to be
able to solve them efficiently. Nevertheless, if a trial wavefunction
approximating the ground state is available, as often happens for many problems
in physics and chemistry, a quantum computer could employ this trial
wavefunction to project the ground state by means of the phase estimation
algorithm (PEA). We performed an experimental realization of this idea by
implementing a variational-wavefunction approach to solve the ground-state
problem of the Heisenberg spin model with an NMR quantum simulator. Our
iterative phase estimation procedure yields a high accuracy for the
eigenenergies (to the 10^-5 decimal digit). The ground-state fidelity was
distilled to be more than 80%, and the singlet-to-triplet switching near the
critical field is reliably captured. This result shows that quantum simulators
can better leverage classical trial wavefunctions than classical computers.Comment: 11 pages, 13 figure
Heralded generation of entangled photon pairs
Entangled photons are a crucial resource for quantum communication and linear
optical quantum computation. Unfortunately, the applicability of many
photon-based schemes is limited due to the stochastic character of the photon
sources. Therefore, a worldwide effort has focused in overcoming the limitation
of probabilistic emission by generating two-photon entangled states conditioned
on the detection of auxiliary photons. Here we present the first heralded
generation of photon states that are maximally entangled in polarization with
linear optics and standard photon detection from spontaneous parametric
down-conversion. We utilize the down-conversion state corresponding to the
generation of three photon pairs, where the coincident detection of four
auxiliary photons unambiguously heralds the successful preparation of the
entangled state. This controlled generation of entangled photon states is a
significant step towards the applicability of a linear optics quantum network,
in particular for entanglement swapping, quantum teleportation, quantum
cryptography and scalable approaches towards photonics-based quantum computing
Implementation of a Toffoli Gate with Superconducting Circuits
The quantum Toffoli gate allows universal reversible classical computation.
It is also an important primitive in many quantum circuits and quantum error
correction schemes. Here we demonstrate the realization of a Toffoli gate with
three superconducting transmon qubits coupled to a microwave resonator. By
exploiting the third energy level of the transmon qubit, the number of
elementary gates needed for the implementation of the Toffoli gate, as well as
the total gate time can be reduced significantly in comparison to theoretical
proposals using two-level systems only. We characterize the performance of the
gate by full process tomography and Monte Carlo process certification. The gate
fidelity is found to be %.Comment: 4 pages, 5figure
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