4,457 research outputs found
Arbitrary state controlled-unitary gate by adiabatic passage
We propose a robust scheme involving atoms fixed in an optical cavity to
directly implement the universal controlled-unitary gate. The present technique
based on adiabatic passage uses novel dark states well suited for the
controlled-rotation operation. We show that these dark states allow the robust
implementation of a gate that is a generalisation of the controlled-unitary
gate to the case where the control qubit can be selected to be an arbitrary
state. This gate has potential applications to the rapid implementation of
quantum algorithms such as of the projective measurement algorithm. This
process is decoherence-free since excited atomic states and cavity modes are
not populated during the dynamics.Comment: 6 pages, 6 figure, submitted to Phys. Rev.
Quantum State Preparation by Controlled Dissipation in Finite Time: From Classical to Quantum Controllers
We propose a general scheme for dissipatively preparing arbitrary pure
quantum states on a multipartite qubit register in a finite number of basic
control blocks. Our "splitting-subspace" approach relies on control resources
that are available in a number of scalable quantum technologies (complete
unitary control on the target system, an ancillary resettable qubit and
controlled-not gates between the target and the ancilla), and can be seen as a
"quantum-controller" implementation of a sequence of classical feedback loops.
We show how a large degree of flexibility exists in engineering the required
conditional operations, and make explicit contact with a stabilization protocol
used for dissipative quantum state preparation and entanglement generation in
recent experiments with trapped ions.Comment: 10 pages, 2 figures. Submitted to CDC 201
Exact two-qubit universal quantum circuit
We provide an analytic way to implement any arbitrary two-qubit unitary
operation, given an entangling two-qubit gate together with local gates. This
is shown to provide explicit construction of a universal quantum circuit that
exactly simulates arbitrary two-qubit operations in SU(4). Each block in this
circuit is given in a closed form solution. We also provide a uniform upper
bound of the applications of the given entangling gates, and find that exactly
half of all the Controlled-Unitary gates satisfy the same upper bound as the
CNOT gate. These results allow for the efficient implementation of operations
in SU(4) required for both quantum computation and quantum simulation.Comment: 5 page
Quantum Algorithm Implementations for Beginners
As quantum computers become available to the general public, the need has
arisen to train a cohort of quantum programmers, many of whom have been
developing classical computer programs for most of their careers. While
currently available quantum computers have less than 100 qubits, quantum
computing hardware is widely expected to grow in terms of qubit count, quality,
and connectivity. This review aims to explain the principles of quantum
programming, which are quite different from classical programming, with
straightforward algebra that makes understanding of the underlying fascinating
quantum mechanical principles optional. We give an introduction to quantum
computing algorithms and their implementation on real quantum hardware. We
survey 20 different quantum algorithms, attempting to describe each in a
succinct and self-contained fashion. We show how these algorithms can be
implemented on IBM's quantum computer, and in each case, we discuss the results
of the implementation with respect to differences between the simulator and the
actual hardware runs. This article introduces computer scientists, physicists,
and engineers to quantum algorithms and provides a blueprint for their
implementations
Fault-tolerant quantum computation with cluster states
The one-way quantum computing model introduced by Raussendorf and Briegel
[Phys. Rev. Lett. 86 (22), 5188-5191 (2001)] shows that it is possible to
quantum compute using only a fixed entangled resource known as a cluster state,
and adaptive single-qubit measurements. This model is the basis for several
practical proposals for quantum computation, including a promising proposal for
optical quantum computation based on cluster states [M. A. Nielsen,
arXiv:quant-ph/0402005, accepted to appear in Phys. Rev. Lett.]. A significant
open question is whether such proposals are scalable in the presence of
physically realistic noise. In this paper we prove two threshold theorems which
show that scalable fault-tolerant quantum computation may be achieved in
implementations based on cluster states, provided the noise in the
implementations is below some constant threshold value. Our first threshold
theorem applies to a class of implementations in which entangling gates are
applied deterministically, but with a small amount of noise. We expect this
threshold to be applicable in a wide variety of physical systems. Our second
threshold theorem is specifically adapted to proposals such as the optical
cluster-state proposal, in which non-deterministic entangling gates are used. A
critical technical component of our proofs is two powerful theorems which
relate the properties of noisy unitary operations restricted to act on a
subspace of state space to extensions of those operations acting on the entire
state space.Comment: 31 pages, 54 figure
Randomized Benchmarking of Multi-Qubit Gates
As experimental platforms for quantum information processing continue to
mature, characterization of the quality of unitary gates that can be applied to
their quantum bits (qubits) becomes essential. Eventually, the quality must be
sufficiently high to support arbitrarily long quantum computations. Randomized
benchmarking already provides a platform-independent method for assessing the
quality of one-qubit rotations. Here we describe an extension of this method to
multi-qubit gates. We provide a platform-independent protocol for evaluating
the performance of experimental Clifford unitaries, which form the basis of
fault-tolerant quantum computing. We implemented the benchmarking protocol with
trapped-ion two-qubit phase gates and one-qubit gates and found an error per
random two-qubit Clifford unitary of , thus setting the first
benchmark for such unitaries. By implementing a second set of sequences with an
extra two-qubit phase gate at each step, we extracted an error per phase gate
of . We conducted these experiments with movable,
sympathetically cooled ions in a multi-zone Paul trap - a system that can in
principle be scaled to larger numbers of ions.Comment: Corrected description of parallel single-qubit benchmark experiment.
Results unchange
Linear optics quantum Toffoli and Fredkin gates
We design linear optics multiqubit quantum logic gates. We assume the
traditional encoding of a qubit onto state of a single photon in two modes
(e.g. spatial or polarization). We suggest schemes allowing direct
probabilistic realization of the fundamental Toffoli and Fredkin gates without
resorting to a sequence of single- and two-qubit gates. This yields more
compact schemes and potentially reduces the number of ancilla photons. The
proposed setups involve passive linear optics, sources of auxiliary single
photons or maximally entangled pairs of photons, and single-photon detectors.
In particular, we propose an interferometric implementation of the Toffoli gate
in the coincidence basis, which does not require any ancilla photons and is
experimentally feasible with current technology.Comment: 8 pages, 4 figures, RevTeX
Ancilla-Driven Universal Quantum Computation
We propose a method of manipulating a quantum register remotely with the help
of a single ancilla that steers the evolution of the register. The fully
controlled ancilla qubit is coupled to the computational register solely via a
fixed unitary two-qubit interaction, E, and then measured in suitable bases. We
characterize all interactions E that induce a unitary, step-wise deterministic
measurement back-action on the register sufficient to implement any arbitrary
quantum channel. Our scheme offers significant experimental advantages for
implementing computations, preparing states and performing generalized
measurements as no direct control of the register is required.Comment: 4 pages, 3 figure
Majorana-based fermionic quantum computation
Because Majorana zero modes store quantum information non-locally, they are
protected from noise, and have been proposed as a building block for a quantum
computer. We show how to use the same protection from noise to implement
universal fermionic quantum computation. Our architecture requires only two
Majoranas to encode a fermionic quantum degree of freedom, compared to
alternative implementations which require a minimum of four Majoranas for a
spin quantum degree of freedom. The fermionic degrees of freedom support both
unitary coupled cluster variational quantum eigensolver and quantum phase
estimation algorithms, proposed for quantum chemistry simulations. Because we
avoid the Jordan-Wigner transformation, our scheme has a lower overhead for
implementing both of these algorithms, and the simulation of Trotterized
Hubbard Hamiltonian in time per unitary step. We finally
demonstrate magic state distillation in our fermionic architecture, giving a
universal set of topologically protected fermionic quantum gates.Comment: 4 pages + 4 page appendix, 4 figures, 2 table
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