667 research outputs found
Hamiltonian quantum simulation with bounded-strength controls
We propose dynamical control schemes for Hamiltonian simulation in many-body
quantum systems that avoid instantaneous control operations and rely solely on
realistic bounded-strength control Hamiltonians. Each simulation protocol
consists of periodic repetitions of a basic control block, constructed as a
suitable modification of an "Eulerian decoupling cycle," that would otherwise
implement a trivial (zero) target Hamiltonian. For an open quantum system
coupled to an uncontrollable environment, our approach may be employed to
engineer an effective evolution that simulates a target Hamiltonian on the
system, while suppressing unwanted decoherence to the leading order. We present
illustrative applications to both closed- and open-system simulation settings,
with emphasis on simulation of non-local (two-body) Hamiltonians using only
local (one-body) controls. In particular, we provide simulation schemes
applicable to Heisenberg-coupled spin chains exposed to general linear
decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian
starting from Ising-coupled qubits, as potentially relevant to the dynamical
generation of a topologically protected quantum memory. Additional implications
for quantum information processing are discussed.Comment: 24 pages, 5 color figure
Combining dynamical decoupling with fault-tolerant quantum computation
We study how dynamical decoupling (DD) pulse sequences can improve the reliability of quantum computers. We prove upper bounds on the accuracy of DD-protected quantum gates and derive sufficient conditions for DD-protected gates to outperform unprotected gates. Under suitable conditions, fault-tolerant quantum circuits constructed from DD-protected gates can tolerate stronger noise and have a lower overhead cost than fault-tolerant circuits constructed from unprotected gates. Our accuracy estimates depend on the dynamics of the bath that couples to the quantum computer and can be expressed either in terms of the operator norm of the bath’s Hamiltonian or in terms of the power spectrum of bath correlations; we explain in particular how the performance of recursively generated concatenated pulse sequences can be analyzed from either viewpoint. Our results apply to Hamiltonian noise models with limited spatial correlations
Optimally combining dynamical decoupling and quantum error correction
We show how dynamical decoupling (DD) and quantum error correction (QEC) can
be optimally combined in the setting of fault tolerant quantum computing. To
this end we identify the optimal generator set of DD sequences designed to
protect quantum information encoded into stabilizer subspace or subsystem
codes. This generator set, comprising the stabilizers and logical operators of
the code, minimizes a natural cost function associated with the length of DD
sequences. We prove that with the optimal generator set the restrictive
local-bath assumption used in earlier work on hybrid DD-QEC schemes, can be
significantly relaxed, thus bringing hybrid DD-QEC schemes, and their
potentially considerable advantages, closer to realization.Comment: 6 pages, 1 figur
Randomized Dynamical Decoupling Strategies and Improved One-Way Key Rates for Quantum Cryptography
The present thesis deals with various methods of quantum error correction. It
is divided into two parts. In the first part, dynamical decoupling methods are
considered which have the task of suppressing the influence of residual
imperfections in a quantum memory. The suppression is achieved by altering the
dynamics of an imperfect quantum memory with the help of a sequence of local
unitary operations applied to the qudits. Whereas up to now the operations of
such decoupling sequences have been constructed in a deterministic fashion,
strategies are developed in this thesis which construct the operations by
random selection from a suitable set. Furthermore, it is investigated if and
how the discussed decoupling strategies can be employed to protect a quantum
computation running on the quantum memory.
The second part of the thesis deals with quantum error-correcting codes and
protocols for quantum key distribution. The focus is on the BB84 and the
6-state protocol making use of only one-way communication during the error
correction and privacy amplification steps. It is shown that by adding
additional errors to the preliminary key (a process called noisy preprocessing)
followed by the use of a structured block code, higher secure key rates may be
obtained. For the BB84 protocol it is shown that iterating the combined
preprocessing leads to an even higher gain.Comment: PhD thesis, 223 pages, TU Darmstadt;
http://tuprints.ulb.tu-darmstadt.de/1389
Automated Synthesis of Dynamically Corrected Quantum Gates
We address the problem of constructing dynamically corrected gates for
non-Markovian open quantum systems in settings where limitations on the
available control inputs and/or the presence of control noise make existing
analytical approaches unfeasible. By focusing on the important case of
singlet-triplet electron spin qubits, we show how ideas from optimal control
theory may be used to automate the synthesis of dynamically corrected gates
that simultaneously minimize the system's sensitivity against both decoherence
and control errors. Explicit sequences for effecting robust single-qubit
rotations subject to realistic timing and pulse-shaping constraints are
provided, which can deliver substantially improved gate fidelity for
state-of-the-art experimental capabilities.Comment: 5 pages; further restructure and expansio
Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
We critically examine the internal consistency of a set of minimal
assumptions entering the theory of fault-tolerant quantum error correction for
Markovian noise. These assumptions are: fast gates, a constant supply of fresh
and cold ancillas, and a Markovian bath. We point out that these assumptions
may not be mutually consistent in light of rigorous formulations of the
Markovian approximation. Namely, Markovian dynamics requires either the
singular coupling limit (high temperature), or the weak coupling limit (weak
system-bath interaction). The former is incompatible with the assumption of a
constant and fresh supply of cold ancillas, while the latter is inconsistent
with fast gates. We discuss ways to resolve these inconsistencies. As part of
our discussion we derive, in the weak coupling limit, a new master equation for
a system subject to periodic driving.Comment: 19 pages. v2: Significantly expanded version. New title. Includes a
debate section in response to comments on the previous version, many of which
appeared here http://dabacon.org/pontiff/?p=959 and here
http://dabacon.org/pontiff/?p=1028. Contains a new derivation of the
Markovian master equation with periodic drivin
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