16,044 research outputs found
Optimal synthesis of general multi-qutrit quantum computation
Quantum circuits of a general quantum gate acting on multiple -level
quantum systems play a prominent role in multi-valued quantum computation. We
first propose a new recursive Cartan decomposition of semi-simple unitary Lie
group (arbitrary -qutrit gate). Note that the decomposition
completely decomposes an n-qutrit gate into local and non-local operations. We
design an explicit quantum circuit for implementing arbitrary two-qutrit gates,
and the cost of our construction is 21 generalized controlled X (GCX) and
controlled increment (CINC) gates less than the earlier best result of 26 GGXs.
Moreover, we extend the program to the -qutrit system, and the quantum
circuit of generic -qutrit gates contained
GGXs and CINCs is presented. Such asymptotically optimal structure is the best
known result so far.Comment: 16 pages, 14 figure
Systematic-Error-Tolerant Multiqubit Holonomic Entangling Gates
Quantum holonomic gates hold built-in resilience to local noises and provide a promising approach for implementing fault-tolerant quantum computation. We propose to realize high-fidelity holonomic (N + 1)-qubit controlled gates using Rydberg atoms confined in optical arrays or superconducting circuits. We identify the scheme, deduce the effective multi-body Hamiltonian, and determine the working condition of the multiqubit gate. Uniquely, the multiqubit gate is immune to systematic errors, i.e., laser parameter fluctuations and motional dephasing, as the N control atoms largely remain in the much stable qubit space during the operation. We show that CN-NOT gates can reach same level of fidelity at a given gate time for N ≤ 5 under a suitable choice of parameters, and the gate tolerance against errors in systematic parameters can be further enhanced through optimal pulse engineering. In case of Rydberg atoms, the proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade. Our study paves a new route to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or with superconducting circuits. It contributes to current efforts in developing scalable quantum computation with trapped atoms and fabricable superconducting devices
Concrete resource analysis of the quantum linear system algorithm used to compute the electromagnetic scattering cross section of a 2D target
We provide a detailed estimate for the logical resource requirements of the
quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)]
including the recently described elaborations [Phys. Rev. Lett. 110, 250504
(2013)]. Our resource estimates are based on the standard quantum-circuit model
of quantum computation; they comprise circuit width, circuit depth, the number
of qubits and ancilla qubits employed, and the overall number of elementary
quantum gate operations as well as more specific gate counts for each
elementary fault-tolerant gate from the standard set {X, Y, Z, H, S, T, CNOT}.
To perform these estimates, we used an approach that combines manual analysis
with automated estimates generated via the Quipper quantum programming language
and compiler. Our estimates pertain to the example problem size N=332,020,680
beyond which, according to a crude big-O complexity comparison, QLSA is
expected to run faster than the best known classical linear-system solving
algorithm. For this problem size, a desired calculation accuracy 0.01 requires
an approximate circuit width 340 and circuit depth of order if oracle
costs are excluded, and a circuit width and depth of order and
, respectively, if oracle costs are included, indicating that the
commonly ignored oracle resources are considerable. In addition to providing
detailed logical resource estimates, it is also the purpose of this paper to
demonstrate explicitly how these impressively large numbers arise with an
actual circuit implementation of a quantum algorithm. While our estimates may
prove to be conservative as more efficient advanced quantum-computation
techniques are developed, they nevertheless provide a valid baseline for
research targeting a reduction of the resource requirements, implying that a
reduction by many orders of magnitude is necessary for the algorithm to become
practical.Comment: 37 pages, 40 figure
Imperfection effects for multiple applications of the quantum wavelet transform
We study analytically and numerically the effects of various imperfections in
a quantum computation of a simple dynamical model based on the Quantum Wavelet
Transform (QWT). The results for fidelity timescales, obtained for a large
range of error amplitudes and number of qubits, imply that for static
imperfections the threshold for fault-tolerant quantum computation is decreased
by a few orders of magnitude compared to the case of random errors.Comment: revtex, 11 pages, 13 figures, research at Quantware MIPS Center
http://www.quantware.ups-tlse.f
Asymptotically Optimal Quantum Circuits for d-level Systems
As a qubit is a two-level quantum system whose state space is spanned by |0>,
|1>, so a qudit is a d-level quantum system whose state space is spanned by
|0>,...,|d-1>. Quantum computation has stimulated much recent interest in
algorithms factoring unitary evolutions of an n-qubit state space into
component two-particle unitary evolutions. In the absence of symmetry, Shende,
Markov and Bullock use Sard's theorem to prove that at least C 4^n two-qubit
unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa
(VMS) use the QR matrix factorization and Gray codes in an optimal order
construction involving two-particle evolutions. In this work, we note that
Sard's theorem demands C d^{2n} two-qudit unitary evolutions to construct a
generic (symmetry-less) n-qudit evolution. However, the VMS result applied to
virtual-qubits only recovers optimal order in the case that d is a power of
two. We further construct a QR decomposition for d-multi-level quantum logics,
proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing
the complexity question for all d-level systems (d finite.) Gray codes are not
required, and the optimal Theta(d^{2n}) asymptotic also applies to gate
libraries where two-qudit interactions are restricted by a choice of certain
architectures.Comment: 18 pages, 5 figures (very detailed.) MatLab files for factoring qudit
unitary into gates in MATLAB directory of source arxiv format. v2: minor
change
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