20 research outputs found
Sufficient condition on noise correlations for scalable quantum computing
I study the effectiveness of fault-tolerant quantum computation against
correlated Hamiltonian noise, and derive a sufficient condition for
scalability. Arbitrarily long quantum computations can be executed reliably
provided that noise terms acting collectively on k system qubits are
sufficiently weak, and decay sufficiently rapidly with increasing k and with
increasing spatial separation of the qubits.Comment: 13 pages, 1 figure. (v2) Minor corrections and clarification
qTorch: The Quantum Tensor Contraction Handler
Classical simulation of quantum computation is necessary for studying the
numerical behavior of quantum algorithms, as there does not yet exist a large
viable quantum computer on which to perform numerical tests. Tensor network
(TN) contraction is an algorithmic method that can efficiently simulate some
quantum circuits, often greatly reducing the computational cost over methods
that simulate the full Hilbert space. In this study we implement a tensor
network contraction program for simulating quantum circuits using multi-core
compute nodes. We show simulation results for the Max-Cut problem on 3- through
7-regular graphs using the quantum approximate optimization algorithm (QAOA),
successfully simulating up to 100 qubits. We test two different methods for
generating the ordering of tensor index contractions: one is based on the tree
decomposition of the line graph, while the other generates ordering using a
straight-forward stochastic scheme. Through studying instances of QAOA
circuits, we show the expected result that as the treewidth of the quantum
circuit's line graph decreases, TN contraction becomes significantly more
efficient than simulating the whole Hilbert space. The results in this work
suggest that tensor contraction methods are superior only when simulating
Max-Cut/QAOA with graphs of regularities approximately five and below. Insight
into this point of equal computational cost helps one determine which
simulation method will be more efficient for a given quantum circuit. The
stochastic contraction method outperforms the line graph based method only when
the time to calculate a reasonable tree decomposition is prohibitively
expensive. Finally, we release our software package, qTorch (Quantum TensOR
Contraction Handler), intended for general quantum circuit simulation.Comment: 21 pages, 8 figure
Quantum gates by resonantly driving many-body eigenstates, with a focus on Polychronakos' model
Accurate, nontrivial quantum operations on many qubits are experimentally
challenging. As opposed to the standard approach of compiling larger unitaries
into sequences of 2-qubit gates, we propose a protocol on Hamiltonian control
fields which implements highly selective multi-qubit gates in a
strongly-coupled many-body quantum system. We exploit the selectiveness of
resonant driving to exchange only 2 out of eigenstates of some background
Hamiltonian, and discuss a basis transformation, the eigengate, that makes this
operation relevant to the computational basis. The latter has a second use as a
Hahn echo which undoes the dynamical phases due to the background Hamiltonian.
We find that the error of such protocols scales favourably with the gate time
as , but the protocol becomes inefficient with a growing number of
qubits N. The framework is numerically tested in the context of a spin chain
model first described by Polychronakos, for which we show that an earlier
solution method naturally gives rise to an eigengate. Our techniques could be
of independent interest for the theory of driven many-body systems.Comment: 21 pages, 7 figure