11 research outputs found
Stimulated Raman adiabatic passage-like protocols for amplitude transfer generalize to many bipartite graphs
Adiabatic passage techniques, used to drive a system from one quantum state
into another, find widespread application in physics and chemistry. We focus on
techniques to spatially transport a quantum amplitude over a strongly coupled
system, such as STImulated Raman Adiabatic Passage (STIRAP) and Coherent
Tunnelling by Adiabatic Passage (CTAP). Previous results were shown to work on
certain graphs, such as linear chains, square and triangular lattices, and
branched chains. We prove that similar protocols work much more generally, in a
large class of (semi-)bipartite graphs. In particular, under random couplings,
adiabatic transfer is possible on graphs that admit a perfect matching both
when the sender is removed and when the receiver is removed. Many of the
favorable stability properties of STIRAP/CTAP are inherited, and our results
readily apply to transfer between multiple potential senders and receivers. We
numerically test transfer between the leaves of a tree, and find surprisingly
accurate transfer, especially when straddling is used. Our results may find
applications in short-distance communication between multiple quantum
computers, and open up a new question in graph theory about the spectral gap
around the value 0.Comment: 17 pages, 3 figures. v2 is made more mathematical and precise than v
Efficient forward propagation of time-sequences in convolutional neural networks using Deep Shifting
When a Convolutional Neural Network is used for on-the-fly evaluation of
continuously updating time-sequences, many redundant convolution operations are
performed. We propose the method of Deep Shifting, which remembers previously
calculated results of convolution operations in order to minimize the number of
calculations. The reduction in complexity is at least a constant and in the
best case quadratic. We demonstrate that this method does indeed save
significant computation time in a practical implementation, especially when the
networks receives a large number of time-frames
Many-body strategies for multi-qubit gates - quantum control through Krawtchouk chain dynamics
We propose a strategy for engineering multi-qubit quantum gates. As a first
step, it employs an eigengate to map states in the computational basis to
eigenstates of a suitable many-body Hamiltonian. The second step employs
resonant driving to enforce a transition between a single pair of eigenstates,
leaving all others unchanged. The procedure is completed by mapping back to the
computational basis. We demonstrate the strategy for the case of a linear array
with an even number N of qubits, with specific XX+YY couplings between nearest
neighbors. For this so-called Krawtchouk chain, a 2-body driving term leads to
the iSWAP gate, which we numerically test for N = 4 and 6.Comment: 10 pages, 3 figure
Quantum protocols for few-qubit devices
Quantum computers promise to dramatically speed up certain algorithms, but remain challenging to build in practice. This thesis focuses on near-term experiments, which feature a small number (say, 10-200) of qubits that lose the stored information after a short amount of time. We propose various theoretical protocols that can get the best out of such highly limited computers. For example, we construct logical operations, the building blocks of algorithms, by exploiting the native physical behavior of the machine. Moreover, we describe how quantum information can be sent between qubits that are only indirectly connected
Signal processing techniques for efficient compilation of controlled rotations in trapped ions
Quantum logic gates with many control qubits are essential in many quantum
algorithms, but remain challenging to perform in current experiments. Trapped
ion quantum computers natively feature a different type of entangling
operation, namely the Molmer-Sorensen (MS) gate which effectively applies an
Ising interaction to all qubits at the same time. We consider a sequence of
equal all-to-all MS operations, interleaved with single qubit gates that act
only on one special qubit. Using a connection with quantum signal processing
techniques, we find that it is possible to perform an arbitray SU(2) rotation
on the special qubit if and only if all other qubits are in the state |1>. Such
controlled rotation gates with N-1 control qubits require 2N applications of
the MS gate, and can be mapped to a conventional Toffoli gate by demoting a
single qubit to ancilla.Comment: 14 pages, 3 figures, comments welcome. v3 includes several fixes and
adds an appendix with explicit angle
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
Efficient forward propagation of time-sequences in convolutional neural networks using Deep Shifting
When a Convolutional Neural Network is used for on-the-fly evaluation of
continuously updating time-sequences, many redundant convolution operations are
performed. We propose the method of Deep Shifting, which remembers previously
calculated results of convolution operations in order to minimize the number of
calculations. The reduction in complexity is at least a constant and in the
best case quadratic. We demonstrate that this method does indeed save
significant computation time in a practical implementation, especially when the
networks receives a large number of time-frames
Signal processing techniques for efficient compilation of controlled rotations in trapped ions
Quantum logic gates with many control qubits are essential in many quantum algorithms, but remain challenging to perform in current experiments. Trapped ion quantum computers natively feature the M\xc3\xb8lmer-S\xc3\xb8rensen (MS) entangling operation, which effectively applies an Ising interaction to all pairs of qubits at the same time. We consider a sequence of equal all-to-all MS operations, interleaved with single-qubit gates that act only on one special qubit. Using a connection with quantum signal processing techniques, we find that it is possible to perform an arbitray SU(2) rotation on the special qubit if and only if all other qubits are in the state \xe2\x89\xa4. Such controlled rotation gates with N - 1 control qubits require 2N applications of the MS gate, and can be mapped to a conventional Toffoli gate by demoting a single qubit to ancilla
High-fidelity method for a single-step N-bit Toffoli gate in trapped ions
Conditional multiqubit gates are a key component for elaborate quantum algorithms. In a recent work, Rasmussen et al. [Phys. Rev. A 101, 022308 (2020)] proposed an efficient single-step method for a prototypical multiqubit gate, a Toffoli gate, based on a combination of Ising interactions between control qubits and an appropriate driving field on a target qubit. Trapped ions are a natural platform to implement this method, since Ising interactions mediated by phonons have been demonstrated in increasingly large ion crystals. However, the simultaneous application of these interactions and the driving field required for the gate results in undesired entanglem
Kent Hoopingarner, Junior Bounous, unidentified man
Photo shows Snowbird employees Kent Hoopingarner (left), Junior Bounous (center), with an unidentified man (possibly a construction worker