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$_N$ 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 $2^N$ 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 $t^{-2}$, 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