Quantum machine learning progress Harvard simulates brain function with just six rubidium atoms

Quantum computing promises to provide a computational advantage for machine learning. However, current noise-containing intermediate-scale quantum (NISQ) devices pose an engineering challenge to realize the benefits of quantum machine learning (QML). To address this challenge, a number of quantum machine learning architectures inspired by models of brain computation have emerged in recent years - simulating controllable multi-body quantum systems for computation without relying on traditional digital circuit architectures.

 

Recently, a team at Harvard University successfully constructed a quantum version of the brain's neural circuit model, the quantum recurrent neural network (qRNN), using an array of Rydberg atoms: the cognitive task was successfully performed using only six rubidium atoms, and was shown to significantly improve computational properties. A related paper titled "Quantum reservoir computing using the Ridderberg atom array" [1] has been submitted on the arXiv website.

 

 

1What is a quantum recurrent neural network (qRNN)?

 

We first recall a typical RNN consisting of N binary neurons: each neuron is in one of two possible states sn(t) ∈ {-1,1} and is updated from time step t to t+1 according to the update rule. where Jnm=Jmn is the symmetric synaptic connection between neurons n and m. The deviation ∆n(t) over time encodes the input to the RNN.

 

 

Now we extend the classical RNN in the above equation to the quantum setting: replace each of the N neurons with a particle with spin (spin) -1/2, for which the spin measurement along the z-axis yields {-1,1} values. Thus, each neuron n is a normalized quantum state in the Hilbert space Hn, yielding the time-varying quantum Hamiltonian quantity formula.

 

 

Compared with RNN, the evolution of qRNN further expands the effectiveness of neural networks. Specifically, the following three features are included.

 

An improved ability to compute complex functions through the use of quantum techniques.

 

The possibility to choose multiple measurement bases (measurement basis).

 

Effective implementation of stochastic processes that cannot be achieved by classical RNNs.

 

Subsequently, the team conducted the following three experiments to verify the corresponding performance advantages of qRNN one by one.

 

The qRNN can compute complex functions: compute the parity of two inputs s1 and s2 - XOR(s1,s2). The computational power of the RNN is a consequence of nonlinear dynamics: for example, an RNN with linear dynamics does not have the ability to compute the parity function between two classical binary inputs XOR(s1, s2)=s1s2. qRNNs can perform linear computations: quantum interference is used to compute XOR, which is a fundamental resource for quantum computing.

 

Z.errors (a quantum computational error) are detected using qRNN for three spins L1,2,3. To detect Z-errors, a set of auxiliary quantum bits A1,2 is introduced to perform parity bit detection for (L1,L2) and (L2,L3). qRNN can effectively measure on different bases other than the computational base and thus discover quantum correlations, improving its performance with respect to RNN.

 

Compare classical RNN and qRNN to randomly evolve a distribution ptf from an initial distribution p0. Top: classical RNN requires O(2N-m) time steps while using m hidden neurons; Bottom: qRNN requires only one time step and has no hidden neurons.

 

02Ridberg atomic construction of qRNN: significant improvement in learning effectiveness

 

The similarity between the evolution of the qRNN and the RNN implies that the qRNN has the ability to replicate the learning of the neural system. To explore the learning efficacy of qRNNs, the research team conducted corresponding experiments on the qRNN architecture on an optical tweezer array of Reedeburg atoms. The team chose the array of Riedberg atoms because they are single-valent electron atoms - these atoms are extremely large in diameter, some of their electrons orbit the nucleus at great distances, and are very sensitive to light, so they can be driven coherently between the atomic ground state and the highly ground state.

 

Schematic diagram of RNN and qRNN. (A) Classical RNN. the inter-neural connection Jnm is arbitrary. (B) The qRNN consists of Riedberg atoms, where Rnm is the physical distance between atoms n and m. The local expectation value of a subset of atoms is used for readout. (C) Schematic diagram of the operation of the Riedberg atom array for the RNN in (B) using optical tweezers.

 

In the task analyzed, the team fixed the geometry of the atoms according to the task at hand, which makes the qRNN resemble a "quantum storage computer". The team then focused on four simple proof-of-principle neural system tasks. The results show that the qRNN of Riedberg atoms can encode both inhibitory and excitatory neurons, which is essential for successful multitasking; the qRNNN of Riedberg atoms can learn to make decisions by distinguishing the properties of stimuli, has working memory, and exhibits long-term memory enhanced by quantum many-body "scar" (scars). memory.

 

1) Experiment 1: Multi-task learning

 

A characteristic of classical RNNs is their ability to learn multiple tasks, which include learning several output functions simultaneously. In the experiments, the performance of qRNNs was tested by simultaneously learning XOR, AND, and OR functions for different concentrations of inhibitory neurons.

 

Encoding of inhibitory neurons using Riedberg atoms and their use for multitasking. (A) Encoding scheme of inhibitory neurons. (B) Squared error of qRNN learning XOR, OR and AND functions with different number of inhibitory neurons. Better performance is observed when 1 out of every 4 neurons is an inhibitory neuron. The example of (C)-(E) using 8 neurons and 2 inhibitory neurons to learn the function results in 40% better performance than when there are no inhibitory neurons.

 

2) Experiment 2: Decision making

 

One of the great successes of classical RNNs is their ability to integrate sensory stimuli in order to choose between two actions. In the experiment, the team demonstrated a variant of the qRNN with Reedeberg atoms with a dotted motor decision task originally studied in monkeys, where several inputs were analyzed to produce a scalar nonlinear function representing the decision. This task demonstrates the qRNN's ability to generate nonlinear functions of inputs and perform simple cognitive tasks.

 

Decision-making experiments with qRNN of Ridberg atoms. (A) Schematic representation of the input stimuli as a pair of time-dependent tunings on two atoms; (B) Mental responses to the decision making task.

 

(3) Experiment 3: Parameterized working memory

 

Working memory (WM) is one of the most important cognitive functions that involves the brain's ability to retain and process information for later execution of a task. This task shows the short-term memory capacity of the qRNN with Riedberg atoms.

 

Working memory for the qRNN of Ridberg atoms. (A) Schematic diagram of network inputs; (B) loss of working memory task as a function of total input time; (C) mental responses to working memory task for two different values of ∆tout; (D) accuracy of working memory task as a function of tdelay for ∆t=0.15 and tout=0.5.

 

(4) Experiment 4: Long-term memory via quantum many-body scars

 

Finally, the team turned to investigate the ability of qRNNs to encode long-term memory. The task consists of encoding the initial state of the qRNN, ψm(0), in order to allow the system to evolve under its inheritance dynamics for a period of time before recovering memory through local measurements of the state ψm(T).

 

Prepare a state encoded as m. In the experiment, the system is a chain of Riedberg atoms, and the final measurement is performed on a single atom, followed by a linear post-processing to retrieve m. If thermalization can be steadily prevented, the memory can be retrieved in a larger time frame.

 

03Quantum computing + neural networks: bringing a new light

 

In this experiment, the team presented a quantum version of a classical RNN on binary neurons - a qRNN was implemented using an array of Riedberg atoms and showed how a small number of Riedberg atoms can be used to successfully perform biological learning tasks.

 

Today, more and more scientific research is attempting to combine quantum computing and neural networks. For example, superconducting circuits have recently been used to encode bio-logically realistic single neuron models [2]. This experimental advantage will likely be used in collective learning tasks with quantum neurons and is also expected to bring light to the research and experiments on related computational architectures.

 

Reference link：

[1]https://arxiv.org/abs/2111.10956

[2]T. Gonzalez-Raya, E. Solano, and M. Sanz, Quantizedthree-ion-channel neuron model for neural action poten-tials, Quantum 4, 224 (2020).