#30: July 10th- July 16th

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Mixer-Phaser Ansätze for Quantum Optimization with Hard Constraints

We introduce multiple parametrized circuit ansätze and present the results of a numerical study comparing their performance with a standard Quantum Alternating Operator Ansatz approach. The ansätze are inspired by mixing and phase separation in the QAOA, and also motivated by compilation considerations with the aim of running on near-term superconducting quantum processors. The methods are tested on random instances of a weighted quadratic binary constrained optimization problem that is fully connected for which the space of feasible solutions has constant Hamming weight. For the parameter setting strategies and evaluation metric used, the average performance achieved by the QAOA is effectively matched by the one obtained by a “mixer-phaser” ansatz that can be compiled in less than half-depth of standard QAOA on most superconducting qubit processors.

Machine classification for probe based quantum thermometry

We consider the problem of probe-based quantum thermometry, and show that machine classification can provide reliable estimates over a broad range of scenarios. Our approach is based on the kk-nearest-neighbor algorithm. Temperature is divided into bins, and the machine trains a predictor based on data from observations at different times (obtained e.g. from computer simulations or other experiments). This yields a predictor, which can then be used to estimate the temperature from new observations. The algorithm is flexible, and works with both populations and coherences. It also allows to incorporate other uncertainties, such as lack of knowledge about the system-probe interaction strength. The proposal is illustrated in the paradigmatic Jaynes-Cummings and Rabi models. In both cases, the mean-squared error is found to decrease monotonically with the number of data points used, showing that the algorithm is asymptotically convergent. This, we argue, is related to the well behaved data structures stemming from thermal phenomena, which indicates that classification may become an experimentally relevant tool for thermometry in the quantum regime.

Playing Atari with Hybrid Quantum-Classical Reinforcement Learning

PDFDespite the successes of recent works in quantum reinforcement learning, there are still severe limitations on its applications due to the challenge of encoding large observation spaces into quantum systems. To address this challenge, we propose using a neural network as a data encoder, with the Atari games as our testbed. Specifically, the neural network converts the pixel input from the games to quantum data for a Quantum Variational Circuit (QVC); this hybrid model is then used as a function approximator in the Double Deep Q Networks algorithm. We explore a number of variations of this algorithm and find that our proposed hybrid models do not achieve meaningful results on two Atari games – Breakout and Pong. We suspect this is due to the significantly reduced sizes of the hybrid quantum-classical systems.

Convergence of numerical approximations to non-Markovian bosonic gaussian environments

Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. A common approach to the analysis of such systems is to approximate the non-Markovian environment by discrete bosonic modes thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been proposed in previous works [D. Tamascelli et al, PRL (2012), A. W. Chin et al, J. of Math. Phys (2010)], the resulting approximation lacks rigorous convergence guarantees. In this paper, we initiate a rigorous study of the convergence properties of these methods. We show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that, for most physically interesting models of non-Markovian environments, the approximation error falls off polynomially with the number of modes. Our results lend rigor to numerical methods used for approximating non-Markovian quantum dynamics and allow for a quantitative assessment of classical as well as quantum algorithms in simulating non-Markovian quantum systems.

Fock State-enhanced Expressivity of Quantum Machine Learning Models

The data-embedding process is one of the bottlenecks of quantum machine learning, potentially negating any quantum speedups. In light of this, more effective data-encoding strategies are necessary. We propose a photonic-based bosonic data-encoding scheme that embeds classical data points using fewer encoding layers and circumventing the need for nonlinear optical components by mapping the data points into the high-dimensional Fock space. The expressive power of the circuit can be controlled via the number of input photons. Our work shed some light on the unique advantages offers by quantum photonics on the expressive power of quantum machine learning models. By leveraging the photon-number dependent expressive power, we propose three different noisy intermediate-scale quantum-compatible binary classification methods with different scaling of required resources suitable for different supervised classification tasks.

Continuous-variable neural-network quantum states and the quantum rotor model

We initiate the study of neural-network quantum state algorithms for analyzing continuous-variable lattice quantum systems in first quantization. A simple family of continuous-variable trial wavefunctons is introduced which naturally generalizes the restricted Boltzmann machine (RBM) wavefunction introduced for analyzing quantum spin systems. By virtue of its simplicity, the same variational Monte Carlo training algorithms that have been developed for ground state determination and time evolution of spin systems have natural analogues in the continuum. We offer a proof of principle demonstration in the context of ground state determination of a stoquastic quantum rotor Hamiltonian. Results are compared against those obtained from partial differential equation (PDE) based scalable eigensolvers. This study serves as a benchmark against which future investigation of continuous-variable neural quantum states can be compared, and points to the need to consider deep network architectures and more sophisticated training algorithms.

Time evolution of an infinite projected entangled pair state: a neighborhood tensor update

The simple update (SU) and full update (FU) are the two paradigmatic time evolution algorithms for a tensor network known as the infinite projected entangled pair state (iPEPS). They differ by an error measure that is either, respectively, local or takes into account full infinite tensor environment. In this paper we test an intermediate neighborhood tensor update (NTU) accounting for the nearest neighbor environment. This small environment can be contracted exactly in a parallelizable way. It provides an error measure that is Hermitian and non-negative down to machine precision. In the 2D quantum Ising model NTU is shown to yield stable unitary time evolution following a sudden quench. It also yields accurate thermal states despite correlation lengths that reach up to 20 lattice sites. The latter simulations were performed with a manifestly Hermitian purification of a thermal state. Both were performed with reduced tensors that do not include physical (and ancilla) indices. This modification naturally leads to two other schemes: a local SVD update (SVDU) and a full tensor update (FTU) being a variant of FU.

Quantum propensities in the brain cortex and free will

Capacity of conscious agents to perform genuine choices among future alternatives is a prerequisite for moral responsibility. Determinism that pervades classical physics, however, forbids free will, undermines the foundations of ethics, and precludes meaningful quantification of personal biases. To resolve that impasse, we utilize the characteristic indeterminism of quantum physics and derive a quantitative measure for the amount of free will manifested by the brain cortical network. The interaction between the central nervous system and the surrounding environment is shown to perform a quantum measurement upon the neural constituents, which actualize a single measurement outcome selected from the resulting quantum probability distribution. Inherent biases in the quantum propensities for alternative physical outcomes provide varying amounts of free will, which can be quantified with the expected information gain from learning the actual course of action chosen by the nervous system. For example, neuronal electric spikes evoke deterministic synaptic vesicle release in the synapses of sensory or somatomotor pathways, with no free will manifested. In cortical synapses, however, vesicle release is triggered indeterministically with probability of 0.35 per spike. This grants the brain cortex, with its over 100 trillion synapses, an amount of free will exceeding 96 terabytes per second. Although reliable deterministic transmission of sensory or somatomotor information ensures robust adaptation of animals to their physical environment, unpredictability of behavioral responses initiated by decisions made by the brain cortex is evolutionary advantageous for avoiding predators. Thus, free will may have a survival value and could be optimized through natural selection.

Neural networks for on-the-fly single-shot state classification

Neural networks have proven to be efficient for a number of practical applications ranging from image recognition to identifying phase transitions in quantum physics models. In this paper we investigate the application of neural networks to state classification in a single-shot quantum measurement. We use dispersive readout of a superconducting transmon circuit to demonstrate an increase in assignment fidelity for both two and three state classification. More importantly, our method is ready for on-the-fly data processing without overhead or need for large data transfer to a hard drive. In addition we demonstrate the capacity of neural networks to be trained against experimental imperfections, such as phase drift of a local oscillator in a heterodyne detection scheme.

Entanglement transitions from restricted Boltzmann machines

The search for novel entangled phases of matter has lead to the recent discovery of a new class of “entanglement transitions”, exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free energy cost of inserting a domain wall. In this paper, we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural network-inspired variational Ansätze, we investigate under what conditions on the variational parameters these Ansätze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite size effects in finite size numerical simulations. Introducing phases with correlations decaying as 1/rα1/rα in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent αα. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.

Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where quantum approximation optimization algorithms (QAOAs) constitute promising candidates for demonstrating tangible quantum advantages based on NISQ devices. In this paper, we consider the maximum likelihood (ML) detection problem of binary symbols transmitted over a multiple-input and multiple-output (MIMO) channel, where finding the optimal solution is exponentially hard using classical computers. Here, we apply the QAOA for the ML detection by encoding the problem of interest into a level-p QAOA circuit having 2p variational parameters, which can be optimized by classical optimizers. This level-p QAOA circuit is constructed by applying the prepared Hamiltonian to our problem and the initial Hamiltonian alternately in p consecutive rounds. More explicitly, we first encode the optimal solution of the ML detection problem into the ground state of a problem Hamiltonian. Using the quantum adiabatic evolution technique, we provide both analytical and numerical results for characterizing the evolution of the eigenvalues of the quantum system used for ML detection. Then, for level-1 QAOA circuits, we derive the analytical expressions of the expectation values of the QAOA and discuss the complexity of the QAOA based ML detector. Explicitly, we evaluate the computational complexity of the classical optimizer used and the storage requirement of simulating the QAOA. Finally, we evaluate the bit error rate (BER) of the QAOA based ML detector and compare it both to the classical ML detector and to the classical MMSE detector, demonstrating that the QAOA based ML detector is capable of approaching the performance of the classical ML detector. This paves the way for a host of large-scale classical optimization problems to be solved by NISQ computers.

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