arXiv subjects

Tyler Volkoff

Publications and source records attributed to Tyler Volkoff.

11 recordsLinked to original sources

arXiv2025

Variational optical phase learning on a continuous-variable quantum compiler

Quantum process learning is a fundamental primitive that draws inspiration from machine learning with the goal of better studying the dynamics of quantum systems. One approach to quantum process learning is quantum compilation, whereby an analog quantum operation is digitized by compiling it into a series of basic gates. While there has been significant focus on quantum compiling for discrete-variable systems, the continuous-variable (CV) framework has received comparatively less attention. We present an experimental implementation of a CV quantum compiler that uses two mode-squeezed light to learn a Gaussian unitary operation. We demonstrate the compiler by learning a parameterized linear phase unitary through the use of target and control phase unitaries to demonstrate a factor of 5.4 increase in the precision of the phase estimation and a 3.6-fold acceleration in the time-to-solution metric when leveraging quantum resources. Our results are enabled by the tunable control of our cost landscape via variable squeezing, thus providing a critical framework to simultaneously increase precision and reduce time-to-solution.

quant-ph↗

arXiv2025

Length scale estimation of excited quantum oscillators

Massive quantum oscillators are finding increasing applications in proposals for high-precision quantum sensors and interferometric detection of weak forces. Although optimal estimation of certain properties of massive quantum oscillators such as phase shifts and displacements have strict counterparts in the theory of quantum estimation of the electromagnetic field, the phase space anisotropy of the massive oscillator is characterized by a length scale parameter that is an independent target for quantum estimation methods. We show that displaced squeezed states and excited eigenstates of a massive oscillator exhibit Heisenberg scaling of the quantum Fisher information for the length scale with respect to excitation number, and discuss asymptotically unbiased and efficient estimation allowing to achieve the predicted sensitivity. We construct a sequence of entangled states of two massive oscillators that provides a boost in length scale sensitivity equivalent to appending a third massive oscillator to a non-entangled system, and a state of $N$ oscillators exhibiting Heisenberg scaling with respect to the total energy.

quant-ph↗

arXiv2024

Quantum Programmable Reflections

Similar to a classical processor, which is an algorithm for reading a program and executing its instructions on input data, a universal programmable quantum processor is a fixed quantum channel that reads a quantum program $\lvert\psi_{U}\rangle$ that causes the processor to approximately apply an arbitrary unitary $U$ to a quantum data register. The present work focuses on a class of simple programmable quantum processors for implementing reflection operators, i.e. $U = e^{i \pi \lvert\psi\rangle\langle\psi\rvert}$ for an arbitrary pure state $\lvert\psi\rangle$ of finite dimension $d$. Unlike quantum programs that assume query access to $U$, our program takes the form of independent copies of the state to be reflected about $\lvert\psi_U\rangle = \lvert\psi\rangle^{\otimes n}$. We then identify the worst-case optimal algorithm among all processors of the form $\text{tr}_{\text{Program}}[V (\lvert\phi\rangle\langle\phi\rvert \otimes (\lvert\psi\rangle\langle\psi\rvert)^{\otimes n}) V^\dagger]$ where the algorithm $V$ is a unitary linear combination of permutations. By generalizing these algorithms to processors for arbitrary-angle rotations, $e^{i \alpha \lvert\psi\rangle\langle\psi\rvert}$ for $\alpha \in \mathbb R$, we give a construction for a universal programmable processor with better scaling in $d$. For programming reflections, we obtain a tight analytical lower bound on the program dimension by bounding the Holevo information of an ensemble of reflections applied to an entangled probe state. The lower bound makes use of a block decomposition of the uniform ensemble of reflected states with respect to irreps of the partially transposed permutation matrix algebra, and two representation-theoretic conjectures based on extensive numerical evidence.

quant-ph↗

arXiv2021

Universal compiling and (No-)Free-Lunch theorems for continuous variable quantum learning

Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete variable hardware, less has been paid to compiling in the continuous variable paradigm. Here we motivate several, closely related, short depth continuous variable algorithms for quantum compilation. We analyse the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr non-linearities. We further make connections between this framework and quantum learning theory in the continuous variable setting by deriving No-Free-Lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using Two-Mode-Squeezed states.

quant-ph↗

arXiv2021

Absence of Barren Plateaus in Quantum Convolutional Neural Networks

Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data. But this excitement has been tempered by the existence of exponentially vanishing gradients, known as barren plateau landscapes, for many QNN architectures. Recently, Quantum Convolutional Neural Networks (QCNNs) have been proposed, involving a sequence of convolutional and pooling layers that reduce the number of qubits while preserving information about relevant data features. In this work we rigorously analyze the gradient scaling for the parameters in the QCNN architecture. We find that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus. This provides an analytical guarantee for the trainability of randomly initialized QCNNs, which highlights QCNNs as being trainable under random initialization unlike many other QNN architectures. To derive our results we introduce a novel graph-based method to analyze expectation values over Haar-distributed unitaries, which will likely be useful in other contexts. Finally, we perform numerical simulations to verify our analytical results.

quant-ph↗

arXiv2021

Variational quantum algorithms to estimate rank, quantum entropies, fidelity and Fisher information via purity minimization

Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, quantum entropies, the Bures fidelity and the quantum Fisher information of mixed quantum states are developed. In addition, variations of these VQAs are also adapted to perform other useful functions such as quantum state learning and approximate fractional inverses. The common theme shared by the proposed algorithms is that their cost functions are all based on minimizing the quantum purity of a quantum state. Strategies to mitigate or avoid the problem of exponentially vanishing cost function gradients are also discussed.

quant-ph↗

arXiv2021

Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits

Variational quantum algorithms (VQAs) optimize the parameters $\vecθ$ of a parametrized quantum circuit $V(\vecθ)$ to minimize a cost function $C$. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming $V(\vecθ)$ is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining $C$ in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when $V(\vecθ)$ is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining $C$ with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of $V(\vecθ)$ is $\mathcal{O}(\log n)$. Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

quant-ph↗

arXiv2021

Large gradients via correlation in random parameterized quantum circuits

Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. In this work, we prove that reducing the dimensionality of the parameter space by utilizing circuit modules containing spatially or temporally correlated gate layers can allow one to circumvent the vanishing gradient phenomenon. Examples are drawn from random separable circuits and asymptotically optimal variational versions of Grover's algorithm based on the quantum alternating operator ansatz (QAOA). In the latter scenario, our bounds on cost function variation imply a transition between vanishing gradients and efficient trainability as the number of layers is increased toward $\mathcal{O}(2^{n/2})$, the optimal oracle complexity of quantum unstructured search.

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arXiv2019

Nonclassicality as a Quantifiable Resource for Quantum Metrology

We establish the nonclassicality of continuous-variable states as a resource for quantum metrology. Based on the quantum Fisher information of multimode quadratures, we introduce the metrological power as a measure of nonclassicality with a concrete operational meaning of displacement sensitivity beyond the classical limit. This measure belongs to the resource theory of nonclassicality, which is nonincreasing under linear optical elements. Our Letter reveals that a single copy, highly nonclassical quantum state is intrinsically advantageous when compared to multiple copies of a quantum state with moderate nonclassicality. This suggests that metrological power is related to the degree of quantum macroscopicity. Finally, we demonstrate that metrological resources useful for nonclassical displacement sensing tasks can be always converted into a useful resource state for phase sensitivity beyond the classical limit.

quant-ph↗

arXiv2017

Quantifying the Coherence Between Coherent States

In this paper, we detail an orthogonalization procedure that allows for the quantification of the amount of coherence present an arbitrary superposition of coherent states. The present construction is based on the quantum coherence resource theory introduced by Baumgratz et al., and the coherence resource monotone that we identify is found to characterize the nonclassicality traditionally analyzed via the Glauber-Sudarshan $P$ distribution. This suggests that identical quantum resources underlie both quantum coherence in the discrete finite dimensional case and the nonclassicality of quantum light. We show that our construction belongs to a family of resource monotones within the framework of a resource theory of linear optics, thus establishing deeper connections between the class of incoherent operations in the finite dimensional regime and linear optical operations in the continuous variable regime.

quant-ph↗

arXiv2016

Path integral Monte Carlo simulation of global and local superfluidity in liquid $^{4}$He reservoirs separated by nanoscale apertures

We present a path integral Monte Carlo study of the global superfluid fraction and local superfluid density in cylindrically-symmetric reservoirs of liquid $^{4}$He separated by nanoaperture arrays. The superfluid response to both translations along the axis of symmetry (longitudinal response) and rotations about the cylinder axis (transverse response) are computed, together with radial and axial density distributions that reveal the microscopic inhomogeneity arising from the combined effects of the confining external potential and the $^4$He-$^4$He interatomic potentials. We make a microscopic determination of the length-scale of decay of superfluidity at the radial boundaries of the system by analyzing the local superfluid density distribution to extract a displacement length that quantifies the superfluid mass displacement away from the boundary. We find that the longitudinal superfluid response is reduced in reservoirs separated by a septum containing sufficiently small apertures compared to a cylinder with no intervening aperture array, for all temperatures below $T_λ$. For a single aperture in the septum, a significant drop in the longitudinal superfluid response is seen when the aperture diameter is made smaller than twice the empirical temperature-dependent $^4$He healing length, consistent with the formation of a weak link between the reservoirs. Increasing the diameter of a single aperture or the number of apertures in the array results in an increase of the superfluid density toward the expected bulk value.

cond-mat.quant-gas↗