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Wiebe, Nathan

Publications and source records attributed to Wiebe, Nathan.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

ARQUIN: Architectures for Multinode Superconducting Quantum Computers

Many proposals to scale quantum technology rely on modular or distributed designs wherein individual quantum processors, called nodes, are linked together to form one large multinode quantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, internode gates in these systems may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require improvements in entanglement generation, use of entanglement distillation, and optimized software and compilers. Still, it remains unclear what performance is possible with current hardware and what performance algorithms require. In this article, we employ a systems analysis approach to quantify overall MNQC performance in terms of hardware models of internode links, entanglement distillation, and local architecture. We show how to navigate tradeoffs in entanglement generation and distillation in the context of algorithm performance, lay out how compilers and software should balance between local and internode gates, and discuss when noisy quantum internode links have an advantage over purely classical links. Here, we find that a factor of 10–100× better link performance is required and introduce a research roadmap for the co-design of hardware and software towards the realization of early MNQCs. While we focus on superconducting devices with optical interconnects, our approach is general across MNQC implementations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Training quantum neural networks using the quantum information bottleneck method

Abstract We provide in this paper a concrete method for training a quantum neural network to maximize the relevant information about a property that is transmitted through the network. This is significant because it gives an operationally well founded quantity to optimize when training autoencoders for problems where the inputs and outputs are fully quantum. We provide a rigorous algorithm for computing the value of the quantum information bottleneck quantity within error ε that requires O ( log 2 ⁡ ( 1 / ϵ ) + 1 / δ 2 ) queries to a purification of the input density operator if its spectrum is supported on { 0 } ⋃ [ δ , 1 − δ ] for δ > 0 and the kernels of the relevant density matrices are disjoint. We further provide algorithms for estimating the derivatives of the QIB function, showing that quantum neural networks can be trained efficiently using the QIB quantity given that the number of gradient steps required is polynomial.

Çatlı, Ahmet Burak (ORCID:0000000152294141)↗
DOE OSTI2024

Generalized Quantum Signal Processing

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that | P | ≤ 1 , a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where P and Q are known. In cases where only P is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding Q for polynomials of degree on the order of 10 7 . We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the ϵ -approximate fractional query problem that requires O ( ( 1 / δ ) + log ( 1 / ϵ ) ) queries to perform where O ( 1 / δ ) is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only O ( d log N + log 2 N ) 1 and 2-qubit gates for a filter of lengths d . Published by the American Physical Society 2024

Motlagh, Danial↗
DOE OSTI2024

Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian

We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O ~ ( Λ N 2 η 2 t 2 / ϵ ) for grid size N , η particles, simulation time t , field cutoff Λ , and error ϵ . Our qubitization algorithm scales as O ~ ( N ( η + N ) ( η + Λ 2 ) t log ( 1 / ϵ ) ) . This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ . We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled- X gates that can be used for better analysis of circuit cost. Published by the American Physical Society 2024

Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗
DOE OSTI2024

Improved Precision Scaling for Simulating Coupled Quantum-Classical Dynamics

In this paper, we present a superpolynomial improvement in the precision scaling of quantum simulations for coupled quantum-classical systems. Such systems are found in, e.g., molecular-dynamics simulations within the Born-Oppenheimer approximation. By employing a framework based on the Koopman–von Neumann formulation of classical mechanics, we express the Liouville equation of motion as unitary dynamics and utilize phase kickback from a dynamical quantum simulation to calculate the quantum forces acting on classical particles. This approach allows us to simulate the dynamics of these classical particles without the overheads associated with measuring gradients and solving the equations of motion on a classical computer, resulting in a superpolynomial advantage at the price of increased space complexity. We demonstrate that these simulations can be performed in both microcanonical and canonical ensembles, enabling the estimation of thermodynamic properties from the prepared probability density. Published by the American Physical Society 2024

Simon, Sophia (ORCID:0000000332612338)↗
DOE OSTI2024

Composite Qdrift-product formulas for quantum and classical simulations in real and imaginary time

Recent study has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian H for a given simulation problem into subsets A and B such that H = A + B , where the terms in A are simulated with a Trotter-Suzuki channel and the B terms are randomly sampled via the Qdrift algorithm. Here we extend Qdrift and composite product formulas to imaginary time, formulating candidate classical algorithms for quantum Monte Carlo calculations. We upper bound the induced Schatten- 1 → 1 norm on both imaginary-time Qdrift and composite channels. Another recent result demonstrated that simulations of lattice Hamiltonians containing geometrically local interactions can be improved using a Lieb-Robinson argument to decompose H into subsets that contain only terms supported on that subset of the lattice. Here, we provide a quantum algorithm by unifying this result with the composite approach into “local composite channels” and we upper bound the diamond distance. We provide exact numerical simulations of algorithmic cost by counting the number of gates of the form e − i H j t and e − H j β to meet a certain error tolerance ε . In doing so, we optimize the partitioning into sets A and B using gradient boosted tree models from machine learning. These numerical studies are important given that product formulas have been historically known to outperform analytic upper bounds. We show constant factor advantages for a variety of interesting Hamiltonians, the maximum of which is a ≈ 20 -fold speedup that occurs in the simulation of Jellium. Published by the American Physical Society 2024

Pocrnic, Matthew (ORCID:0000000203089376)↗
DOE OSTI2024

Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation

Quantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause deviations from this fundamental limit. In this work, we show how algorithmic errors due to Trotterized time evolution can be mitigated through the use of standard polynomial interpolation techniques. Our approach is to extrapolate to zero Trotter step size, akin to zero-noise extrapolation techniques for mitigating hardware errors. We perform a rigorous error analysis of the interpolation approach for estimating eigenvalues and time-evolved expectation values, and show that the Heisenberg limit is achieved up to polylogarithmic factors in the error. Our work suggests that accuracies approaching those of state-of-the-art simulation algorithms may be achieved using Trotter and classical resources alone for a number of relevant algorithmic tasks.

Rendon, Gumaro↗
DOE OSTI2024

Analyzing Prospects for Quantum Advantage in Topological Data Analysis

Lloyd [Nat. Commun. , 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Entanglement area law for one-dimensional gauge theories and bosonic systems

Here, we prove an entanglement area law for a class of one-dimensional quantum systems involving infinite-dimensional local Hilbert spaces. This class of quantum systems includes bosonic models and lattice gauge theories in one spatial dimension. Our proof relies on results concerning the robustness of the ground state and spectral gap to the truncation of Hilbert space, applied within the approximate-ground-state projector (AGSP) framework. Our result provides theoretical justification for using tensor networks to study the ground-state properties of quantum systems with infinite local degrees of freedom.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2023

Quantum Neural Networks: Issues, Training, and Applications

Our work in the field aims at explaining the limitations and expressive power of Quantum Machine Learning models, as well as finding feasible training algorithms that could be implemented in near-term Quantum Computers. The promise of Quantum Machine Learning is that by incorporating quantum effects, such as entanglement, into machine learning models researchers can improve model performance and understand more complex datasets. This pledge is particularly pronounced in the design of Quantum neural networks (QNNs), a promising framework for creating quantum algorithms, that promise to outperform classical models by combining the speedups of quantum computation with the widespread successes of deep learning. We show that applying this approach alone to quantum deep learning is problematic given that an excess of entanglement between the hidden and visible layers can destroy the predictive power of our QNN models. We address the barren plateau problem by suggesting the use of a generative, unbounded, nonlinear loss function with simple gradients. The loss function quantifies how much the quantum states generated by the QNNs differ from the data and the goal during training is to minimize it. Finally, we showcase how to use generative training to construct a "classical-quantum" neural network to accurately interpolate between the ground states of a Molecular Hamiltonian, a central question in Quantum Chemistry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum Simulation for High-Energy Physics

It is for the first time that quantum simulation for high-energy physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in quantum information sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This Roadmap is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Gate-based quantum computing for protein design

Protein design is a technique to engineer proteins by permuting amino acids in the sequence to obtain novel functionalities. However, exploring all possible combinations of amino acids is generally impossible due to the exponential growth of possibilities with the number of designable sites. The present work introduces circuits implementing a pure quantum approach, Grover’s algorithm, to solve protein design problems. Our algorithms can adjust to implement any custom pair-wise energy tables and protein structure models. Moreover, the algorithm’s oracle is designed to consist of only adder functions. Quantum computer simulators validate the practicality of our circuits, containing up to 234 qubits. However, a smaller circuit is implemented on real quantum devices. Our results show that using iterations, the circuits find the correct results among all N possibilities, providing the expected quadratic speed up of Grover’s algorithm over classical methods (i.e.,).

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Synthesizing efficient circuits for Hamiltonian simulation

Abstract We provide an approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations. The total number of gates, especially CNOT, reduce in many cases. We show that it is possible to implement an exponentiated sum of commuting Paulis with at most m (controlled)-rotation gates, where m is the number of distinct non-zero eigenvalues (ignoring sign). Thus we can collect mutually commuting Hamiltonian terms into groups satisfying one of several symmetries identified in this work. This allows an inexpensive simulation of the entire group of terms. We further show that the cost can in some cases be reduced by partially allocating Hamiltonian terms to several groups and provide a polynomial time classical algorithm that can greedily allocate the terms to appropriate groupings.

Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗