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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
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 OSTI2021

Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated , also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundaries. We show how maintaining particle-hole symmetry when sampling through the Brillouin zone is critical to obtaining high accuracy. This work illustrates how topological protection intrinsic to a quantum model can be employed to perform robust calculations on NISQ hardware, when one measures the appropriate protected quantum properties. It opens the door for further simulation of topological quantum models on quantum hardware available today.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Automated quantum error mitigation based on probabilistic error reduction

Current quantum computers suffer from a level of noise that prohibits extracting useful results directly from longer computations. The figure of merit in many near-term quantum algorithms is an expectation value measured at the end of the computation, which experiences a bias in the presence of hardware noise. A systematic way to remove such bias is probabilistic error cancellation (PEC). PEC requires a full characterization of the noise and introduces a sampling overhead that increases exponentially with circuit depth, prohibiting high-depth circuits at realistic noise levels. Probabilistic error reduction (PER) is a related quantum error mitigation method that systematically reduces the sampling overhead at the cost of reintroducing bias. In combination with zero-noise extrapolation, PER can yield expectation values with an accuracy comparable to PEC.Noise reduction through PER is broadly applicable to near-term algorithms, and the automated implementation of PER is thus desirable for facilitating its widespread use. To this end, we present an automated quantum error mitigation software framework that includes noise tomography and application of PER to user-specified circuits. We provide a multi-platform Python package that implements a recently developed Pauli noise tomography (PNT) technique for learning a sparse Pauli noise model and exploits a Pauli noise scaling method to carry out PER.We also provide software tools that leverage a previously developed toolchain, employing PyGSTi for gate set tomography and providing a functionality to use the software Mitiq for PER and zero-noise extrapolation to obtain error-mitigated expectation values on a user-defined circuit.

McDonough, Benjamin↗
DOE OSTI2026

A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers

We present Q-SASS, a quasi-Newton method for unconstrained stochastic optimization that does not rely on common random numbers. Most existing quasi-Newton approaches leverage common random numbers to construct second-order updates. However, motivated by challenges in variational quantum algorithms—where such coordination is not possible—we consider the setting in which function values and gradients are accessible only through noisy probabilistic zeroth- and first-order oracles, and no common random numbers can be exploited. We derive high-probability tail bounds on the iteration complexity of our algorithm for nonconvex, convex, and strongly convex (more generally, those satisfying the PL condition) objective functions. Finally, we demonstrate the empirical benefits of our quasi-Newton updating scheme on both synthetic and quantum chemistry problems.

Complexity bound↗
DOE OSTI2023

Basic Research Needs in Quantum Computing and Networking

Employing quantum mechanical resources in computing, information processing, and networking opens the door to potential exponential advantages over classical counterparts. However, quantifying and realizing such advantages poses extensive scientific and engineering challenges. Department of Energy (DOE) investments have driven steady progress in addressing such challenges. Recently developed quantum algorithms offer asymptotic exponential advantages in speed or accuracy for fundamental scientific problems. These problems include simulating physical systems, solving systems of linear equations, differential equations, and optimization problems. Empirical demonstrations on nascent quantum hardware suggest better performance on contrived computational tasks than classical analogs. However, the requirements for a quantum computer or network to demonstrate an end-to-end rigorously quantifiable performance improvement over classical analogs remains a grand challenge, especially for problems of practical value. In particular, what will be required for quantum technology to ultimately exhibit scalable, rigorous, and transformative performance advantages for practical applications? In July 2023, DOE’s Advanced Scientific Computing Research program in the Office of Science convened the Workshop on Basic Research Needs in Quantum Computing and Networking, where major opportunities and grand challenges were identified. The following five priority research directions (PRDs) were identified as a result of the workshop.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Comparative Study of Variations in Quantum Approximate Optimization Algorithms for the Traveling Salesman Problem

The traveling salesman problem (TSP) is one of the most often-used NP-hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the feasibility of the quantum computing paradigm for this class of problems. In this paper, we tackle the TSP using the quantum approximate optimization algorithm (QAOA) approach by formulating it as an optimization problem. By adopting an improved qubit encoding strategy and a layer-wise learning optimization protocol, we present numerical results obtained from the gate-based digital quantum simulator, specifically targeting TSP instances with 3, 4, and 5 cities. We focus on the evaluations of three distinctive QAOA mixer designs, considering their performances in terms of numerical accuracy and optimization cost. Notably, we find that a well-balanced QAOA mixer design exhibits more promising potential for gate-based simulators and realistic quantum devices in the long run, an observation further supported by our noise model simulations. Furthermore, we investigate the sensitivity of the simulations to the TSP graph. Overall, our simulation results show that the digital quantum simulation of problem-inspired ansatz is a successful candidate for finding optimal TSP solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Preparing exact eigenstates of the open XXZ chain on a quantum computer

The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. Here, we formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of L spins with M down spins, which contains a total of $(^{L}_{M})$ $2^{M} M!$ terms, the algorithm requires L+M 2 +2M qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Short-depth circuits for efficient expectation-value estimation

The evaluation of expectation values Tr[$\rho \mathcal{O}$] for some pure state $\rho$ and Hermitian operator $\mathcal{O}$ is of central importance in a variety of quantum algorithms. Near-optimal techniques have been developed in the past and require a number of measurements N approaching the Heisenberg limit N = O(1/ ε) as a function of target accuracy ε. The use of quantum phase estimation (QPE) requires, however, long circuit depths C = O(1/ ε) making its implementation difficult on near-term noisy devices. The more direct strategy of operator averaging is usually preferred as it can be performed using N = O(1/ε 2 ) measurements and no additional gates aside from those needed for the state preparation. In this work we use a simple but realistic model to describe the bound state of a neutron and a proton (the deuteron) to show that the latter strategy can require an overly large number of measurements in order to achieve a prefixed relative target accuracy ε r . Further, we propose to overcome this problem using a single step of QPE and classical postprocessing. This approach leads to a circuit depth C = O (ε μ ) (with μ ≥ 0) and to a number of measurements N = O (1/ε 2 + ν ) for 0 < ν ≤ 1 and a much smaller prefactor. We provide detailed descriptions of two implementations of our strategy for ν = 1 and ν ≈ 0.5 and derive appropriate conditions that a particular problem instance has to satisfy in order for our method to provide an advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Report for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking - 2023

Employing quantum mechanical resources in computing and networking opens the door to new computation and communication models and potential disruptive advantages over classical counterparts. However, quantifying and realizing such advantages face extensive scientific and engineering challenges. Investments by the Department of Energy (DOE) have driven progress toward addressing such challenges. Quantum algorithms have been recently developed, in some cases offering asymptotic exponential advantages in speed or accuracy, for fundamental scientific problems such as simulating physical systems, solving systems of linear equations, or solving differential equations. Empirical demonstrations on nascent quantum hardware suggest better performance than classical analogs on specialized computational tasks favorable to the quantum computing systems. However, demonstration of an end-to-end, substantial and rigorously quantifiable quantum performance advantage over classical analogs remains a grand challenge, especially for problems of practical value. The definition of requirements for quantum technologies to exhibit scalable, rigorous, and transformative performance advantages for practical applications also remains an outstanding open question, namely, what will be required to ultimately demonstrate practical quantum advantage?

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Report for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking - 2023

Employing quantum mechanical resources in computing and networking opens the door to new computation and communication models and potential disruptive advantages over classical counterparts. However, quantifying and realizing such advantages face extensive scientific and engineering challenges. Investments by the Department of Energy (DOE) have driven progress toward addressing such challenges. Quantum algorithms have been recently developed, in some cases offering asymptotic exponential advantages in speed or accuracy, for fundamental scientific problems such as simulating physical systems, solving systems of linear equations, or solving differential equations. Empirical demonstrations on nascent quantum hardware suggest better performance than classical analogs on specialized computational tasks favorable to the quantum computing systems. However, demonstration of an end-to-end, substantial and rigorously quantifiable quantum performance advantage over classical analogs remains a grand challenge, especially for problems of practical value. The definition of requirements for quantum technologies to exhibit scalable, rigorous, and transformative performance advantages for practical applications also remains an outstanding open question, namely, what will be required to ultimately demonstrate practical quantum advantage?

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Quantum Workforce Development at Lawrence Livermore National Laboratory

The students applying to LLNL that are interested in quantum computing are being brought up with a universal quantum algorithm experience. The candidates we see have played with Qiskit or the IBM experience, they understand spin dynamics, and a few of them have attended hackathons by Rigetti or another company. These students have all been exposed to universal quantum computing, but not quantum engineering, quantum hardware, or even descriptions of noise. This is in a large part due to the simplified interface in current commercial quantum systems. To broaden the applicant pool, we have begun collaborating with several institutions to train quantum scientists and engineers. We are using the LLNL whitebox approach to testbed access in order to give students a look under the hood of quantum computing operations because that is what we desire in research scientists.

42 ENGINEERING↗
DOE OSTI2025

Learning to classify quantum phases of matter with a few measurements

We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance. Following a supervised learning approach, we show how to use our previous knowledge to construct an observable capable of classifying the phase even in the unknown region. By using a combination of classical and quantum techniques, such as tensor networks, kernel methods, generalization bounds, quantum algorithms, and shadow estimators, we show that, in some cases, the certification of new ground states can be obtained with a polynomial number of measurements. An important application of our findings is the classification of the phases of matter obtained in quantum simulators, e.g. cold atom experiments, capable of efficiently preparing ground states of complex many-particle systems and applying simple measurements, e.g. single qubit measurements, but unable to perform a universal set of gates.

quantum machine learning↗
NASA NTRS2017

Temporal Planning for Compilation of Quantum Approximate Optimization Algorithm Circuits

We investigate the application of temporal planners to the problem of compiling quantum circuits to newly emerging quantum hardware. While our approach is general, we focus our initial experiments on Quantum Approximate Optimization Algorithm (QAOA) circuits that have few ordering constraints and allow highly parallel plans. We report on experiments using several temporal planners to compile circuits of various sizes to a realistic hardware. This early empirical evaluation suggests that temporal planning is a viable approach to quantum circuit compilation.

planning↗
DOE OSTI2026

Testing Classical Properties from Quantum Data

Many properties of Boolean functions can be tested far more efficiently than the function itself can be learned. However, this dramatic advantage often disappears when testers are limited to random samples of ƒ instead of adaptively chosen queries to f. In this work we investigate the quantum version of this restriction: quantum algorithms that test properties of a Boolean function f solely from copies of either the function state |ƒ⟩ ∝ ∑ x |x, ƒ(x)⟩ or the phase state |(-1) ƒ ⟩ ∝ ∑ x (-1) ƒ(x) |x⟩. For monotonicity, symmetry, and triangle-freeness, we show passive quantum testers are unboundedly or super-polynomially better than their classical passive testing counterparts. They are competitive with classic query -based testers in each case. Our new testers use techniques beyond quantum Fourier sampling, and it turns out this is necessary: we show a certain class of bent functions can be tested from 𝒪(1) function states but has a sample complexity lower bound of 2 Ω(n) for any tester relying exclusively on Fourier and classical samples. Our passive quantum testers are competitive with classical query -based testers, but this isn't universal: we exhibit a testing problem that can be solved from 𝒪(1) classical queries but requires Ω(2 n/2 ) function state copies. The Forrelation problem provides a separation of the same magnitude in the opposite direction, so we conclude that quantum data and classical queries are "maximally incomparable" resources for testing. We also begin the study of lower bounds for testing from quantum data. For quantum monotonicity testing, we prove that the ensembles of [Goldreich et al., 2000; Black, 2024], which give exponential lower bounds for classical sample-based testing, do not yield any nontrivial lower bounds for testing from quantum data. New insights specific to quantum data will be required for proving copy complexity lower bounds for testing in this model.

Boolean Functions↗
DOE OSTI2024

Identifiability and characterization of transmon qutrits through Bayesian experimental design

Robust control of a quantum system is essential to utilize the current noisy quantum hardware to its full potential, such as quantum algorithms. To achieve such a goal, a systematic search for an optimal control for any given experiment is essential. The design of optimal control pulses requires accurate numerical models and, therefore, accurate characterization of the system parameters. We present an online Bayesian approach for quantum characterization of qutrit systems, which automatically and systematically identifies optimal experiments that provide maximum information on the system parameters, thereby greatly reducing the number of experiments that need to be performed on the quantum testbed. Unlike most characterization protocols that provide point-estimates of the parameters, the proposed approach is able to estimate their probability distribution. The applicability of the Bayesian experimental design technique was demonstrated on test problems, where each experiment was defined by a parameterized control pulse. In addition to this, we also present an approach for iterative pulse extension, which is robust under uncertainties in transition frequencies and coherence times, and shot noise, despite being initialized with wide uninformative priors. Furthermore, we provide a mathematical proof of the theoretical identifiability of the model parameters and present conditions on the quantum state under which the parameters are identifiable. The proof and conditions for identifiability are presented for both closed and open quantum systems using the Schrödinger equation and the Lindblad master equation, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantum search on noisy intermediate-scale quantum devices

Abstract Quantum search algorithm (also known as Grover's algorithm) lays the foundation for many other quantum algorithms. Although it is very simple, its implementation is limited on noisy intermediate-scale quantum (NISQ) processors. Grover's algorithm was designed without considering the physical resources, such as depth, in the real implementations. Therefore, Grover's algorithm can be improved for NISQ devices. In this paper, we demonstrate how to implement quantum search algorithms better on NISQ devices. We present detailed benchmarks of the five-qubit quantum search algorithm on different quantum processors, including IBMQ, IonQ, and Honeywell quantum devices. We report the highest success probability of the five-qubit search algorithm compared to previous works. Our results show that designing the error-aware quantum search algorithms is possible, which can maximally harness the power of NISQ computers.

Physics↗
DOE OSTI2025

Unified architecture for quantum lookup tables

Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications depends crucially on gate-efficient implementations of these oracles, which are commonly some reversible versions of the Boolean circuit for a classical lookup table. Here, we present a general parametrized architecture for quantum circuits implementing a lookup table that encompasses all prior work in realizing a continuum of optimal trade-offs between qubits, non-Clifford gates, and error resilience, up to logarithmic factors. Our architecture assumes only local 2D connectivity, yet recovers results, with the appropriate parameters, polylogarithmic error scaling. We also identify regimes, such as simultaneous sublinear scaling, in all parameters. These results enable tailoring implementations of the commonly used lookup table primitive to any given quantum device with constrained resources.

quantum circuits↗