arXiv subjects

Christian W. Bauer

Publications and source records attributed to Christian W. Bauer.

At least 37 records · Page 2Linked to original sources

arXiv2023

Overcoming exponential scaling with system size in Trotter-Suzuki implementations of constrained Hamiltonians: 2+1 U(1) lattice gauge theories

For many quantum systems of interest, the classical computational cost of simulating their time evolution scales exponentially in the system size. At the same time, quantum computers have been shown to allow for simulations of some of these systems using resources that scale polynomially with the system size. Given the potential for using quantum computers for simulations that are not feasible using classical devices, it is paramount that one studies the scaling of quantum algorithms carefully. This work identifies a term in the Hamiltonian of a class of constrained systems that naively requires quantum resources that scale exponentially in the system size. An important example is a compact U(1) gauge theory on lattices with periodic boundary conditions. Imposing the magnetic Gauss' law a priori introduces a constraint into that Hamiltonian that naively results in an exponentially deep circuit. A method is then developed that reduces this scaling to polynomial in the system size, using a redefinition of the operator basis. An explicit construction of the matrices defining the change of operator basis, as well as the scaling of the associated computational cost, is given.

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arXiv2022

Overcoming exponential volume scaling in quantum simulations of lattice gauge theories

Real-time evolution of quantum field theories using classical computers requires resources that scale exponentially with the number of lattice sites. Because of a fundamentally different computational strategy, quantum computers can in principle be used to perform detailed studies of these dynamics from first principles. Before performing such calculations, it is important to ensure that the quantum algorithms used do not have a cost that scales exponentially with the volume. In these proceedings, we present an interesting test case: a formulation of a compact U(1) gauge theory in 2+1 dimensions free of gauge redundancies. A naive implementation onto a quantum circuit has a gate count that scales exponentially with the volume. We discuss how to break this exponential scaling by performing an operator redefinition that reduces the non-locality of the Hamiltonian. While we study only one theory as a test case, it is possible that the exponential gate scaling will persist for formulations of other gauge theories, including non-Abelian theories in higher dimensions.

hep-lat↗

arXiv2022

Efficient quantum implementation of 2+1 U(1) lattice gauge theories with Gauss law constraints

The study of real-time evolution of lattice quantum field theories using classical computers is known to scale exponentially with the number of lattice sites. Due to a fundamentally different computational strategy, quantum computers hold the promise of allowing for detailed studies of these dynamics from first principles. However, much like with classical computations, it is important that quantum algorithms do not have a cost that scales exponentially with the volume. Recently, it was shown how to break the exponential scaling of a naive implementation of a U(1) gauge theory in two spatial dimensions through an operator redefinition. In this work, we describe modifications to how operators must be sampled in the new operator basis to keep digitization errors small. We compare the precision of the energies and plaquette expectation value between the two operator bases and find they are comparable. Additionally, we provide an explicit circuit construction for the Suzuki-Trotter implementation of the theory using the Walsh function formalism. The gate count scaling is studied as a function of the lattice volume, for both exact circuits and approximate circuits where rotation gates with small arguments have been dropped. We study the errors from finite Suzuki-Trotter time-step, circuit approximation, and quantum noise in a calculation of an explicit observable using IBMQ superconducting qubit hardware. We find the gate count scaling for the approximate circuits can be further reduced by up to a power of the volume without introducing larger errors.

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arXiv2022

Initial-State Dependent Optimization of Controlled Gate Operations with Quantum Computer

There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivity, and coherence times, a quantum circuit optimization is essential to make the best use of near-term quantum devices. We introduce a new circuit optimizer called AQCEL, which aims to remove redundant controlled operations from controlled gates, depending on initial states of the circuit. Especially, the AQCEL can remove unnecessary qubit controls from multi-controlled gates in polynomial computational resources, even when all the relevant qubits are entangled, by identifying zero-amplitude computational basis states using a quantum computer. As a benchmark, the AQCEL is deployed on a quantum algorithm designed to model final state radiation in high energy physics. For this benchmark, we have demonstrated that the AQCEL-optimized circuit can produce equivalent final states with much smaller number of gates. Moreover, when deploying AQCEL with a noisy intermediate scale quantum computer, it efficiently produces a quantum circuit that approximates the original circuit with high fidelity by truncating low-amplitude computational basis states below certain thresholds. Our technique is useful for a wide variety of quantum algorithms, opening up new possibilities to further simplify quantum circuits to be more effective for real devices.

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arXiv2022

Report of the Snowmass 2021 Theory Frontier Topical Group on Quantum Information Science

We summarize current and future applications of quantum information science to theoretical high energy physics. Three main themes are identified and discussed; quantum simulation, quantum sensors and formal aspects of the connection between quantum information and gravity. Within these themes, there are important research questions and opportunities to address them in the years and decades ahead. Efforts in developing a diverse quantum workforce are also discussed. This work summarizes the subtopical area Quantum Information for High Energy Physics TF10 which forms part of the Theory Frontier report for the Snowmass 2021 planning process.

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arXiv2022

Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory

Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report.

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arXiv2022

Active Readout Error Mitigation

Mitigating errors is a significant challenge for near term quantum computers. One of the most important sources of errors is related to the readout of the quantum state into a classical bit stream. A variety of techniques have been proposed to mitigate these errors with post-hoc corrections. We propose a complementary scheme to actively reduce readout errors on a shot-by-shot basis by encoding single qubits, immediately prior to readout, into multi-qubit states. The computational resources of our technique are independent of the circuit depth and fully compatible with current hardware error rates and connectivity. We analyze the potential of our approach using two types of error-correcting codes and, as a proof of principle, demonstrate an 80% improvement in readout error on the IBMQ Mumbai quantum computer.

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arXiv2022

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 community whitepaper 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.

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arXiv2022

Computationally Efficient Zero Noise Extrapolation for Quantum Gate Error Mitigation

Zero noise extrapolation (ZNE) is a widely used technique for gate error mitigation on near term quantum computers because it can be implemented in software and does not require knowledge of the quantum computer noise parameters. Traditional ZNE requires a significant resource overhead in terms of quantum operations. A recent proposal using a targeted (or random) instead of fixed identity insertion method (RIIM versus FIIM) requires significantly fewer quantum gates for the same formal precision. We start by showing that RIIM can allow for ZNE to be deployed on deeper circuits than FIIM, but requires many more measurements to maintain the same statistical uncertainty. We develop two extensions to FIIM and RIIM. The List Identity Insertion Method (LIIM) allows to mitigate the error from certain CNOT gates, typically those with the largest error. Set Identity Insertion Method (SIIM) naturally interpolates between the measurement-efficient FIIM and the gate-efficient RIIM, allowing to trade off fewer CNOT gates for more measurements. Finally, we investigate a way to boost the number of measurements, namely to run ZNE in parallel, utilizing as many quantum devices as are available. We explore the performance of RIIM in a parallel setting where there is a non-trivial spread in noise across sets of qubits within or across quantum computers.

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arXiv2021

Efficient Representation for Simulating U(1) Gauge Theories on Digital Quantum Computers at All Values of the Coupling

We derive a representation for a lattice U(1) gauge theory with exponential convergence in the number of states used to represent each lattice site that is applicable at all values of the coupling. At large coupling, this representation is equivalent to the Kogut-Susskind electric representation, which is known to provide a good description in this region. At small coupling, our approach adjusts the maximum magnetic field that is represented in the digitization as in this regime the low-lying eigenstates become strongly peaked around zero magnetic field. Additionally, we choose a representation of the electric component of the Hamiltonian that gives minimal violation of the canonical commutation relation when acting upon low-lying eigenstates, motivated by the Nyquist-Shannon sampling theorem. For (2+1) dimensions with 4 lattice sites the expectation value of the plaquette operator can be calculated with only 7 states per lattice site with per-mille level accuracy for all values of the coupling constant.

hep-ph↗

arXiv2021

Practical considerations for the preparation of multivariate Gaussian states on quantum computers

We provide explicit circuits implementing the Kitaev-Webb algorithm for the preparation of multi-dimensional Gaussian states on quantum computers. While asymptotically efficient due to its polynomial scaling, we find that the circuits implementing the preparation of one-dimensional Gaussian states and those subsequently entangling them to reproduce the required covariance matrix differ substantially in terms of both the gates and ancillae required. The operations required for the preparation of one-dimensional Gaussians are sufficiently involved that generic exponentially-scaling state-preparation algorithms are likely to be preferred in the near term for many states of interest. Conversely, polynomial-resource algorithms for implementing multi-dimensional rotations quickly become more efficient for all but the very smallest states, and their deployment will be a key part of any direct multidimensional state preparation method in the future.

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arXiv2021

Quantum Gate Pattern Recognition and Circuit Optimization for Scientific Applications

There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce two separate ideas for circuit optimization and combine them in a multi-tiered quantum circuit optimization protocol called AQCEL. The first ingredient is a technique to recognize repeated patterns of quantum gates, opening up the possibility of future hardware co-optimization. The second ingredient is an approach to reduce circuit complexity by identifying zero- or low-amplitude computational basis states and redundant gates. As a demonstration, AQCEL is deployed on an iterative and efficient quantum algorithm designed to model final state radiation in high energy physics. For this algorithm, our optimization scheme brings a significant reduction in the gate count without losing any accuracy compared to the original circuit. Additionally, we have investigated whether this can be demonstrated on a quantum computer using polynomial resources. Our technique is generic and can be useful for a wide variety of quantum algorithms.

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arXiv2021

Dark Matter Spectra from the Electroweak to the Planck Scale

We compute the decay spectrum for dark matter (DM) with masses above the scale of electroweak symmetry breaking, all the way to the Planck scale. For an arbitrary hard process involving a decay to the unbroken standard model, we determine the prompt distribution of stable states including photons, neutrinos, positrons, and antiprotons. These spectra are a crucial ingredient in the search for DM via indirect detection at the highest energies as being probed in current and upcoming experiments including IceCube, HAWC, CTA, and LHAASO. Our approach improves considerably on existing methods. For example, we include all relevant electroweak interactions. The importance of these effects grow with DM mass, and by an EeV our spectra can differ by orders of magnitude from existing results.

hep-ph↗

arXiv2021

Mitigating depolarizing noise on quantum computers with noise-estimation circuits

A significant problem for current quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model often appropriately describes average noise for large circuits involving many qubits and gates. We present a method to mitigate the depolarizing noise by first estimating its rate with a noise-estimation circuit and then correcting the output of the target circuit using the estimated rate. The method is experimentally validated on the simulation of the Heisenberg model. We find that our approach in combination with readout-error correction, randomized compiling, and zero-noise extrapolation produces results close to exact results even for circuits containing hundreds of CNOT gates.

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arXiv2021

Simulating collider physics on quantum computers using effective field theories

Simulating the full dynamics of a quantum field theory over a wide range of energies requires exceptionally large quantum computing resources. Yet for many observables in particle physics, perturbative techniques are sufficient to accurately model all but a constrained range of energies within the validity of the theory. We demonstrate that effective field theories (EFTs) provide an efficient mechanism to separate the high energy dynamics that is easily calculated by traditional perturbation theory from the dynamics at low energy and show how quantum algorithms can be used to simulate the dynamics of the low energy EFT from first principles. As an explicit example we calculate the expectation values of vacuum-to-vacuum and vacuum-to-one-particle transitions in the presence of a time-ordered product of two Wilson lines in scalar field theory, an object closely related to those arising in EFTs of the Standard Model of particle physics. Calculations are performed using simulations of a quantum computer as well as measurements using the IBMQ Manhattan machine.

hep-ph↗

arXiv2020

Disentangling observable dependence in SCETI and SCETII anomalous dimensions: angularities at two loops

The resummation of radiative corrections to collider jet observables using soft collinear effective theory is encoded in differential renormalization group equations (RGEs), with anomalous dimensions depending on the observable under consideration. This observable dependence arises from the ultraviolet (UV) singular structure of real phase space integrals in the effective field theory. We show that the observable dependence of anomalous dimensions in SCETI problems can be disentangled by introducing a suitable UV regulator in real radiation integrals. Resummation in the presence of the new regulator can be performed by solving a two-dimensional system of RGEs in the collinear and soft sectors, and resembles many features of resummation in SCETII theories by means of the rapidity renormalization group. We study the properties of SCETI with the additional regulator and explore the connection with the system of RGEs in SCETII theories, highlighting some universal patterns that can be exploited in perturbative calculations. As an application, we compute the two-loop soft and jet anomalous dimensions for a family of recoil-free angularities and give new analytic results. This allows us to study the relations between the SCETI and SCETII limits for these observables. We also discuss how the extra UV regulator can be exploited to calculate anomalous dimensions numerically, and the prospects for numerical resummation.

hep-ph↗

arXiv2020

Readout Rebalancing for Near Term Quantum Computers

Readout errors are a significant source of noise for near term intermediate scale quantum computers. Mismeasuring a qubit as a 1 when it should be 0 occurs much less often than mismeasuring a qubit as a 0 when it should have been 1. We make the simple observation that one can improve the readout fidelity of quantum computers by applying targeted X gates prior to performing a measurement. These X gates are placed so that the expected number of qubits in the 1 state is minimized. Classical post processing can undo the effect of the X gates so that the expectation value of any observable is unchanged. We show that the statistical uncertainty following readout error corrections is smaller when using readout rebalancing. The statistical advantage is circuit- and computer-dependent, and is demonstrated for the $W$ state, a Grover search, and for a Gaussian state. The benefit in statistical precision is most pronounced (and nearly a factor of two in some cases) when states with many qubits in the excited state have high probability.

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arXiv2020

Unfolding Quantum Computer Readout Noise

In the current era of noisy intermediate-scale quantum (NISQ) computers, noisy qubits can result in biased results for early quantum algorithm applications. This is a significant challenge for interpreting results from quantum computer simulations for quantum chemistry, nuclear physics, high energy physics, and other emerging scientific applications. An important class of qubit errors are readout errors. The most basic method to correct readout errors is matrix inversion, using a response matrix built from simple operations to probe the rate of transitions from known initial quantum states to readout outcomes. One challenge with inverting matrices with large off-diagonal components is that the results are sensitive to statistical fluctuations. This challenge is familiar to high energy physics, where prior-independent regularized matrix inversion techniques (`unfolding') have been developed for years to correct for acceptance and detector effects when performing differential cross section measurements. We study various unfolding methods in the context of universal gate-based quantum computers with the goal of connecting the fields of quantum information science and high energy physics and providing a reference for future work. The method known as iterative Bayesian unfolding is shown to avoid pathologies from commonly used matrix inversion and least squares methods.

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