The evaluation of expectation values Tr[ρO] for some pure state ρ and Hermitian operator O is of central importance in a variety of quantum algorithms. Near optimal techniques developed in the past 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 requires however long circuit depths C=O(1/ϵ) making their 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/ϵ²) measurements and no additional gates besides 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) and show that the latter strategy can require an overly large number of measurement in order to achieve a reasonably small relative target accuracy ϵr. We propose to overcome this problem using a single step of QPE and classical post-processing. This approach leads to a circuit depth C=O(ϵ^m) (with m≥0) and to a number of measurements N=O(1/ϵ²⁺ⁿ) for 0<n≤1. We provide detailed descriptions of two implementations of our strategy for n=1 and n≈0.5 and derive appropriate conditions that a particular problem instance has to satisfy in order for our method to provide an advantage.

Initializing a single site of a lattice scalar field theory into an arbitrary state requires O(2^nQ) entangling gates on a quantum computer with n_Q qubits per site. It is conceivable that, instead, initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a non-interacting scalar field theory, initializing to a symmetric exponential wavefunction requires n_Q − 1 entangling gates, compared with the 2^nQ−1 + n_Q − 3 + δ_nQ,1 required for a symmetric Gaussian wavefunction. In this work, we explore the initialization of 1-site (n_Q = 4), 2-site (n_Q = 3) and 3-site (n_Q = 3) non- interacting scalar field theories with symmetric exponential wavefunctions using IBM’s quantum simulators and quantum devices (Poughkeepsie and Tokyo). With the digitizations obtainable with n_Q = 3, 4, these tensor-product wavefunctions are found to have large overlap with a Gaussian wavefunction, and provide a suitable low-noise initialization for subsequent quantum simulations. In performing these simulations, we have employed a workflow that interleaves calibrations to mitigate systematic errors in production. The calibrations allow tolerance cuts on gate performance including the fidelity of the symmetrizing Hadamard gate, both in vacuum (|0⟩^⊗nQ ) and in medium (n_Q − 1 qubits initialized to an exponential function). The results obtained in this work are relevant to systems beyond scalar field theories, such as the deuteron radial wavefunction, 2- and 3-dimensional cartesian-space wavefunctions, and non-relativistic multi-nucleon systems built on a localized eigenbasis.

We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (arXiv:1912.06133) as a basis for digital quantum computation easily solves an important problem of fundamental interest: implementing gauge invariance (or Gauss’s law) exactly. We first discuss the structure of the LSH Hilbert space in d spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality “oracles,” so we decompose circuits that flag gauge invariant wavefunctions. We then analyze the logical qubit costs and entangling gate counts involved with the protocols. The LSH basis could save or cost more qubits than a Kogut-Susskind-type representation basis, depending on how that is digitized as well as the spatial dimension. The numerous other clear benefits encourage future studies into applying this framework.

Entanglement suppression in the strong interaction S-matrix is shown to be correlated with approximate spin-flavor symmetries that are observed in low-energy baryon interactions, the Wigner SU(4) symmetry for two flavors and an SU(16) symmetry for three flavors. We conjecture that dynamical entanglement suppression is a property of the strong interactions in the infrared, giving rise to these emergent symmetries and providing powerful constraints on the nature of nuclear and hypernuclear forces in dense matter.

Formulating a lattice gauge theory using only physical degrees of freedom generically leads to non-local interactions. A local Hamiltonian is desirable for quantum simulation, and this is possible by treating the Hilbert space as a subspace of a much larger Hilbert space in which Gauss’s law is not automatic. Digital quantum simulations of this local formulation will wander into unphysical sectors due to errors from Trotterization or from quantum noise. In this work, oracles are constructed that use local Gauss law constraints to projectively distinguish physical and unphysical wave functions in Abelian lattice gauge theories. Such oracles can be used to detect errors that break Gauss’s law.

Simulating complex many-body quantum phenomena is a major scientific impetus behind the development of quantum computing, and a range of technologies are being explored to address such systems. We present the results of the largest photonics-based simulation to date, applied in the context of subatomic physics. Using an all-optical quantum frequency processor, the ground-state energies of light nuclei including the triton (3H), 3He, and the alpha particle (4He) are computed. Complementing these calculations and utilizing a 68-dimensional Hilbert space, our photonic simulator is used to perform sub-nucleon calculations of the two-body and three-body forces between heavy mesons in the Schwinger model. This work is a first step in simulating subatomic many-body physics on quantum frequency processors—augmenting classical computations that bridge scales from quarks to nuclei.[Image (left) was created by Pavel Lougovski.]

Qubit, operator and gate resources required for the digitization of lattice λϕ4 scalar field theories onto quantum computers in the NISQ era are considered, building upon the foundational work by Jordan, Lee and Preskill. The Nyquist-Shannon sampling theorem, introduced in this context by Macridin, Spetzouris, Amundson and Harnik building on the work of Somma, provides a guide with which to evaluate the efficacy of two field-space bases, the eigenstates of the field operator, as used by Jordan, Lee and Preskill, and eigenstates of a harmonic oscillator, to describe 0+1- and 1+1-dimensional scalar field theory. We show how techniques associated with improved actions, which are heavily utilized in Lattice QCD calculations to systematically reduce lattice-spacing artifacts, can be used to reduce the impact of the field digitization in λϕ4, but are found to be inferior to a complete digitization-improvement of the Hamiltonian using a Quantum Fourier Transform. When the Nyquist-Shannon sampling theorem is satisfied, digitization errors scale as |log|log|ϵdig|||∼nQ (number of qubits describing the field at a given spatial site) for the low-lying states, leaving the familiar power-law lattice-spacing and finite-volume effects that scale as |log|ϵlatt||∼NQ (total number of qubits in the simulation). We find that fewer than nQ=10 qubits per spatial lattice site are sufficient to reduce digitization errors below noise levels expected in NISQ-era quantum devices for both localized and delocalized field-space wavefunctions. For localized wavefunctions, nQ=4 qubits are likely to be sufficient for calculations requiring modest precision.

Quantum computers have the potential to explore the vast Hilbert space of entangled states that play an important role in the behavior of strongly interacting matter. This opportunity motivates reconsidering the Hamiltonian formulation of gauge theories, with a suitable truncation scheme to render the Hilbert space finite-dimensional. Conventional formulations lead to a Hilbert space largely spanned by unphysical states; given the current inability to perform large scale quantum computations, we examine here how one might restrict wave function evolution entirely or mostly to the physical subspace. We consider such constructions for the simplest of these theories containing dynamical gauge bosons—U(1) lattice gauge theory without matter in d=2,3 spatial dimensions—and find that electric-magnetic duality naturally plays an important role. We conclude that this approach is likely to significantly reduce computational overhead in d=2 by a reduction of variables and by allowing one to regulate magnetic fluctuations instead of electric. The former advantage does not exist in d=3, but the latter might be important for asymptotically-free gauge theories.

The dynamic linear response of a quantum system is critical for understanding both the structure and dynamics of strongly-interacting quantum systems, including neutron scattering from materials, photon and electron scattering from atomic systems, and electron and neutrino scattering by nuclei. We present a general algorithm for quantum computers to calculate the dynamic linear response function with controlled errors and to obtain information about specific final states that can be directly compared to experimental observations.

We present a quantum-classical algorithm to study the dynamics of the two-spatial-site Schwinger model on IBM’s quantum computers. Using rotational symmetries, total charge, and parity, the number of qubits needed to perform computation is reduced by a factor of ∼5, removing exponentially-large unphysical sectors from the Hilbert space. Our work opens an avenue for exploration of other lattice quantum field theories, such as quantum chromodynamics, where classical computation is used to find symmetry sectors in which the quantum computer evaluates the dynamics of quantum fluctuations.