We designed a protocol for digital quantum computation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on <math><mn>1</mn><mo>+</mo><mn>1</mn></math> dimensional quantum electrodynamics with the <math><mi>θ</mi></math> term known as the Schwinger model and test our protocol for this on an IBM simulator. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in the massless case agrees with the known exact result. In the massive case, we find an agreement with mass perturbation theory in the small-mass regime and deviations in the large-mass regime. We estimate computational costs required to take a reasonable continuum limit. Our results imply that digital quantum simulation appears a promising tool to explore nonperturbative aspects of gauge theories with real time and topological terms.

United Kingdom

Bipasha Chakraborty

Masazumi Honda

United States

Taku Izubuchi

Yuta Kikuchi

Akio Tomiya

Classically emulated digital quantum simulation of the Schwinger model with a topological term via adiabatic state preparation

Abstract We study some properties of generalized global symmetry for the charge-q Schwinger model in the Hamiltonian formalism, which is the (1 + 1)D quantum electrodynamics with a charge-q Dirac fermion. This model has the -form symmetry, which is a remnant of the electric -form symmetry in the pure Maxwell theory. It is known that, if we put the theory on closed space, then the Hilbert space is decomposed into q distinct sectors, called universes, and some states with higher energy density do not decay to the ground state due to the selection rule of the 1-form symmetry. Even with open boundaries, we can observe the stability of such states by seeing a negative string tension behavior, meaning that opposite charges repel each other. In order to see negative string tensions, the vacuum angle θ has to be large enough and the standard path-integral Monte Carlo method suffers from the sign problem. We develop a method based on the adiabatic state preparation to see this feature with digital quantum simulation and confirm it using a classical simulator of quantum devices. In particular, we measure the local energy density and see how it jumps between the inside and outside of the insertion of the probe charges. We explicitly see that the energy density inside is lower than that outside. This is a clear signature of the negative string tension.

Japan

Etsuko Itou

Yuya Tanizaki

Negative string tension of a higher-charge Schwinger model via digital quantum simulation

We perform digital quantum simulation, using a classical simulator, to study screening and confinement in a gauge theory with a topological term, focusing on (<math><mn>1</mn><mo>+</mo><mn>1</mn></math>)-dimensional quantum electrodynamics (Schwinger model) with a theta term. We compute the ground state energy in the presence of probe charges to estimate the potential between them, via adiabatic state preparation. We compare our simulation results and analytical predictions for a finite volume, finding good agreements. In particular our result in the massive case shows a linear behavior for noninteger charges and a nonlinear behavior for integer charges, consistently with the expected confinement (screening) behavior for noninteger (integer) charges.

Lento Nagano

Takuya Okuda

Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term

The real-time topological susceptibility is studied in <math><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></math>-dimensional massive Schwinger model with a <math><mi>θ</mi></math>-term. We evaluate the real-time correlation function of electric field that represents the topological Chern-Pontryagin number density in (<math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>) dimensions. Near the parity-breaking critical point located at <math><mi>θ</mi><mo>=</mo><mi>π</mi></math> and fermion mass <math><mi>m</mi></math> to coupling <math><mi>g</mi></math> ratio of <math><mrow><mi>m</mi><mo>/</mo><mi>g</mi><mo>≈</mo><mn>0.33</mn></mrow></math>, we observe a sharp maximum in the topological susceptibility. We interpret this maximum in terms of the growth of critical fluctuations near the critical point, and draw analogies between the massive Schwinger model, QCD near the critical point, and ferroelectrics near the Curie point.

Kazuki Ikeda

Dmitri E. Kharzeev

Real-time dynamics of Chern-Simons fluctuations near a critical point

In the Hayden-Preskill thought experiment, the Hawking radiation emitted before a quantum state is thrown into the black hole is used along with the radiation collected later for the purpose of decoding the quantum state. A natural question is how the recoverability is affected if the stored early radiation is damaged or subject to decoherence, and/or the decoding protocol is imperfectly performed. We study the recoverability in the thought experiment in the presence of decoherence or noise in the storage of early radiation.

Ning Bao

Hayden-Preskill decoding from noisy Hawking radiation

We elucidate that the phase diagram of massless <math><mi>N</mi></math>-flavor QCD under a <math><msub><mi>Z</mi><mi>N</mi></msub></math> flavor-twisted boundary condition (massless <math><msub><mi>Z</mi><mi>N</mi></msub></math>-QCD) is constrained by a ’t Hooft anomaly involving two-form gauge fields. As a consequence, massless <math><msub><mi>Z</mi><mi>N</mi></msub></math>-QCD turns out to realize persistent order at any temperature and quark chemical potential; namely, the symmetric and gapped phase is strictly forbidden. This is the first result on the finite-<math><mo>(</mo><mi>T</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math> phase diagram in QCD-type theories based on anomaly matching related to center and discrete axial symmetries.

Tatsuhiro Misumi

Norisuke Sakai

Anomaly matching for the phase diagram of massless <math><msub><mi>Z</mi><mi>N</mi></msub></math>-QCD

An ’t Hooft anomaly is the obstruction for gauging symmetries, and it constrains possible low-energy behaviors of quantum field theories by excluding trivial infrared theories. The global inconsistency condition has recently been proposed as a milder condition but is expected to play almost the same role by comparing high symmetry points in the theory space. In order to clarify the consequences of this new condition, we discuss several quantum-mechanical models with topological angles and explicitly compute their energy spectra. It turns out that the global inconsistency can be saturated not only by the ground-state degeneracy at either of the high symmetry points but also by the level crossing (phase transition) separating those high symmetry points.

Global inconsistency, ’t Hooft anomaly, and level crossing in quantum mechanics

We discuss possible vacuum structures of SU( n ) × SU( n ) gauge theories with bifundamental matters at finite θ angles. In order to give a precise constraint, a mixed ’t Hooft anomaly is studied in detail by gauging the center ℤ n one-form symmetry of the bifundamental gauge theory. We propose phase diagrams that are consistent with the con-straints, and also give a heuristic explanation of the result based on the dual superconductor scenario of confinement.