Entanglement bounds on the performance of quantum computing architectures.

There are many possible architectures of qubit connectivity that designers of future quantum computers will need to choose between. However, the process of evaluating a particular connectivity graph's performance as a quantum architecture can be difficult. In this paper, we show that a quantity known as the isoperimetric number establishes a lower bound on the time required to create highly entangled states. This metric we propose counts resources based on the use of two-qubit unitary operations, while allowing for arbitrarily fast measurements and classical feedback. We use this metric to evaluate the hierarchical architecture proposed by A. Bapat et al. [Phys. Rev. A 98, 062328 (2018)] and find it to be a promising alternative to the conventional grid architecture. We also show that the lower bound that this metric places on the creation time of highly entangled states can be saturated with a constructive protocol, up to a factor logarithmic in the number of qubits.

Probing Ground-State Phase Transitions through Quench Dynamics.

The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.

Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator.

The multiscale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with a finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wave function with a nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.

Locality and Digital Quantum Simulation of Power-Law Interactions.

The propagation of information in nonrelativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/r α . The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al., FOCS'18. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α > 3D (where D is the number of dimensions).

Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics.

We study the nonequilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast to the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through nonequilibrium dynamics.

Unitary entanglement construction in hierarchical networks.

The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement-the translation from circuit diagrams to machine qubits-on quantum systems whose connectivity is described by hierarchies.

Extracting Entanglement Geometry from Quantum States.

Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network-and hence the geometry-is largely fixed a priori by the choice of the tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of noninteracting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.

Lieb-Robinson bounds on n-partite connected correlation functions.

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

Theory of a competitive spin liquid state for weak Mott insulators on the triangular lattice.

We propose a novel quantum spin liquid state that can explain many of the intriguing experimental properties of the low-temperature phase of the organic spin liquid candidate materials κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2. This state of paired fermionic spinons preserves all symmetries of the system, and it has a gapless excitation spectrum with quadratic bands that touch at momentum k[over →]=0. This quadratic band touching is protected by symmetries. Using variational Monte Carlo techniques, we show that this state has highly competitive energy in the triangular lattice Heisenberg model supplemented with a realistically large ring-exchange term.

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons.

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit 'strange metal' behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal--the 'd-wave metal'. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian--the usual t-J model with electron kinetic energy t and two-spin exchange J supplemented with a frustrated electron 'ring-exchange' term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.