QAMBS

Nonstabilizerness, or magic, is a critical quantum resource that, together with entanglement, characterizes the non‐classical complexity of quantum states. Here, we address the problem of quantifying the magic of Matrix Product States (MPS) with bond dimension $\latex \chi$. First, we show how Stabilizer Rényi Entropies (SRE) can be estimated by means of a simple perfect sampling of the MPS over the Pauli string configurations. Second, we consider random Matrix Product States (RMPS). We demonstrate that the 2-SRE converges to that of Haar random states as N/$\latex \chi^2$, where N is the system size. This indicates that MPS with a modest bond dimension are as magical as generic states. Finally, we introduce the ensemble of Clifford enhanced Matrix Product States (CMPS), built by the action of Clifford unitaries on RMPS. Leveraging our previous result, we show that CMPS can approximate $\latex 4$-spherical designs with arbitrary accuracy. Our findings indicate that combining Clifford unitaries with polynomially complex tensor network states can generate highly non-trivial quantum states.

An important step in the compilation of a given quantum circuit on a given target device is qubit routing; the insertion of SWAP gates so that the required two-qubit gates can be performed on the hardware given the restricted qubit connectivity. Noisy intermediate-scale and early fault-tolerant quantum computers will be severely limited in their capabilities. This motivates the search for optimal SWAP strategies. This is at stake with the fact that finding the optimal SWAP strategy is NP hard. However, both (A) quantum circuits for the quantum simulation of condensed matter systems and (B) hardware connectivity graphs—typically having a spatial periodic structure—can be exploited to make the problem tractable. I will present a method that does so and apply it to various circuits arising in quantum simulation. Assuming arbitrary two-qubit gates have unit depth, this leads to surprisingly low SWAP overheads. For example, the quantum circuit for the simulation of the Heisenberg model on a square grid (A) can be performed on a quantum computer with a square-grid coupling graph (B) with no SWAP overhead at all.

I will describe a novel class of exactly solvable quantum unitary circuits on qudits. Their key feature is an architecture that breaks parity and time-reversal symmetries while retaining the combined PT symmetry. A consequence of this chirality is a spin transport with a finite drift: the circuit acts as a quantum spin pump. The drift velocity is universal in that it depends only on the Casimir invariant of the local quantum spaces and survives non-integrable perturbations. I will comment on the connection to integrable trotterizations and, if time permits, discuss spin transport coefficients and hydrodynamics.

The simulation of quantum systems is one of the most promising applications of quantum computers. In this paper we present a quantum algorithm to perform digital quantum simulations of the BCS model on a quantum register with a star-shaped connectivity map, as it is, e.g., featured by color centers in diamond. We show how to effectively translate the problem onto the quantum hardware and implement the algorithm using only the native interactions between the qubits. Furthermore, we discuss the complexity of the circuit. We use the algorithm to simulate the dynamics of the BCS model by subjecting its mean-field ground state to a time-dependent perturbation. The quantum simulation algorithm is studied using a classical simulation.

When simulating the time evolution of quantum many-body systems on a digital quantum computer, one faces the challenges of quantum noise and the Trotter error due to time discretization. The Trotter error in integrable spin chains can be controlled if the discrete time evolution preserves integrability. In this work we implement, on a real quantum computer and on classical simulators, the integrable Trotterization of the spin-1/2 Heisenberg XXX spin chain. We study how quantum noise affects the time evolution of several conserved charges and observe the decay of their expectation values. We also study early-time behavior, which can potentially be used to benchmark quantum devices and algorithms. Finally, we provide an efficient method to generate the conserved charges at higher orders.

The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical situations relevant to condensed matter physics, high energy physics, quantum chemistry, and quantum computing. We provide a pedagogical overview of the universal features of these states—focusing on mathematically rigorous statements inspired by quantum information theory—including bounds on correlations, the structure of subsystems, statistical properties, and the performance of classical and quantum algorithms. We also summarize several key technical tools along with self-contained proofs.

Many quantum computing platforms have a restricted connectivity of their qubits, as captured by their connectivity graphs. This poses a challenge for running algorithms that require a different connectivity than what the hardware offers. Such algorithms naturally arise in the simulation of lattice-based spin models on quantum computers when there is a mismatch between the simulated lattice and the hardware’s connectivity graph. To overcome this, we present line‑graph routing: a general method for qubit routing when the algorithm’s connectivity is a line graph and the hardware connectivity is a heavy graph. We demonstrate our approach by routing circuits on kagome and shuriken lattices to hardware with heavy‑hex and heavy‑square‑octagon connectivity, respectively. Benchmarking shows that line‑graph routing outperforms established methods.

The intensive pursuit for quantum algorithms with a computational speedup has led to the crucial question: When and how will quantum computers outperform classical computers? The next milestone in quantum transcendence is the realization of quantum acceleration in practical problems. Here, we provide clear evidence and arguments that condensed matter physics is the primary target. Our contributions include: 1) a systematic error/runtime analysis of state-of-the-art tensor network algorithms; 2) a high-resolution analysis of quantum resource requirements at the level of executable logical instructions; and 3) a clarification of the quantum-classical crosspoint for ground-state simulation achievable within hours using only a few hundred thousand physical qubits for 2D Heisenberg and 2D Fermi‑Hubbard models. We argue that condensed matter problems offer the earliest feasible platform for demonstrating practical quantum advantage.

The ground state of the spin‑1 Affleck, Kennedy, Lieb and Tasaki (AKLT) model is a paradigmatic example of both a matrix product state and a symmetry‑protected topological phase. It also holds promise as a resource state for measurement‑based quantum computation. Due to its nonzero correlation length, the AKLT state cannot be exactly prepared by a constant‑depth unitary circuit composed of local gates. In this talk, I will demonstrate that this no‑go limit can be evaded by augmenting a constant‑depth circuit with fusion measurements—making the total preparation time independent of system size. Experimental results collected on an IBM Quantum processor indicate that our measurement‑assisted scheme outperforms a purely unitary protocol. I will also demonstrate the utility of prepared AKLT states as “quantum wires” for teleportation.

The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several models in statistical mechanics and condensed‑matter physics. Here we reformulate the ABA into unitary form for its direct implementation on a quantum computer. This is achieved by distilling the non‑unitary R matrices via a QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method on the spin‑12 XX and XXZ models and show that it can efficiently prepare eigenstates of the XX model on a quantum computer with resources comparable to state‑of‑the‑art approaches. Small‑scale error‑mitigated implementations on IBM Quantum devices are also presented, including the preparation of ground states for the XX and XXZ models on 4 sites. Finally, we derive a new form of the Yang‑Baxter equation using unitary matrices, and verify it on a quantum computer.

Simulating complex molecules and materials is an anticipated application of quantum devices. With hardware increasingly designed to target strong quantum advantage in artificial tasks, we examine how the same hardware behaves when modeling physical problems of correlated electronic structure. By simplifying the electronic structure into low‑energy spin models that fit the device, and using extensive error mitigation plus classical recompilation, we achieve quantitatively meaningful results using about one‑fifth of the gate resources employed in artificial quantum advantage experiments. This increases to over half of the resources when using a model suited to the hardware. Our work thus converts artificial measures of quantum advantage into a physically relevant setting.

I will explain recent work on constructing integrable quantum circuits using methods from the statistical mechanics of lattice models, such as the Yang‑Baxter relation and star‑triangle relation. I will demonstrate the construction using the renowned 6‑vertex model and Potts model, and present a proof of the recently conjectured integrability in so‑called Potts circuits by Vladimir, Denis and their collaborators (Phys. Rev. B 105, 144306). This construction can be extended to what I call the “Ashkin‑Teller circuit,” which has not been previously studied.

Estimating the ground state energy of a local Hamiltonian is a central problem in quantum many-body physics. Gharibian and Le Gall (STOC 2022) recently introduced the guided local Hamiltonian problem (GLH) – a variant of the local Hamiltonian problem (LH) where a classical approximation of a ground state is provided as input. While LH is known to be QMA‑complete (and thus ‘hard’ even for quantum computers), they showed that GLH with 6‑local Hamiltonians is BQP‑complete when the guiding vector has fidelity (inverse‑polynomially) close to 1/2 with a ground state—yielding a worst‑case quantum advantage. In this talk, I introduce the GLH problem, explain its relevance, and share results in which both the locality and overlap parameters are optimally improved, along with an extension of the hardness results to excited states.

Simulation of materials is one of the most promising applications of quantum computers. On near‑term hardware the critical constraint is circuit depth. Many quantum simulation algorithms rely on a layer of unitary evolutions generated by each term in a Hamiltonian—appearing as a single Trotter step in dynamics or as a layer in variational quantum eigensolvers. We present a new quantum algorithm design for materials modelling where the depth per layer is independent of system size. This design exploits the locality of materials in the Wannier basis and employs a tailored fermionic encoding that preserves locality. We analyze the circuit costs and introduce a compiler that transforms density functional theory data into quantum circuit instructions, connecting material physics with simulation circuits. Numerical results for materials across a wide range demonstrate a drastic reduction in circuit depth compared to standard methods.