Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the dynamics of open quantum systems governed by Lindbladians. We introduce a new approximation channel for short-time evolution, inspired by the quantum trajectory method, which underpins the efficiency of our algorithms. The first algorithm achieves a gate complexity independent of the number of jump operators, $m$, marking a significant improvement in efficiency. The second algorithm achieves near-optimal dependence on the evolution time $t$ and precision $ϵ$ and introduces only an additional $\tilde{O}(m)$ factor, which strictly improves upon state-of-the-art gate-based quantum algorithm that has an $\tilde{O}(m^2)$ factor. The improvement stems from the integration of the new approximation channel with a novel structured linear combination of unitaries method. In both our algorithms, the reduction of dependence on $m$ significantly enhances the efficiency of simulating practical dissipative processes characterized by a large number of jump operators.

Qudits, generalizations of qubits to multilevel quantum systems, offer enhanced computational efficiency by encoding more information per lattice cell, avoiding costly swap operations and providing even exponential speedup in some cases. Utilizing the $d$-level manifold, however, requires high-speed gate operations because of the stronger decoherence at higher levels. While analytical control methods have proven effective for qubits in achieving fast gates with minimal control errors, their extension to qudits is nontrivial due to the increased complexity of the energy-level structure arising from additional ancillary states. In this work, we present a universal pulse construction for generating rapid, high-fidelity unitary rotations between adjacent qudit levels, thereby providing a prescription for any gate in $\mathrm{SU}(d)$. Control errors in these operations are effectively analyzed within a four-level subspace, including two leakage levels with approximately opposite detuning. By identifying the optimal degrees of freedom, we derive concise analytical pulse schemes that suppress multiple control errors and outperform existing methods. Remarkably, our approach achieves consistent coherent error scaling across all levels, approaching the quantum speed limit independently of parameter variations between levels. Numerical validation on transmon circuits demonstrates significant improvements in gate fidelity for various qudit sizes aiming for ${10}^{-4}$ error. This method provides a scalable solution for improving qudit control and can be broadly applied to other quantum systems with ladder structures or operations involving multiple ancillary levels.

Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local control of chemical potentials and tunnelings, and thus enable us to operate this platform digitally as a programmable quantum simulator. Here, we explore these opportunities and develop ground-state preparation algorithms for different fermionic models, based on the ability to implement both single-particle and many-body high-fidelity fermionic gates, as provided by the native FH Hamiltonian. In particular, we first design variational precompiled quantum circuits to prepare the ground state of the natively implemented FH model, with significant speedups relative to competing adiabatic protocols. Besides, the versatility of this variational approach enables us to target extended FH models, i.e., including terms that are not natively realized on the platform. As an illustration, we include next-nearest-neighbor tunnelings at finite dopings, relevant in the context of $d$-wave superconductivity. Furthermore, we discuss how to approximate the imaginary-time evolution using variational fermionic circuits, both as an alternative state-preparation strategy and as a subroutine for the quantum Lanczos algorithm to further improve the energy estimation. We benchmark our protocols for ladder geometries, though they can be readily applied to two-dimensional experimental setups to address regimes beyond the capabilities of current classical methods. These results pave the way for more efficient and comprehensive explorations of relevant many-body phases with existing programmable fermionic quantum simulators.

Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory is affected by realistic coherent noise, such as random rotation noise and amplitude-damping noise. In this work, we investigate the intrinsic error threshold of the two-dimensional toric code (TC), a paradigmatic topological quantum memory, under these types of coherent noise by employing both analytical and numerical methods based on the doubled-Hilbert-space formalism. A connection between the mixed-state phase of the decohered TC and a non-Hermitian Ashkin-Teller-type statistical-mechanics model is established, and the mixed-state phase diagrams under the coherent noise are obtained. We find remarkable stability of mixed-state topological order under random rotation noise with axes near the $Y$ axis of qubits. We also identify intriguing extended critical regions at the phase boundaries, highlighting a connection with non-Hermitian physics. We argue that these phase boundaries provide upper bounds for the intrinsic error threshold, beyond which quantum error correction becomes impossible. We complement these findings by estimating the error thresholds for random rotation noise under standard quantum error correction, thereby providing lower bounds on the intrinsic error threshold.

Cross-platform verification is the task of comparing the output states produced by different physical platforms using solely local quantum operations and classical communication. While protocols have previously been suggested for this task, their exponential sample complexity renders them impractical even for intermediate-scale quantum systems. In this work, we propose a novel protocol for this task based on Pauli sampling, a subroutine that generates Paulis distributed according to their weight in the expansion of a quantum state in the Pauli basis. We show that our protocols for both Pauli sampling and cross-platform verification are efficient for pure states with low magic and entanglement [i.e., of the order $O(\log n)$]. Conversely, we show superpolynomial lower bounds on the complexity of both tasks for states with $\omega (\log (n))$ magic and entanglement. Interestingly, when considering states with real amplitudes, the requirements of our protocol for cross-platform verification can be significantly weakened.

The benefit of exchange-only qubits compared to other spin-qubit types is the universal control using only voltage-controlled exchange interactions between neighboring spins. As a compromise, qubit operations have to be constructed from nonorthogonal rotation axes of the Bloch sphere and result in rather long pulsing sequences. This paper aims to develop a faster implementation of single-qubit gates using simultaneous exchange pulses and manifests their potential for the construction of two-qubit gates. We introduce pulse sequences in which single-qubit gates could be executed faster and show that subsequences on three spins in two-qubit gates could be implemented in fewer steps. Our findings can particularly speed up gate sequences for realistic idle times between sequential pulses and we show that this advantage increases with more interconnectivity of the quantum dots. We further demonstrate how a phase operation can introduce a relative phase between the computational and some of the leakage states, which can be advantageous for the construction of two-qubit gates. In addition to our theoretical analysis, we experimentally demonstrate and characterize a simultaneous exchange implementation of $X$ rotations in a $\mathrm{Si}\mathrm{Ge}$ quantum dot device and compare to the state of the art with sequential exchange pulses.

We show that a self-correcting Gottesman-Kitaev-Preskill (GKP) qubit can be realized with a high-impedance $LC$ circuit coupled to a resistor and a Josephson junction via a controllable switch. When activating the switch in a particular stepwise pattern, the resonator relaxes into a subspace of GKP states that encode a protected qubit. Under continued operation, the resistor dissipatively error corrects the qubit against bit flips and decoherence by absorbing noise-induced entropy. We show that this leads to an exponential enhancement of the coherence time ($T_1$ and $T_2$), even in the presence of extrinsic noise, imperfect control, and device-parameter variations. We show that the qubit supports exponentially robust single-qubit Clifford gates, implemented via appropriate control of the switch, and readout and/or initialization via supercurrent measurement. The self-correcting properties of the qubit allow it to operate at approximately 1-K temperatures and resonator $Q$ factors down to approximately $1000$ for realistic parameters, and make it amenable to parallel control through global control signals. We discuss how the effects of quasiparticle poisoning—potentially, though not necessarily, a limiting factor—might be mitigated. We finally demonstrate that a related device supports a self-correcting magic $T$ gate.

Color centers in silicon are emerging as spin-photon interfaces operating at telecommunication wavelengths. The nanophotonic device integration of silicon color centers via ion implantation leads to significant optical-linewidth broadening, which makes indistinguishable photon generation challenging. Here, we study the optical spectral diffusion of T centers in a silicon photonic crystal cavity. We investigate the linewidth-broadening timescales and origins by measuring the temporal correlations of the resonance frequency under different conditions. Spectral hole-burning measurements reveal no spectral broadening at short timescales from 102 ns to 725 ns. We probe broadening at longer timescales using a check pulse to herald the T-center frequency and a probe pulse to measure the frequency after a wait time. The optical resonance frequency is stable up to 3 ms in the dark. Laser pulses below the silicon band gap applied during the wait time lead to linewidth broadening. Our observations establish laser-induced processes as the dominant spectral-diffusion mechanism for T centers in devices and inform materials and feedback strategies for indistinguishable photon generation.

To find practical application as photon sources for entangled optical-resource states or as spin-photon interfaces in entangled networks, semiconductor emitters must produce indistinguishable photons with high efficiency and spectral stability. Nanophotonic cavity integration increases efficiency and bandwidth but it also introduces environmental charge instability and spectral diffusion. Among various candidates, silicon color centers have emerged as compelling platforms for integrated-emitter quantum technologies. Here, we investigate the dynamics of spectral wandering in nanophotonics-coupled individual silicon T centers using spectral correlation measurements. We observe that spectral fluctuations are driven predominantly by the near-infrared excitation laser, consistent with a power-dependent Ornstein-Uhlenbeck process, and we show that the spectrum is stable for up to $1.5\mathrm{ms}$ in the dark. We demonstrate a factor-of-$35$ narrowing of the emitter linewidth to $110\mathrm{MHz}$ using a resonance-check scheme and discuss the advantage for pairwise entanglement rates and optical-resource-state generators. Finally, we report laser-induced spin mixing in the excited state and discuss potential mechanisms common to both phenomena. These effects must be considered in calibrating T-center devices for high-performance entanglement generation.

We present a new technique for efficiently simulating (in polynomial time) a class of one-dimensional (1D) dissipative spin chains that, when mapped to fermions, have quadratic Hamiltonians, with the only nonlinearity coming from Jordan-Wigner strings appearing in the jump operators, despite the fact that these models cannot be mapped to quadratic fermionic master equations. We show that many such Lindblad master equations admit an exact stochastic unraveling, with individual trajectories evolving as Gaussian fermionic states, even though the full master equation describes a system inequivalent to free fermions. This allows one to calculate arbitrary observables efficiently without sign problems, and with bounded sampling complexity. We utilize this new technique to study three paradigmatic dissipative effects: the melting of antiferromagnetic order in the presence of local loss, many-body subradiant phenomenon in systems with correlated loss, and nonequilibrium steady states of a 1D dissipative transverse-field Ising model. Beyond simply providing a powerful numerical technique, our method can also be used to gain both qualitative and quantitative insights into the role of interactions in these models.

Quantum simulations of strongly interacting fermionic systems, such as those described by the Hubbard model, are promising candidates for useful early fault-tolerant quantum computing applications. This paper presents tile Trotterization, a generalization of plaquette Trotterization, which uses a set of tiles to construct Trotter decompositions of arbitrary lattice Hubbard models. The tile Trotterization scheme also enables the simulation of more complex models, including the extended Hubbard model. We improve previous Hubbard-model commutator bounds, further provide tight commutator bounds for periodic extended Hubbard models, and demonstrate the use of tensor network methods for this task. We consider applications of tile Trotterization to simulate hexagonal lattice Hubbard models and compare the resource requirements of tile Trotterization for performing quantum phase estimation to a qubitization-based approach, demonstrating that tile Trotterization scales more efficiently with system size. These advancements significantly broaden the potential applications of early fault-tolerant quantum computers to models of practical interest in materials research and organic chemistry.

It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless midcircuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as depolarizing noise. Building on the idea of the “quantum refrigerator” Ben-Or et al. [Quantum refrigerator, arXiv1301.1995 (2013)], we improve upon previous results and show that geometrically local circuits in the presence of nonunital noise, in any dimension $d\ge 1$, can correct errors without midcircuit measurements and extend computation to any depth, with only polylogarithmic overhead in the depth and the number of qubits. This implies that local quantum dynamics subjected to sufficiently weak nonunital noise are computationally universal and nearly as hard to simulate as noiseless dynamics. Additionally, we quantify the contraction property of local random circuits in the presence of nonunital noise.

We propose a quantum algorithm, termed the universal quantum emulator, that emulates the action of an unknown unitary transformation or its inverse on a given input state, using multiple copies of some unknown sample input states of the unitary and their corresponding output states. The algorithm does not assume any prior information about the unitary to be emulated, the sample input states, or the relation between them. We rigorously prove that if the sample input states are tomographically complete, such that the action of an unknown unitary on the input subspace can be uniquely determined by its action on the sample input states, then our proposed algorithm succeeds in generating the desired output, with an error that becomes arbitrarily small by increasing the number of copies of the samples. Remarkably, the run-time of the algorithm is logarithmic in $D$, the dimension of the Hilbert space, and increases polynomially with $d$, the dimension of the subspace spanned by the sample input states. Furthermore, the sample complexity of the algorithm—i.e., the total number of copies of the sample input-output pairs needed to run the algorithm—is independent of $D$ and polynomial in $d$. In contrast, the run-time and sample complexity of algorithms that perform tomography on the sample states are both linear in $D$. This algorithm can be used as a subroutine in other algorithms, such as quantum phase estimation. We discuss some applications of this algorithm in areas including complexity theory, secure quantum computation, and quantum resource theories.

We investigate unitary and state $t$-designs from a computational complexity perspective. First, we address the problems of computing frame potentials that characterize (approximate) $t$-designs. We present a quantum algorithm for computing frame potentials and establish the following: (1) exact computation can be achieved by a single query to a $\mathrm{\#}\mathsf{P}$ oracle and is $\mathrm{\#}\mathsf{P}$-hard; (2) for state vectors, deciding whether the frame potential is larger than or smaller than certain values is $\mathsf{B}\mathsf{Q}\mathsf{P}$-complete, provided that the promise gap between the two values is inverse polynomial in the number of qubits; and (3) for both state vectors and unitaries, this promise problem is $\mathsf{P}\mathsf{P}$-complete if the promise gap is exponentially small. Second, we address the promise problem of deciding whether or not a given set is a good approximation to a design. Given a certain promise gap that could be constant, we show that this problem is $\mathsf{P}\mathsf{P}$-hard, highlighting the inherent computational difficulty of determining properties of unitary and state designs. We further identify implications of our results, including variational methods for constructing designs, diagnosing quantum chaos, and exploring emergent designs in Hamiltonian systems.

We put forward a user-friendly framework of the truncated Wigner approximation (TWA) for dissipative quantum many-body systems. Our approach is computationally affordable and it features a straightforward implementation. The leverage of the method can be ultimately traced to an intimate connection between the TWA and the semiclassical limit of the quantum Langevin equation, which we unveil by resorting to a path-integral representation of the Lindbladian. Our approach allows us to explore dynamics from early to late times in a variety of models at the core of modern atomic, molecular, and optical research, including lasing, central-spin models, driven arrays of Rydbergs, and correlated emission in free space. Notably, our TWA approach outperforms the cumulant-expansion method in certain models and performs comparably well in others, all while offering significantly lower computational costs and a much simpler formulation of the dynamical equations. We therefore argue that TWA could, in the near future, become a primary tool for a fast and efficient first exploration of driven-dissipative many-body dynamics on consumer-grade computers.

We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error-correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group, and impose constraints based on the Clifford operators permitted. We provide a rigorous formulation of the method for finding automorphisms of stabilizer codes and generalize the $ZX$ dualities previously introduced for Calderbank-Shor-Steane (CSS) codes to non-CSS codes. We provide a python package implementing our algorithms that uses the computational-algebra magma software system for certain subroutines. Our algorithms map automorphism-group generators to physical circuits, calculate Pauli corrections based on the destabilizers of the code, and determine their logical action. We discuss the fault tolerance of the circuits and include examples of gates through automorphisms for the $[[4,2,2]]$ and perfect $[[5,1,3]]$ codes, bivariate bicycle codes, and the best-known distance codes.

One of the key features of hole-doped cuprates is the presence of an extended pseudogap phase, whose microscopic origin has been the subject of intense investigation since its discovery and is believed to be crucial for understanding high-temperature superconductivity. Various explanations have been proposed for the pseudogap, including links to symmetry-breaking orders such as stripes or pairing, and the emergence of novel fractionalized Fermi liquid (${\mathrm{FL}}^{\ast }$) and orthogonal metal (OM) phases. The topological nature of ${\mathrm{FL}}^{\ast }$ and OM phases has been identified as scenarios compatible with a small Fermi surface without symmetry breaking, as suggested experimentally. With recent experimental and numerical studies supporting an intricate relationship between stripe order and the pseudogap phase, we here propose an alternative scenario: an orthogonal metal with a geometric origin (GOM) driven by fluctuating domain walls. The essential mechanism behind our proposal is hidden order, where the proliferation of domain walls stabilized by charge fluctuations obscures the underlying long-range antiferromagnetic order in real space, but order is preserved in the reference frame of the background spins. As a result, well-defined fermionic quasiparticles in the form of magnetic polarons exist, which couple to ${\mathbb{Z}}_2$ topological excitations of the domain-wall string-net condensate in the ground state and constitute a small Fermi surface. At a critical doping value, we argue that hidden order is lost, driving a transition to a regular Fermi liquid at a hidden quantum critical point featuring quantum critical transport properties. Our GOM framework establishes a deep connection between the antiferromagnetic, stripe, and pseudogap phases, and suggests a possible unification of superconductivity in (electron- and hole-) doped cuprates and heavy fermion compounds.

Free-fermionic states, also known as fermionic Gaussian states, represent an important class of quantum states that are ubiquitous in physics. They are uniquely and efficiently described by their correlation matrix. However, in practical experiments, the correlation matrix can only be estimated with finite accuracy. This raises the question: How does the error in estimating the correlation matrix affect the trace-distance error of the state? We show that if the correlation matrix is known with an error $\epsilon$, the trace-distance error also scales as $\epsilon$ (and vice versa). Specifically, we provide distance bounds between (both pure and mixed) free-fermionic states in relation to their correlation-matrix distance. Our analysis also extends to cases in which one state may not be free-fermionic. Importantly, we leverage our preceding results to derive significant advancements in property testing and tomography of free-fermionic states. Property testing involves determining whether an unknown state is close to or far from being a free-fermionic state. We first demonstrate that any algorithm capable of testing arbitrary (possibly mixed) free-fermionic states would inevitably be inefficient, implying that there is no efficient strategy to estimate the non-Gaussianity of a state. Then, we present an efficient algorithm for testing low-rank free-fermionic states. For free-fermionic state tomography, we provide improved bounds on the sample complexity in the pure-state scenario, substantially improving over previous literature, and we generalize the efficient algorithm to mixed states, discussing its noise robustness.

The bottom-up design of strongly interacting quantum materials with prescribed ground-state properties is a highly nontrivial task, especially if only simple constituents with realistic two-body interactions are available on the microscopic level. Here we study two- and three-dimensional structures of two-level systems that interact via a simple blockade potential in the presence of a coherent coupling between the two states. For such strongly interacting quantum many-body systems, we introduce the concept of blockade graph automorphisms to construct symmetric blockade structures with strong quantum fluctuations that lead to equal-weight superpositions of tailored states. Drawing from these results, we design a quasi-two-dimensional periodic quantum system that—as we show rigorously—features a topological ${\mathbb{Z}}_2$ spin liquid as its ground state. Our construction is based on the implementation of a local symmetry on the microscopic level in a system with only two-body interactions.