Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in deterministic circuits with similar applications, we construct classes of nonrandom unitary Clifford circuits by imposing translation invariance in both time and space. Further imposing dual unitarity, our circuits effectively become crystalline spacetime lattices whose vertices are swap or iswap two-qubit gates and whose edges may contain one-qubit gates. One can then require invariance under (subgroups of) the crystal’s point group. Working on the square and kagome lattices, we use the formalism of Clifford quantum cellular automata to describe operator spreading, entanglement generation, and recurrence times of these circuits. A full classification on the square lattice reveals, of particular interest, a “nonfractal good scrambling class” with dense operator spreading that generates codes with linear contiguous code distance and high performance under erasure errors at the end of the circuit. We also break unitarity by adding spacetime translation-invariant measurements and find a class of such circuits with fractal dynamics.

Three-level $\mathrm{\Lambda }$ systems appear in various quantum information processing platforms. In several control schemes, the excited level serves as an auxiliary state for implementing gate operations between the lower qubit states. However, extra excited levels give rise to unwanted transitions that cause leakage and other errors, degrading the gate fidelity. We focus on a coherent-population-trapping scheme for gates and design protocols that reduce the effects of the unwanted off-resonant couplings and improve the gate performance up to several orders of magnitude. For a particular setup of unwanted couplings, we find an exact solution, which leads to error-free gate operations via only a static detuning modification. In the general case, we improve gate operations by adding corrective modulations to the pulses, thereby generalizing the derivative removal by adiabatic gates protocol to $\mathrm{\Lambda }$ systems. Our techniques enable fast and high-fidelity gates and apply to a wide range of optically driven platforms, such as quantum dots, color centers, and trapped ions.

Trapped atomic ion qubits or effective spins are a powerful quantum platform for quantum computation and simulation, featuring densely connected and efficiently programmable interactions between the spins. While native interactions between trapped-ion spins are typically pairwise, many quantum algorithms and quantum spin models naturally feature couplings between triplets, quartets, or higher orders of spins. Here, we formulate and analyze a mechanism that extends the standard Mølmer-Sørensen pairwise entangling gate and generates a controllable and programmable coupling between $N$ spins of trapped ions. We show that spin-dependent optical parametric drives applied at twice the motional frequency generate a coordinate transformation of the collective ion motion in phase space, rendering displacement forces that are nonlinear in the spin operators. We formulate a simple framework that enables a systematic and faithful construction of high-order spin Hamiltonians and gates, including the effect of multiple modes of motion, and characterize the performance of such operations under realistic conditions.

Single flux quantum (SFQ) digital logic has been proposed for the scalable control of next-generation superconducting-qubit arrays. In the initial implementation, SFQ-based gate fidelity was limited by quasiparticle (QP) poisoning induced by the dissipative on-chip SFQ driver circuit. In this work, we introduce a multichip-module architecture to suppress phonon-mediated QP poisoning. Here, the SFQ elements and qubits are fabricated on separate chips that are joined with $\mathrm{In}$-bump bonds. We use interleaved randomized benchmarking to characterize the fidelity of SFQ-based gates and we demonstrate an error per Clifford gate of 1.2(1)%, an order-of-magnitude reduction over the gate error achieved in the initial realization of SFQ-based qubit control. We use purity benchmarking to quantify the contribution of incoherent error at 0.96(2)%; we attribute this error to photon-mediated QP poisoning mediated by the resonant millimeter-wave antenna modes of the qubit and SFQ-qubit coupler. We anticipate that a straightforward redesign of the SFQ driver circuit to limit the bandwidth of the SFQ pulses will eliminate this source of infidelity, allowing SFQ-based gates with error approaching approximate known theoretical limits, of order 0.1% for resonant sequences and 0.01% for more complex pulse sequences involving variable pulse-to-pulse separation.

We use the tip of an atomic force microscope (AFM) to charge floating metallic gates defined on the surface of a $\mathrm{Si}/\mathrm{Si}\mathrm{Ge}$ heterostructure. The AFM tip serves as an ideal and movable cryogenic switch, allowing us to bias a floating gate to a specific voltage and then lock the charge on the gate by withdrawing the tip. Biasing with an AFM tip allows us to reduce the size of a quantum dot floating-gate electrode down to approximately $100\mathrm{nm}$. Measurements of the conductance through a quantum dot formed beneath the floating gate indicate that its charge changes in discrete steps. From the statistics of the single-electron leakage events, we determine the floating-gate leakage resistance $R\sim {10}^{19}\mathrm{Ohm}$—a value that is immeasurable by conventional means.

The sine-Gordon model emerges as a low-energy theory in a plethora of quantum many-body systems. Here, we theoretically investigate tunnel-coupled Bose-Hubbard chains with strong repulsive interactions as a realization of the sine-Gordon model deep in the quantum regime. We propose protocols for quantum gas microscopes of ultracold atoms to prepare and analyze solitons, which are the fundamental topological excitations of the emergent sine-Gordon theory. With numerical simulations based on matrix product states, we characterize the preparation and detection protocols and discuss the experimental requirements.

A balanced description of both static and dynamic correlations in electronic systems with nearly degenerate low-lying states presents a challenge for multiconfigurational methods on classical computers. We present here a quantum algorithm utilizing the action of correlating cluster operators to provide high-quality wave-function ansätze employing a nonorthogonal multireference basis that captures a significant portion of the exact wave function in a highly compact manner and that allows computation of the resulting energies and wave functions at polynomial cost with a quantum computer. This enables a significant improvement over the corresponding classical nonorthogonal solver, which incurs an exponential cost when evaluating off-diagonal matrix elements between the ansatz states and is therefore intractable. We implement the nonorthogonal quantum eigensolver (NOQE) here with an efficient ansatz parametrization inspired by classical quantum chemistry methods that succeed in capturing significant amounts of electronic correlation accurately. Crucially, we avoid the need to perform any optimization of the ansatz on the quantum device. By taking advantage of such classical approaches, NOQE provides a flexible, compact, and rigorous description of both static and dynamic electronic correlation, making it an attractive method for the calculation of electronic states of a wide range of molecular systems.

We study light-matter interactions in the bulk of a two-dimensional photonic lattice system, where photons are subject to the combined effect of a synthetic magnetic field and an orthogonal synthetic electric field. In this configuration, chiral waveguide modes appear in the bulk region of the lattice, in direct analogy to transverse Hall currents in electronic systems. By evaluating the non-Markovian dynamics of emitters that are coupled to those modes, we identify critical coupling conditions, under which the shape of the spontaneously emitted photons becomes almost fully symmetric. Combined with a directional, dispersionless propagation, this property enables a complete reabsorption of the photon by another distant emitter, without relying on any time-dependent control. We show that this mechanism can be generalized to arbitrary in-plane synthetic potentials, thereby enabling flexible realizations of reconfigurable networks of quantum emitters with arbitrary chiral connectivity.

Efficient approaches to quantum control and feedback are essential for quantum technologies, from sensing to quantum computation. Open-loop control tasks have been successfully solved using optimization techniques, including methods such as gradient-ascent pulse engineering (GRAPE) , relying on a differentiable model of the quantum dynamics. For feedback tasks, such methods are not directly applicable, since the aim is to discover strategies conditioned on measurement outcomes. In this work, we introduce feedback GRAPE, which borrows some concepts from model-free reinforcement learning to incorporate the response to strong stochastic (discrete or continuous) measurements, while still performing direct gradient ascent through the quantum dynamics. We illustrate its power considering various scenarios based on cavity-QED setups. Our method yields interpretable feedback strategies for state preparation and stabilization in the presence of noise. Our approach could be employed for discovering strategies in a wide range of feedback tasks, from calibration of multiqubit devices to linear-optics quantum computation strategies, quantum enhanced sensing with adaptive measurements, and quantum error correction.

The study of quantum many-body physics in Liouvillian open quantum systems becomes increasingly important with the recent progress in experimental control on dissipative systems and their exploitation for technological purposes. A central question in open quantum systems concerns the fate of quantum correlations, and the possibility of controlling them by engineering the competition between the Hamiltonian dynamics and the coupling of the system to a bath. Such a question is very challenging from a theoretical point of view, as numerical methods faithfully accounting for quantum correlations are either relying on exact diagonalization, drastically limiting the sizes that can be treated numerically, or on approximations on the range or strength of quantum correlations, associated with the choice of a specific ansatz for the density matrix. In this work we propose a new method to treat open quantum spin lattices, based on stochastic quantum trajectories for the solution of the open-system dynamics. Along each trajectory, the hierarchy of equations of motion for many-point spin-spin correlators is truncated to a given finite order, assuming that multivariate $k\mathrm{th}$-order cumulants vanish for $k$ exceeding a cutoff $k_c$. This scheme allows one to track the evolution of quantum spin-spin correlations up to order $k_c$ for all length scales. We validate this approach in the paradigmatic case of the dissipative phase transitions of the two-dimensional $XYZ$ lattice subject to spontaneous decay. We convincingly assess the existence of steady-state phase transitions from paramagnetic to ferromagnetic, and back to paramagnetic, upon increasing one of the Hamiltonian spin-spin couplings, as well as the classical Ising nature of such transitions. Moreover, the approach allows us to show the presence of significant quantum correlations in the vicinity of the dissipative critical point, and to unveil the presence of spin squeezing, which can be proven to be a tight lower bound to the quantum Fisher information.

Coherent links between qubits separated by tens of micrometers are expected to facilitate scalable quantum computing architectures for spin qubits in electrically defined quantum dots. These links create space for classical on-chip control electronics between qubit arrays, which can help to alleviate the so-called wiring bottleneck. A promising method of achieving coherent links between distant spin qubits consists of shuttling the spin through an array of quantum dots. Here, we use a linear array of four tunnel-coupled quantum dots in a ${}^{28}$$\mathrm{Si}/\mathrm{Si}\mathrm{Ge}$ heterostructure to create a short quantum link. We move an electron spin through the quantum dot array by adjusting the electrochemical potential for each quantum dot sequentially. By pulsing the gates repeatedly, we shuttle an electron forward and backward through the array up to $250$ times, which corresponds to a total distance of approximately $80\text{μ}\mathrm{m}$. We make an estimate of the spin-flip probability per hop in these experiments and conclude that this is well below $0.01\mathrm{\%}$ per hop.

We analyze a Floquet circuit with random Clifford gates in one and two spatial dimensions. By using random graphs and methods from percolation theory, we prove in the two-dimensional (2D) setting that some local operators grow at a ballistic rate, which implies the absence of localization. In contrast, the one-dimensional model displays a strong form of localization, characterized by the emergence of left- and right-blocking walls in random locations. We provide additional insights by complementing our analytical results with numerical simulations of operator spreading and entanglement growth, which show the absence (presence) of localization in two dimensions (one dimension). Furthermore, we unveil how the spectral form factor of the Floquet unitary in 2D circuits behaves like that of quasifree fermions with chaotic single-particle dynamics, with an exponential ramp that persists up to times scaling linearly with the size of the system. Our work sheds light on the nature of disordered Floquet Clifford dynamics and their relationship to fully chaotic quantum dynamics.

Shor and Steane ancillae are two well-known methods for fault-tolerant logical measurements, which are successful on small codes and their concatenations. On large quantum low-density-parity-check codes, however, Shor and Steane measurements have impractical time and space overhead, respectively. In this work, we widen the choice of ancilla codes by unifying Shor and Steane measurements into a single framework, called homomorphic measurements. For any Calderbank-Shor-Steane code with the appropriate ancilla code, one can avoid repetitive measurements or complicated ancilla state preparation procedures such as distillation, which overcomes the difficulties of both Shor and Steane methods. As an example, we utilize the theory of covering spaces to construct homomorphic measurement protocols for arbitrary $X$- or $Z$-type logical Pauli operators on surface codes in general, including the toric code and hyperbolic surface codes. Conventional surface code decoders, such as minimum-weight perfect matching, can be directly applied to our constructions.

Magic states are fundamental building blocks on the road to fault-tolerant quantum computing. Calderbank-Shor-Steane (CSS) codes play a crucial role in the construction of magic distillation protocols. Previous work has cast quantum computing with magic states for odd dimension $d$ within a phase-space setting in which universal quantum computing is described by the statistical mechanics of quasiprobability distributions. Here we extend this framework to the important $d=2$ qubit case and show that we can exploit common structures in CSS circuits to obtain distillation bounds capable of outperforming previous monotone bounds in regimes of practical interest. Moreover, in the case of CSS-code projections, we arrive at a novel cutoff result on the code length $n$ of the CSS code in terms of parameters characterizing a desired distillation, which implies that for fixed target error rate and acceptance probability, one needs to consider only CSS codes below a threshold number of qubits. These entropic constraints are not due simply to the data-processing inequality but rely explicitly on the stochastic representation of such protocols.

Erasures, or errors with known locations, are a more favorable type of error for quantum error-correcting codes than Pauli errors. Converting physical noise into erasures can significantly improve the performance of quantum error correction. Here, we apply the idea of performing erasure conversion by encoding qubits into metastable atomic states, proposed by Wu, Kolkowitz, Puri, and Thompson [Nat. Comm. 13, 4657 (2022)], to trapped ions. We suggest an erasure-conversion scheme for metastable trapped-ion qubits and develop a detailed model of various types of errors. We then compare the logical performance of ground and metastable qubits on the surface code under various physical constraints and conclude that metastable qubits may outperform ground qubits when the achievable laser power is higher for metastable qubits.

We present a systematic recipe for generating and classifying duality transformations in one-dimensional quantum lattice systems. Our construction emphasizes the role of global symmetries, including those described by Abelian and non-Abelian groups but also more general categorical symmetries. These symmetries can be realized as matrix product operators that allow the extraction of a fusion category that characterizes the algebra of all symmetric operators commuting with the symmetry. Known as the bond algebra, its explicit realizations are classified by module categories over the fusion category. A duality is then defined by a pair of distinct module categories giving rise to dual realizations of the bond algebra, as well as dual Hamiltonians. Symmetries of dual models are, in general, distinct but satisfy a categorical Morita equivalence. A key novelty of our categorical approach is the explicit construction of matrix product operators that intertwine dual bond algebra realizations at the level of the Hilbert space and, in general, map local order operators to nonlocal string-order operators. We illustrate this approach for known dualities such as the Kramers-Wannier, Jordan-Wigner, and Kennedy-Tasaki dualities and the interaction-round-the-face–vertex correspondence, a new duality of the $t$-$J_z$ chain model, and dualities in models with the exotic Haagerup symmetry. Finally, we comment on generalizations to higher dimensions.

Superconducting qubit lifetimes must be both long and stable to provide an adequate foundation for quantum computing. This stability is imperiled by two-level systems (TLSs), currently a dominant loss mechanism, which exhibit slow spectral dynamics that destabilize qubit lifetimes on hour time scales. Stability is also threatened at millisecond time scales, where ionizing radiation has recently been found to cause bursts of correlated multiqubit decays, complicating quantum error correction. Here, we study both ionizing radiation and TLS dynamics on a 27-qubit processor, repurposing the standard transmon qubits as sensors of both radiation impacts and TLS dynamics. Unlike prior literature, we observe resilience of the qubit lifetimes to the transient quasiparticles generated by the impact of radiation. However, we also observe a new interaction between these two processes, “TLS scrambling,” in which a radiation impact causes multiple TLSs to jump in frequency, which we suggest is due to the same charge rearrangement sensed by qubits near a radiation impact. As TLS scrambling brings TLSs out of or into resonance with the qubit, the lifetime of the qubit increases or decreases. Our findings thus identify radiation as a new contribution to fluctuations in qubit lifetimes, with implications for efforts to characterize and improve device stability.

Encoding a qubit in a high-quality superconducting microwave cavity offers the opportunity to perform the first layer of error correction in a single device but presents a challenge: how can quantum oscillators be controlled while introducing a minimal number of additional error channels? We focus on the two-qubit portion of this control problem by using a three-wave-mixing coupling element to engineer a programmable beam-splitter interaction between two bosonic modes separated by more than an octave in frequency, without introducing major additional sources of decoherence. Combining this with single-oscillator control provided by a dispersively coupled transmon provides a framework for quantum control of multiple encoded qubits. The beam-splitter interaction $g_{\mathrm{bs}}$ is fast relative to the time scale of oscillator decoherence, enabling over ${10}^3$ beam-splitter operations per coherence time and approaching the typical rate of the dispersive coupling $\chi$ used for individual oscillator control. Further, the programmable coupling is engineered without adding unwanted interactions between the oscillators, as evidenced by the high on-off ratio of the operations, which can exceed ${10}^5$. We then introduce a new protocol to realize a hybrid controlled-swap operation in the regime $g_{\mathrm{bs}}\approx \chi$, in which a transmon provides the control bit for the swap of two bosonic modes. Finally, we use this gate in a swap test to project a pair of bosonic qubits into a Bell state with measurement-corrected fidelity of $95.5\mathrm{\%}\pm 0.2\mathrm{\%}$.

Bosonic quantum error correction has proven to be a successful approach for extending the coherence of quantum memories, but to execute deep quantum circuits, high-fidelity gates between encoded qubits are needed. To that end, we present a family of error-detectable two-qubit gates for a variety of bosonic encodings. From a new geometric framework based on a “Bloch sphere” of bosonic operators, we construct $Z{Z}_L(\theta )$ and exponential-swap$(\theta )$ gates for the binomial, four-legged cat, dual-rail, and several other bosonic codes. The gate Hamiltonian is simple to engineer, requiring only a programmable beam splitter between two bosonic qubits and an ancilla dispersively coupled to one qubit. This Hamiltonian can be realized in circuit QED hardware with ancilla transmons and microwave cavities. The proposed theoretical framework was developed for circuit QED but is generalizable to any platform that can effectively generate this Hamiltonian. Crucially, one can also detect first-order errors in the ancilla and the bosonic qubits during the gates. We show that this allows one to reach error-detected gate fidelities at the $0.01\mathrm{\%}$ level with today’s hardware, limited only by second-order hardware errors.