Abstract: We present a method for reducing the number of non-Clifford quantum gates, in particularly T-gates, in a circuit, an important task for efficiently implementing fault-tolerant quantum computations. This method matches or beats previous approaches to ancillae-free T-count reduction on the majority of our benchmark circuits, in some cases yielding up to 50% improvement. Our method begins by representing the quantum circuit as a ZX-diagram, a tensor networklike structure that can be transformed and simplified according to the rules of the ZX-calculus. We then extend a recent simplification strategy with a different ingredient, phase gadgetization, which we use to propagate non-Clifford phases through a ZX-diagram to find nonlocal cancellations. Our procedure extends unmodified to arbitrary phase angles and to parameter elimination for variational circuits. Finally, our optimization is self-checking, in the sense that the simplification strategy we propose is powerful enough to independently validate equality of the input circuit and the optimized output circuit. We have implemented the routines of this paper in the open-source library pyzx.

Abstract: In the worldwide endeavor for disruptive quantum technologies, germanium is emerging as a versatile material to realize devices capable of encoding, processing, or transmitting quantum information. These devices leverage special properties of the germanium valence-band states, commonly known as holes, such as their inherently strong spin-orbit coupling and the ability to host superconducting pairing correlations. In this Review, we initially introduce the physics of holes in low-dimensional germanium structures with key insights from a theoretical perspective. We then examine the material science progress underpinning germanium-based planar heterostructures and nanowires. We review the most significant experimental results demonstrating key building blocks for quantum technology, such as an electrically driven universal quantum gate set with spin qubits in quantum dots and superconductor-semiconductor devices for hybrid quantum systems. We conclude by identifying the most promising prospects toward scalable quantum information processing.

Abstract: Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.

Abstract: Pauli channels are ubiquitous in quantum information, both as a dominant noise source in many computing architectures and as a practical model for analyzing error correction and fault tolerance. Here, we prove several results on efficiently learning Pauli channels and more generally the Pauli projection of a quantum channel. We first derive a procedure for learning a Pauli channel on n qubits with high probability to a relative precision ϵ using O(ϵ-2n2n) measurements, which is efficient in the Hilbert space dimension. The estimate is robust to state preparation and measurement errors, which, together with the relative precision, makes it especially appropriate for applications involving characterization of high-accuracy quantum gates. Next, we show that the error rates for an arbitrary set of s Pauli errors can be estimated to a relative precision ϵ using O(ϵ-4log s log s/ϵ) measurements. Finally, we show that when the Pauli channel is given by a Markov field with at most k-local correlations, we can learn an entire n-qubit Pauli channel to relative precision ϵ with only Ok(ϵ-2n2logn) measurements, which is efficient in the number of qubits. These results enable a host of applications beyond just characterizing noise in a large-scale quantum system: they pave the way to tailoring quantum codes, optimizing decoders, and customizing fault tolerance procedures to suit a particular device.

Abstract: An important entangling quantum gate is significantly improved, leading to a demonstrable increase in quantum volume.

Abstract: Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabatic geometric quantum gate set in a superconducting qubit chain. We characterize the realized single- and two-qubit geometric gates with both quantum process tomography and randomized benchmarking methods. The measured average fidelities for the single-qubit rotation gates and two-qubit controlled-Z gate are 0.9977(1) and 0.977(9), respectively. Besides, we also experimentally demonstrate the noise-resilient feature of the realized single-qubit geometric gates by comparing their performance with the conventional dynamical gates with different types of errors in the control field. Thus, our experiment proves a way to achieve high-fidelity geometric quantum gates for robust quantum computation.

Abstract: Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing, allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g., wave plates for polarization. However, for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations at high quality by using only a few phase modulation planes. More importantly, we experimentally implement several high-dimensional quantum gates for up to five-dimensional states encoded in the full-field mode structure of photons. In particular, we realize cyclic and quantum Fourier transformations, known as Pauli $ \hat X $X^-gates and Hadamard $ \hat H $H^-gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect “unitarity” by means of quantum process tomography, unveiling a process purity of 99%. Last, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e., azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation, and sensing schemes.

Abstract: Quantum-gate errors are a significant challenge for achieving precision measurements on noisy intermediate-scale quantum (NISQ) computers. This paper focuses on zero-noise extrapolation (ZNE), a technique that can be implemented on existing hardware, studying it in detail and proposing modifications to existing approaches. In particular, we consider identity insertion methods for amplifying noise because they are hardware agnostic. We build a mathematical formalism for studying existing ZNE techniques and show how higher order polynomial extrapolations can be used to systematically reduce depolarizing errors. Furthermore, we introduce a method for amplifying noise that uses far fewer gates than traditional methods. This approach is compared with existing methods for simulated quantum circuits. Comparable or smaller errors are possible with fewer gates, which illustrates the potential for empowering an entirely new class of moderate-depth circuits on near term hardware.

Abstract: Universal quantum computation1 is striking for its unprecedented capability in processing information, but its scalability is challenging in practice because of the inevitable environment noise. Although quantum error correction (QEC) techniques2–8 have been developed to protect stored quantum information from leading orders of error, the noise-resilient processing of the QEC-protected quantum information is highly demanded but remains elusive9. Here, we demonstrate phase gate operations on a logical qubit encoded in a bosonic oscillator in an error-transparent (ET) manner. Inspired by refs. 10,11, the ET gates are extended to the bosonic code and are able to tolerate errors on the logical qubit during gate operations, regardless of the random occurrence time of the error. With precisely designed gate Hamiltonians through photon-number-resolved a.c. Stark shifts, the ET condition is fulfilled experimentally. We verify that the ET gates outperform the non-ET gates with a substantial improvement of gate fidelity after an occurrence of the single-photon-loss error. Our ET gates in superconducting quantum circuits can be readily extended to multiple encoded qubits and a universal gate set is within reach, holding the potential for reliable quantum information processing. Error-transparent quantum gates that can tolerate certain error during the execution of quantum operations have been demonstrated. Substantial improvement of the gate fidelity sheds lights on large-scale universal quantum computation.

Abstract: A key challenge in quantum computation is the implementation of fast and local qubit control while simultaneously maintaining coherence. Qubits based on hole spins offer, through their strong spin-orbit interaction, a way to implement fast quantum gates. Strikingly, for hole spins in one-dimensional germanium and silicon devices, the spin-orbit interaction has been predicted to be exceptionally strong yet highly tunable with gate voltages. Such electrical control would make it possible to switch on demand between qubit idling and manipulation modes. Here, we demonstrate ultrafast and universal quantum control of a hole spin qubit in a germanium/silicon core/shell nanowire, with Rabi frequencies of several hundreds of megahertz, corresponding to spin-flipping times as short as ~1 ns - a new record for a single-spin qubit. Next, we show a large degree of electrical control over the Rabi frequency, Zeeman energy, and coherence time - thus implementing a switch toggling from a rapid qubit manipulation mode to a more coherent idling mode. We identify an exceptionally strong but gate-tunable spin-orbit interaction as the underlying mechanism, with a short associated spin-orbit length that can be tuned over a large range down to 3 nm for holes of heavy-hole mass. Our work demonstrates a spin-orbit qubit switch and establishes hole spin qubits defined in one-dimensional germanium/silicon nanostructures as a fast and highly tunable platform for quantum computation.

Abstract: Universal quantum information processing requires the execution of single-qubit and two-qubit logic. Across all qubit realizations1, spin qubits in quantum dots have great promise to become the central building block for quantum computation2. Excellent quantum dot control can be achieved in gallium arsenide3–5, and high-fidelity qubit rotations and two-qubit logic have been demonstrated in silicon6–9, but universal quantum logic implemented with local control has yet to be demonstrated. Here we make this step by combining all of these desirable aspects using hole quantum dots in germanium. Good control over tunnel coupling and detuning is obtained by exploiting quantum wells with very low disorder, enabling operation at the charge symmetry point for increased qubit performance. Spin–orbit coupling obviates the need for microscopic elements close to each qubit and enables rapid qubit control with driving frequencies exceeding 100 MHz. We demonstrate a fast universal quantum gate set composed of single-qubit gates with a fidelity of 99.3 per cent and a gate time of 20 nanoseconds, and two-qubit logic operations executed within 75 nanoseconds. Planar germanium has thus matured within a year from a material that can host quantum dots to a platform enabling two-qubit logic, positioning itself as an excellent material for use in quantum information applications. Spin qubits based on hole states in strained germanium could offer the most scalable platform for quantum computation.

Abstract: One of the key challenges in current Noisy Intermediate-Scale Quantum (NISQ) computers is to control a quantum system with high-fidelity quantum gates. There are many reasons a quantum gate can go wrong – for superconducting transmon qubits in particular, one major source of gate error is the unwanted crosstalk between neighboring qubits due to a phenomenon called frequency crowding. We motivate a systematic approach for understanding and mitigating the crosstalk noise when executing near-term quantum programs on superconducting NISQ computers. We present a general software solution to alleviate frequency crowding by systematically tuning qubit frequencies according to input programs, trading parallelism for higher gate fidelity when necessary. The net result is that our work dramatically improves the crosstalk resilience of tunable-qubit, fixed-coupler hardware, matching or surpassing other more complex architectural designs such as tunable-coupler systems. On NISQ benchmarks, we improve worst-case program success rate by 13.3x on average, compared to existing traditional serialization strategies.

Abstract: Majorana modes, typically arising at the edges of one-dimensional topological superconductors, are considered to be a promising candidate for encoding nonlocal qubits in fault-tolerant quantum computing. Here we exploit the two-dimensional geometry of Majorana corner modes in second-order topological superconductors to establish measurement-only quantum computation. It is shown that eight Majorana corner modes emerge when such systems are periodically driven, through which two nonlocal logical qubits and one nonlocal ancilla qubit can be constructed. Quantum gate operations can then be implemented by a designed series of parity measurements of topologically protected Majorana corner modes, accomplished via Mach-Zehnder type interference in the conductance between different corners of a second-order topological superconductor. Our theoretical proposal represents a scenario in which topologically protected single- and two-qubit gate operations can be carried out in a minimal setup, thus potentially establishing an efficient and low-cost building block for Majorana-based qubit architectures.

Abstract: For building a scalable quantum processor with superconducting qubits, ZZ interaction is of great concern because its residual has a crucial impact to two-qubit gate fidelity. Two-qubit gates with fidelity meeting the criterion of fault-tolerant quantum computation have been demonstrated using ZZ interaction. However, as the performance of quantum processors improves, the residual static ZZ can become a performance-limiting factor for quantum gate operation and quantum error correction. Here, we introduce a superconducting architecture using qubits with opposite-sign anharmonicity, a transmon qubit, and a C-shunt flux qubit, to address this issue. We theoretically demonstrate that by coupling the two types of qubits, the high-contrast ZZ interaction can be realized. Thus, we can control the interaction with a high on-off ratio to implement two-qubit controlled-Z gates, or suppress it during two-qubit gate operation using XY interaction (e.g., an iSWAP gate). The proposed architecture can also be scaled up to multiqubit cases. In a fixed coupled system, ZZ crosstalk related to neighboring spectator qubits could also be heavily suppressed.

Abstract: We present a variational quantum circuit that produces the singular value decomposition of a bipartite pure state. The proposed circuit, which we name quantum singular value decomposer or QSVD, is made of two unitaries respectively acting on each part of the system. The key idea of the algorithm is to train this circuit so that the final state displays exact output coincidence from both subsystems for every measurement in the computational basis. Such circuit preserves entanglement between the parties and acts as a diagonalizer that delivers the eigenvalues of the Schmidt decomposition. Our algorithm only requires measurements in one single setting, in striking contrast to the ${3}^{n}$ settings required by state tomography. Furthermore, the adjoints of the unitaries making the circuit are used to create the eigenvectors of the decomposition up to a global phase. Some further applications of QSVD are readily obtained. The proposed QSVD circuit allows us to construct a SWAP between the two parties of the system without the need of any quantum gate communicating them. We also show that a circuit made with QSVD and CNOTs acts as an encoder of information of the original state onto one of its parties. This idea can be reversed and used to create random states with a precise entanglement structure.

Abstract: Nonclassical states of light are an essential resource for many emerging quantum technologies and applications ranging from information processing, encrypted communications, and networking to sensing, metrology, and imaging. Nonlinear optical processes in solid-state materials are widely used for generating quantum light, including single photons, entangled-photon pairs, and quadrature-squeezed states. Recent advances in nonlinear photonics have enabled the functionality of benchtop nonlinear instruments to be scaled down to a single chip without sacrificing efficiency or degrading the key performance metrics. The dramatic improvement in the size, weight, power, cost, and stability enabled by photonic integrated circuits has been essential for enabling the chip-scale generation, manipulation, and detection of quantum light at a steadily increasing degree of complexity and scale. Within the last decade, the authors have seen the progression from few-component photonic circuits operating on two photons to arrays of 18 identical heralded single-photon sources and reconfigurable devices operating with more than 650 components for multidimensional entanglement and arbitrary two-photon quantum gates. In this review, the authors summarize the history and recent key technological developments of chip-scale nonlinear quantum light generation based on integrated nonlinear photonics, recent advances in heterogeneous integrated methods, and approaches for system-level integration and demonstrated applications.

Abstract: Majorana fermions feature non-Abelian exchange statistics and promise fascinating applications in topological quantum computation. Recently, second-order topological superconductors (SOTSs) have been proposed to host Majorana fermions as localized quasiparticles with zero excitation energy, pointing out a new avenue to facilitate topological quantum computation. We provide a minimal model for SOTSs and systematically analyze the features of Majorana zero modes with analytical and numerical methods. We further construct the fundamental fusion principles of zero modes stemming from a single or multiple SOTS islands. Finally, we propose concrete schemes in different setups formed by SOTSs, enabling us to exchange and fuse the zero modes for non-Abelian braiding and holonomic quantum gate operations.

Abstract: An open question in quantum optics is how to manipulate and control complex quantum states in an experimentally feasible way. Here we present concepts for transformations of high-dimensional multiphotonic quantum systems. The proposals rely on two new ideas: (i) a novel high-dimensional quantum nondemolition measurement, (ii) the encoding and decoding of the entire quantum transformation in an ancillary state for sharing the necessary quantum information between the involved parties. Many solutions can readily be performed in laboratories around the world and thereby we identify important pathways for experimental research in the near future. The concepts have been found using the computer algorithm melvin for designing computer-inspired quantum experiments. As opposed to the field of machine learning, here the human learns new scientific concepts by interpreting and analyzing the results presented by the machine. This demonstrates that computer algorithms can inspire new ideas in science, which has a widely unexplored potential that goes far beyond experimental quantum information science.

Abstract: Implementation of the two-qubit controlled-NOT (CNOT) gate is necessary to develop a complete set of universal gates for quantum computing. Here, we demonstrate that a photogenerated radical (spin qubit) pair within a covalent donor-chromophore-acceptor molecule can be used to successfully execute a CNOT gate with high fidelity. The donor is tetrathiafulvalene (TTF), the chromophore is 8-aminonaphthalene-1,8-dicarboximide (ANI), and the acceptor is pyromellitimide (PI). Selective photoexcitation of ANI with a 416 nm laser pulse results in subnanosecond formation of the TTF•+-ANI-PI•- radical (spin qubit) pair at 85 K having a 1.8 µs phase memory time. This is sufficiently long to execute a CNOT gate using a sequence of five microwave pulses followed by a sequence of two pulses that read out all the elements of the density matrix. Comparing these data to a simulation of the data that assumes ideal conditions results in a fidelity of 0.97 for the execution of the CNOT gate. These results show that photogenerated molecular spin qubit pairs can be used to execute this essential quantum gate at modest temperatures, which affords the possibility that chemical synthesis can be used to develop structures to execute more complex quantum logic operations using electron spins.

Abstract: Adiabatic quantum computing enables the preparation of many-body ground states. Realization poses major experimental challenges: Direct analog implementation requires complex Hamiltonian engineering, while the digitized version needs deep quantum gate circuits. To bypass these obstacles, we suggest an adiabatic variational hybrid algorithm, which employs short quantum circuits and provides a systematic quantum adiabatic optimization of the circuit parameters. The quantum adiabatic theorem promises not only the ground state but also that the excited eigenstates can be found. We report the first experimental demonstration that many-body eigenstates can be efficiently prepared by an adiabatic variational algorithm assisted with a multiqubit superconducting coprocessor. We track the real-time evolution of the ground and excited states of transverse-field Ising spins with a fidelity that can reach about 99%.

Abstract: Electromagnetically induced transparency, as a quantum interference effect to eliminate optical absorption in an opaque medium, has found extensive applications in slow-light generation, optical storage, frequency conversion, optical quantum memory and enhanced nonlinear interactions at the few-photon level in all kinds of systems. Recently, there has been great interest in exceptional points, a type of spectral singularity that could be reached by tuning various parameters in open systems, to render unusual features to the physical systems, such as optical states with chirality. Here we theoretically and experimentally study transparency and absorption modulated by chiral optical states at exceptional points in an indirectly coupled resonator system. By tuning one resonator to an exceptional point, transparency or absorption occurs depending on the chirality of the eigenstate. Our results demonstrate a new strategy to manipulate the light flow and the spectra of a photonic resonator system by exploiting a discrete optical state associated with a specific chirality at an exceptional point as a unique control bit. Such an approach is compatible with the state control utilized in quantum gate operation and may open up new avenues for controlling slow light using optical states for optical quantum memory and computing. The optical analogue of electromagnetically induced transparency and absorption can be modulated by chiral optical states at an exceptional point, which is shown in a system of indirectly coupled microresonators.

Abstract: We simulate the dynamics of braiding Majorana zero modes on an IBM Quantum computer. We find the native quantum gates introduce too much noise to observe braiding. Instead, we use Qiskit Pulse to develop scaled two-qubit quantum gates that better match the unitary time evolution operator and enable us to observe braiding. This work demonstrates that quantum computers can be used for simulation, and highlights the use of pulse-level control for programming quantum computers and constitutes the first experimental evidence of braiding via dynamical Hamiltonian evolution.

Abstract: Quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault-tolerant quantum computation, owing to its robustness against operational noise. However, because of the parametric restrictions in previous schemes, the main robust advantage of holonomic quantum gates is reduced. Here, we experimentally demonstrate a solution scheme, obtaining nonadiabatic holonomic single-qubit quantum gates with optimal control in a trapped ${}^{171}{\mathrm{Yb}}^{+}$ ion based on a three-level system with resonant driving, which also has the advantages of rapid evolution and convenient implementation. Compared with previous geometric gates and conventional dynamical gates, the superiority of our scheme is that it is more robust against control amplitude errors, which is confirmed by the gate infidelity as measured by both quantum-process tomography and random benchmarking methods. In addition, we outline how nontrivial two-qubit holonomic gates can also be realized using currently available experimental technology. Thus, our experiment confirms the feasibility of this robust and fast holonomic quantum-computation strategy.

Abstract: Hybrid quantum registers, such as electron-nuclear spin systems, have emerged as promising hardware for implementing quantum information and computing protocols in scalable systems. Nevertheless, the coherent control of such systems still faces challenges. Particularly, the lower gyromagnetic ratios of the nuclear spins cause them to respond slowly to control fields, resulting in gate times that are generally longer than the coherence time of the electron. Here, we demonstrate a scheme for circumventing this problem by indirect control: we apply a small number of short pulses only to the electron and let the full system undergo free evolution under the hyperfine coupling between the pulses. Using this scheme, we realize robust quantum gates in an electron-nuclear spin system, including a Hadamard gate on the nuclear spin and a controlled-NOT gate with the nuclear spin as the target qubit. The durations of these gates are shorter than the electron coherence time, and thus additional operations to extend the system coherence time are not needed. Our demonstration serves as a proof of concept for achieving efficient coherent control of electron-nuclear spin systems, such as nitrogen vacancy centers in diamond. Our scheme is still applicable when the nuclear spins are only weakly coupled to the electron.

Abstract: Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA), an approach to solve combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) systems. Gaining computational power from QAOA critically relies on the mitigation of errors during the execution of the algorithm, which for coherence-limited operations is achievable by reducing the gate count. Here, we demonstrate an improvement of up to a factor of 3 in algorithmic performance as measured by the success probability, by implementing a continuous hardware-efficient gate set using superconducting quantum circuits. This gate set allows us to perform the phase separation step in QAOA with a single physical gate for each pair of qubits instead of decomposing it into two C$Z$-gates and single-qubit gates. With this reduced number of physical gates, which scales with the number of layers employed in the algorithm, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances mapped onto three and seven qubits, using up to a total of 399 operations and up to 9 layers. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.

Abstract: The main challenges in achieving high-fidelity quantum gates are to reduce the influence of control errors caused by imperfect Hamiltonians and the influence of decoherence caused by environment noise. To overcome control errors, a promising proposal is nonadiabatic holonomic quantum computation, which has attracted much attention in both theories and experiments. While the merit of holonomic operations resisting control errors has been well exploited, an important issue following is how to shorten the evolution time needed for realizing a holonomic gate so as to avoid the influence of environment noise as much as possible. In this paper, we put forward a general approach of constructing Hamiltonians for nonadiabatic holonomic quantum computation, which makes it possible to minimize the evolution time and might open a new horizon for the realistic implementation of nonadiabatic holonomic quantum computation.

Abstract: Geometric phases induced in quantum evolutions have built-in noise-resilient characters, and thus can find applications in many robust quantum manipulation tasks. Here, we propose a feasible and fast scheme for universal quantum computation on superconducting circuits with nonadiabatic non-Abelian geometric phases, using resonant interaction of three-level quantum system. In our scheme, arbitrary single-qubit quantum gates can be implemented in a single-loop scenario by shaping both the amplitudes and phases of the two driving microwave fields resonantly coupled to a transmon device. Moreover, nontrivial two-qubit gates can also be realized with an auxiliary transmon simultaneously coupled to the two target transmons in an effective resonant way. In particular, our proposal can be compatible to various optimal control techniques, which further enhances the robustness of the quantum operations. Therefore, our proposal represents a promising way towards fault-tolerant quantum computation on solid-state quantum circuits.

Abstract: Flag qubits have recently been proposed in syndrome extraction circuits to detect high-weight errors arising from fewer faults. The use of flag qubits allows the construction of fault-tolerant protocols with the fewest number of ancillas known to date. In this work, we prove some critical properties of Calderbank-Shor-Steane (CSS) codes constructed from classical cyclic codes that enable the construction of a flag fault-tolerant error correction scheme. We then develop fault-tolerant protocols as well as a family of circuits for flag fault-tolerant error correction and operator measurement, requiring only four ancilla qubits and applicable to cyclic CSS codes of distance 3. The measurement protocol can be further used for logical Clifford gate implementation via quantum gate teleportation. We also provide examples of cyclic CSS codes with large encoding rates.

Abstract: Universal quantum computing by braiding defects in topological stabilizer codes of any dimension is proven to be impossible. Notwithstanding this no-go theorem, it is shown how braiding defects can yield all Clifford gates in three or more dimensions, and that universal quantum computing in three-dimensional surface codes is possible by supplementing braiding with adaptive gates.