Quantum Computation Schemes Research Articles

Universal quantum processors in spin systems via robust local pulse sequences

We propose a protocol to realize quantum simulation and computation in spin systems with long-range interactions. Our approach relies on the local addressing of single spins with external fields parametrized by Walsh functions. This enables a mapping from a class of target Hamiltonians, defined by the graph structure of their interactions, to pulse sequences. We then obtain a recipe to implement arbitrary two-body Hamiltonians and universal quantum circuits. Performance guarantees are provided in terms of bounds on Trotter errors and total number of pulses. Additionally, Walsh pulse sequences are shown to be robust against various types of pulse errors, in contrast to previous hybrid digital-analog schemes of quantum computation. We demonstrate and numerically benchmark our protocol with examples from the dynamics of spin models, quantum error correction and quantum optimization algorithms.

Hamilton-Jacobi-Bellman equations for Rydberg-blockade processes

We discuss time-optimal control problems for two setups involving globally driven Rydberg atoms in the blockade limit by deriving the associated Hamilton-Jacobi-Bellman equations. From these equations, we extract the globally optimal trajectories and the corresponding controls for several target processes of the atomic system, using a generalized method of characteristics. We apply this method to retrieve known results for CZ and C-phase gates, and to find new optimal pulses for all elementary processes involved in the universal quantum computation scheme introduced in []. Published by the American Physical Society 2024

Encoded-Fusion-Based Quantum Computation for High Thresholds with Linear Optics.

We propose a fault-tolerant quantum computation scheme in a measurement-based manner with finite-sized entangled resource states and encoded-fusion scheme with linear optics. The encoded fusion is an entangled measurement devised to enhance the fusion success probability in the presence of losses and errors based on a quantum error-correcting code. We apply an encoded-fusion scheme, which can be performed with linear optics and active feedforwards to implement the generalized Shor code, to construct a fault-tolerant network configuration in a three-dimensional Raussendorf-Harrington-Goyal lattice based on the surface code. Numerical simulations show that our scheme allows us to achieve up to 10 times higher loss thresholds than nonencoded fusion approaches with limited numbers of photons used in fusion. Our scheme paves an efficient route toward fault-tolerant quantum computing with finite-sized entangled resource states and linear optics.

Applicability of measurement-based quantum computation towards physically-driven variational quantum eigensolver

Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to developing quantum algorithms with the measurement-based quantum computation (MBQC) scheme is resource cost. Recently, we discovered that the realization of multi-qubit rotation operations only requires a constant number of single-qubit measurements with the MBQC scheme, providing a potential advantage in terms of resource cost. The structure of the Hamiltonian variational ansatz aligns well with this characteristic. Thus, we propose an efficient measurement-based quantum algorithm for quantum many-body system simulation tasks, called measurement-based Hamiltonian variational ansatz (MBHVA). We then demonstrate its effectiveness, efficiency, and advantages with the two-dimensional Heisenberg model and the Fermi–Hubbard chain. Numerical experiments show that MBHVA can have similar performance as circuit-based ansatz, and is expected to reduce operation counts during execution compared to quantum circuits, bringing the advantage of running time. We conclude that the MBQC scheme is potentially feasible for achieving near-term quantum advantages in the noisy intermediate-scale quantum era, especially in the presence of large multi-qubit rotation operations.

High-efficiency realization of the super-robust Rydberg Deutsch gate

Quantum logic gates are the essential components of quantum computation and have broad practical applications, especially for the multiple-qubit logic gates. Compared with appliying a series of single- and two-qubit gates, constrcuting quantum computation with multiple-qubit logic gates can be more efficient and high-fidelity. As a three-qubit logic gate, Deutsch gate enables the realization of any feasible quantum computations. Based on neutral atoms, we present a scheme of super-robust Deutsch gate via optimal control technique. Utilizing the Rydberg blockade effect of neutral atoms, we design an implementable D(β) based on the three-step program. One of the notable advantages of this function is that β can be achieved arbitrarily between 0 and π with the operation of target atom. In addition, we give an analytical solution agreed very well with numerical simulations for the residual blocking effect between next-neighbor atoms that affects the performance quality of Deutsch gate. The fidelity of our proposed scheme is demonstrated by numerical simulation of the master equation based on the full Hamiltonian, and the robustness of our scheme with control errors is also illustrated. Our proposal offers an alternative promising scheme for fault-tolerant quantum computation. Published by the American Physical Society 2024

Defect bulk-boundary correspondence of topological skyrmion phases of matter

Unpaired Majorana zero-modes are central to topological quantum computation schemes as building blocks of topological qubits, and are therefore under intense experimental and theoretical investigation. Their generalizations to parafermions and Fibonacci anyons are also of great interest, in particular for universal quantum computation schemes. In this work, we find a different generalization of Majorana zero-modes in effectively non-interacting systems, which are zero-energy bound states that exhibit a cross structure -- two straight, perpendicular lines in the complex plane -- composed of the complex number entries of the zero-mode wavefunction on a lattice, rather than a single straight line formed by complex number entries of the wavefunction on a lattice as in the case of an unpaired Majorana zero-mode. These cross zero-modes are realized for topological skyrmion phases under certain open boundary conditions when their characteristic momentum-space spin textures trap topological defects. They therefore serve as a second type of bulk-boundary correspondence for the topological skyrmion phases. In the process of characterizing this defect bulk-boundary correspondence, we develop recipes for constructing physically-relevant model Hamiltonians for topological skyrmion phases, efficient methods for computing the skyrmion number, and introduce three-dimensional topological skyrmion phases into the literature.

Linear Optical Quantum Computation with Frequency-Comb Qubits and Passive Devices.

We propose a linear optical quantum computation scheme using time-frequency degrees of freedom. In this scheme, a qubit is encoded in single-photon frequency combs, and manipulation of the qubits is performed using time-resolving detectors, beam splitters, and optical interleavers. This scheme does not require active devices such as high-speed switches and electro-optic modulators and is robust against temporal and spectral errors, which are mainly caused by the detectors' finite resolution. We show that current technologies almost meet the requirements for fault-tolerant quantum computation.

Research progress of ion trap quantum computing

Ion trap is one of the leading physical platforms to implement quantum computation. Currently, high-fidelity elementary quantum operations above the fault-tolerant threshold, including state preparation, measurement and universal gates, have been demonstrated for tens of ionic qubits. One important future research direction is to further enlarge the qubit number to the scale required for solving practical problems while maintaining the high performance of individual qubits. This paper introduces the current mainstream schemes for scalable ion trap quantum computation like quantum charge-coupled device (QCCD) and ion-photon quantum network, and describes the main limiting factors in current research. Then we further explore new schemes to scale up the qubit number like two-dimensional ion crystals and dual-type qubit, and discuss the future research directions.

Universal quantum computation with symmetric qubit clusters coupled to an environment

One of the most challenging problems for the realization of a scalable quantum computer is to design a physical device that keeps the error rate for each quantum processing operation low. These errors can originate from the accuracy of quantum manipulation, such as the sweeping of a gate voltage in solid state qubits or the duration of a laser pulse in optical schemes. Errors also result from decoherence, which is often regarded as more crucial in the sense that it is inherent to the quantum system, being fundamentally a consequence of the coupling to the external environment. Grouping small collections of qubits into clusters with symmetries may serve to protect parts of the calculation from decoherence. In this work, we use four-level cores with a straightforward generalization of discrete rotational symmetry, called $\ensuremath{\omega}$-rotation invariance, to encode pairs of coupled qubits and universal two-qubit logical gates. We include quantum errors as a main source of decoherence, and show that symmetry makes logical operations particularly resilient to untimely anisotropic qubit rotations. We propose a scalable scheme for universal quantum computation where cores play the role of quantum-computational transistors, or quansistors for short. Initialization and readout are achieved by tunnel-coupling the quansistor to leads. The external leads are explicitly considered and are assumed to be the other main source of decoherence. We show that quansistors can be dynamically decoupled from the leads by tuning their internal parameters, giving them the versatility required to act as controllable quantum memory units. With this dynamical decoupling, logical operations within quansistors are also symmetry-protected from unbiased noise in their parameters. We identify technologies that could implement $\ensuremath{\omega}$-rotation invariance. Many of our results can be generalized to higher-level $\ensuremath{\omega}$-rotation-invariant systems, or adapted to clusters with other symmetries.

Detection of single phonons via phonon drag in two-dimensional materials

The capacity to electrically detect phonons, ultimately at the single-phonon limit, is a key requirement for many schemes for phonon-based quantum computing; so-called quantum phononics. Here, we predict that by exploiting the strong coupling of their electrons to surface-polar phonons, van der Waals heterostructures can offer a suitable platform for phonon sensing, capable of resolving energy transfer at the single-phonon level. The geometry we consider is one in which a drag momentum is exerted on electrons in a graphene layer, by a single out-of-equilibrium phonon in a dielectric layer of hexagonal boron nitride, giving rise to a measurable induced voltage $({V}_{\mathrm{drag}})$. Our numerical solution of the Boltzmann transport equation shows that this drag voltage can reach a level of a few hundred microvolts per phonon, well above experimental detection limits. Furthermore, we predict that ${V}_{\mathrm{drag}}$ should be highly insensitive to the mobility of carriers in the graphene layer and to increasing the temperature to at least 300 K, offering the potential of a versatile material platform for single-phonon sensing.

Fast evolution of single qubit gate in non-adiabatic geometric quantum computing

We implemented arbitrarythe arbitrary single qubit gates of geometric quantum computing for a three-level system in a single-shot manner. The evolution time of the gate has been minimized by considering the shortest trajectory of the state on the Bloch sphere. The duration of gates grows from zero with the rotation angle γ, and the tested T gate time can be reduced to ∼40% of those in the traditional orange-sliced-shaped path non-adiabatic holonomic quantum computing (NHQC) scheme by the parametrization of Rabi frequency. We also demonstrated that certain pulses are robust against static detuning errors and Rabi errors. The time-dependent detuning and Rabi frequency are found to be proportional to each other by a constant which is determined by the geometric phase. In this way, some previous NHQC schemes can be treated as special cases in our generalized model.

Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms

Neutral-atom arrays have recently emerged as a promising platform for quantum information processing. One important remaining roadblock for the large-scale application of these systems is the ability to perform error-corrected quantum operations. To entangle the qubits in these systems, atoms are typically excited to Rydberg states, which could decay or give rise to various correlated errors that cannot be addressed directly through traditional methods of fault-tolerant quantum computation. In this work, we provide the first complete characterization of these sources of error in a neutral-atom quantum computer and propose hardware-efficient, fault-tolerant quantum computation schemes that mitigate them. Notably, we develop a novel and distinctly efficient method to address the most important errors associated with the decay of atomic qubits to states outside of the computational subspace. These advances allow us to significantly reduce the resource cost for fault-tolerant quantum computation compared to existing, general-purpose schemes. Our protocols can be implemented in the near term using state-of-the-art neutral-atom platforms with qubits encoded in both alkali and alkaline-earth atoms.9 MoreReceived 6 June 2021Revised 3 February 2022Accepted 12 April 2022DOI:https://doi.org/10.1103/PhysRevX.12.021049Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasOptical pumpingQuantum algorithmsQuantum computationQuantum gatesQuantum information processingQuantum protocolsSpontaneous emissionQuantum InformationAtomic, Molecular & Optical

Low-overhead fault-tolerant quantum computing using long-range connectivity.

Vast numbers of qubits will be needed for large-scale quantum computing because of the overheads associated with error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density parity-check (LDPC) codes, where long-range interactions enable many logical qubits to be encoded with a modest number of physical qubits. In our approach, logic gates operate via logical Pauli measurements that preserve both the protection of the LDPC codes and the low overheads in terms of the required number of additional qubits. Compared with surface codes with the same code distance, we estimate order-of-magnitude improvements in the overheads for processing around 100 logical qubits using this approach. Given the high thresholds demonstrated by LDPC codes, our estimates suggest that fault-tolerant quantum computation at this scale may be achievable with a few thousand physical qubits at comparable error rates to what is needed for current approaches.

Verification of graph states in an untrusted network

Graph states are a large class of multipartite entangled quantum states that form the basis of schemes for quantum computation, communication, error correction, metrology, and more. In this work, we consider verification of graph states generated by an untrusted source and shared between a network of possibly dishonest parties. This has implications in certifying the application of graph states for various distributed tasks. We present a protocol which is globally efficient for a large family of useful graph states, including cluster states, GHZ states, cycle graph states, and more. For general graph states, efficiency with respect to the security parameter is maintained, though there is a cost increase with the size of the graph state. The protocols are practical, requiring only multiple copies of the graph state, local measurements, and classical communication.

Error correction of the continuous-variable quantum hybrid computation on two-node cluster states: Limit of squeezing

In this paper, we investigate the error correction of universal Gaussian transformations obtained in the process of continuous-variable quantum computations. We have tried to bring our theoretical studies closer to the actual picture in the experiment. When investigating the error correction procedure, we have considered that both the resource GKP state itself and the entanglement transformation are imperfect. In reality, the GKP state has a finite width associated with the finite degree of squeezing, and the entanglement transformation is performed with error. We have considered a hybrid scheme to implement the universal Gaussian transformations. In this scheme, the transformations are realized through computations on the cluster state, supplemented by linear optical operation. This scheme gives the smallest error in the implementation of universal Gaussian transformations. The use of such a scheme made it possible to reduce the oscillator squeezing threshold required for the implementing of fault-tolerant quantum computation schemes close to reality to -19.25 dB.

Parallel-path implementation of nonadiabatic geometric quantum gates in a decoherence-free subspace with nitrogen-vacancy centers

We propose a scheme for nonadiabatic noncyclic geometric quantum computation in a decoherence-free subspace (DFS). The physical system we used is a cavity quantum electrodynamics system consisting of nitrogen-vacancy (NV) centers in diamond and a whispering-gallery-mode (WGM) microresonator. This scheme not only has the feature of DFSs insensitive to decoherence, but also has the advantage of nonadiabatic noncyclic geometric quantum computation which has the built-in noise-resilience geometric feature and further enhances the robustness due to the ability beyond the limitation of the cyclic condition. An unconventional two-qubit phase gate in DFS has been realized in one step with our parallel protocol, which can largely shorten the computation time and the system error caused by decoherence. In addition, a scheme to realize a parallel process of two evolution paths is put forward to achieve the distribution quantum computation of two WGM microresonators containing a NV center in each. Our scheme may provide a promising way towards the practical realization of high-fidelity geometric quantum computation with the features of a DFS, geometric phase, and parallel implementation process.

Anomalous Josephson Effect in Topological Insulator-Based Josephson Trijunction

We studied anomalous Josephson effect (AJE) in Josephson trijunctions fabricated on Bi2Se3, and found that the AJE in T-shaped trijunctions significantly alters the Majorana phase diagram of the trijunctions, when an in-plane magnetic field is applied parallel to two of the three single junctions. Such a phenomenon in topological insulator-based Josephson trijunction provides unambiguous evidence for the existence of AJE in the system, and may provide an additional knob for controlling the Majorana bound states in the Fu–Kane scheme of topological quantum computation.

Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation (GQC) on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric phase, π/8 and Hadamard gates can be obtained as 99.93%, 99.95% and 99.95%, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as 99.87%. Therefore, our scheme provides a new perspective for GQC, making it more promising in the application of large-scale fault-tolerant quantum computation.

Ladder of Loschmidt anomalies in the deep strong-coupling regime of a qubit-oscillator system

We uncover a remarkably regular array of singularitylike structures within the deep strong-coupling limit of qubit-oscillator (e.g., light-matter) systems described by the quantum Rabi model as a function of time and coupling strength. These nonanalytic anomalies in the Loschmidt amplitude (echoes) suggest the existence of new forms of dynamical phase transition within this deep strong-coupling regime. The key feature whereby the initial state collapses into orthogonal states at select values of the interaction strength and select times may be used to enhance---or attack---quantum information processing or computation schemes that rely on removing---or retaining---a given quantum state.

Ultrafast Holonomic Quantum Gates

Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus faster gate operations are highly desired. Here, we propose a nonadiabatic holonomic quantum computation (NHQC) scheme with detuned interactions on $\Delta$-type three-level system, which combines the time-optimal control technique with the time-independent detuning adjustment to further accelerate universal gate operations, {so that the gate-time can be greatly shortened within the hardware limitation}, and thus high-fidelity gates can be obtained. Meanwhile, our numerical simulations show that the gate robustness is also stronger than previous schemes. Finally, we present an implementation of our proposal on superconducting quantum circuits, with a decoherence-free subspace encoding, based on the experimentally demonstrated parametrically tunable coupling technique, which simplifies previous investigations. Therefore, our protocol provides a more promising alternative for future fault-tolerant quantum computation.