Measurement-based Quantum Computation Research Articles

Error of an arbitrary single-mode Gaussian transformation on a weighted cluster state using a cubic phase gate

In this paper, we propose two strategies for decreasing the error of arbitrary single-mode Gaussian transformations implemented using one-way quantum computation on a four-node linear cluster state. We show that it is possible to minimize the error of the arbitrary single-mode Gaussian transformation by a proper choice of the weight coefficients of the cluster state. We modify the computation scheme by adding a non-Gaussian state obtained using a cubic phase gate as one of the nodes of the cluster. This further decreases the computation error. We evaluate the efficiencies of the proposed optimization schemes comparing the probabilities of the error correction of the quantum computations with and without optimizations. We have shown that for some transformations, the error probability can be reduced by up to 900 times.

Native measurement-based quantum approximate optimization algorithm applied to the Max K -Cut problem

Photonic quantum computers, programed within the framework of the measurement-based quantum computing (MBQC), and gate-based platforms are racing toward useful quantum advantage, and some algorithms have emerged as main candidates to reach this goal in the near term. The majority of these algorithms are only expressed in the gate-based model of computation, which is incompatible with photonic platforms. Methods to translate gate-based algorithms into the MBQC framework exist, but they are not always optimal in terms of resource cost. In our work, we propose an MBQC algorithm to run the quantum approximate optimization algorithm (QAOA). Furthermore, we apply the MBQC-QAOA algorithm to the Max $K$-Cut problem, for all values of $K$, expressing the cost Hamiltonian and its constraints in a form easily implementable in the MBQC model. We conclude by analyzing the resource cost of our algorithm, compared to the case of translating a gate-based QAOA algorithm into MBQC rules, and show up to a 30-fold improvement. With our work, we contribute to closing the gap between gate-based and MBQC near-term algorithms, a gap not reflecting the current status of the hardware development.

Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps.

It has recently been established that clusterlike states-states that are in the same symmetry-protected topological phase as the cluster state-provide a family of resource states that can be utilized for measurement-based quantum computation. In this Letter, we ask whether it is possible to prepare clusterlike states in finite time without breaking the symmetry protecting the resource state. Such a symmetry-preserving protocol would benefit from topological protection to errors in the preparation. We answer this question in the positive by providing a Hamiltonian in one higher dimension whose finite-time evolution is a unitary that acts trivially in the bulk, but pumps the desired cluster state to the boundary. Examples are given for both the 1D cluster state protected by a global symmetry, and various 2D cluster states protected by subsystem symmetries. We show that even if unwanted symmetric perturbations are present in the driving Hamiltonian, projective measurements in the bulk along with feed-forward correction is sufficient to recover a clusterlike state.

Sequential generation of multiphoton entanglement with a Rydberg superatom

Multiqubit entanglement is an indispensable resource for quantum information science. In particular, the entanglement of photons is of conceptual interest due to its implications in measurement-based quantum computing, communication, and metrology. The traditional way of spontaneous parametric down-conversion already demonstrates entanglement of up to a dozen photons but is hindered by its probabilistic nature. Here, we experimentally demonstrate an efficient approach for multi-photon generation with a Rydberg superatom, a mesoscopic atomic ensemble under Rydberg blockade. Using it as an efficient single-photon interface, we iterate the photon creation process that gives rise to a train of temporal photonic modes entangled in photon number degree. We detect the multiphoton entanglement via converting the photon number degree to a time-bin degree. Photon correlations verify entanglement up to 12 modes. The efficiency scaling factor for adding one photon is 0.27, surpassing previous results, and can be increased significantly without fundamental limitations.

On-Demand Source of Dual-Rail Photon Pairs Based on Chiral Interaction in a Nanophotonic Waveguide

Entanglement is the fuel of advanced quantum technology, enabling, e.g., measurement-based quantum computing and loss-tolerant encoding of quantum information. In photonics, entanglement has traditionally been generated probabilistically, requiring massive multiplexing for scaling up to many photons. An alternative approach utilizing quantum emitters in nanophotonic devices can realize deterministic generation of entangled photons. However, such sources generate polarization entanglement that is incompatible with spatial dual-rail qubit encoding employed in scalable photonic quantum-computing platforms utilizing integrated circuits. Here we propose and experimentally realize an on-demand source of dual-rail photon pairs using a quantum dot in a planar nanophotonic waveguide. The source exploits the cascaded decay of a biexciton state and chiral light-matter coupling to achieve deterministic generation of spatial dual-rail Bell pairs with the amount of entanglement determined by the chirality. The operational principle can readily be extended to multiphoton entanglement generation required for efficient preparation of resource states for photonic quantum computing.Received 17 January 2022Revised 22 May 2022Accepted 8 June 2022DOI:https://doi.org/10.1103/PRXQuantum.3.020363Published 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 AreasPhotonic crystalsPhotonicsQuantum communicationQuantum correlations in quantum informationQuantum entanglementSingle photon sourcesPhysical SystemsQuantum dotsWaveguidesPropertiesChiral symmetryAtomic, Molecular & OpticalQuantum Information

How to Simulate Quantum Measurement without Computing Marginals

We describe and analyze algorithms for classically simulating measurement of an n-qubit quantum state in the standard basis, that is, sampling a bit string from the probability distribution determined by the Born rule. Our algorithms reduce the sampling task to computing poly(n) amplitudes of n-qubit states; unlike previously known techniques they do not require computation of marginal probabilities. Two classes of quantum states are considered: output states of polynomial-size quantum circuits, and ground states of local Hamiltonians with an inverse polynomial spectral gap. We show that our algorithms can significantly accelerate quantum circuit simulations based on tensor network contraction or low-rank stabilizer decompositions. As another striking consequence we obtain the first efficient classical simulation algorithm for measurement-based quantum computation with the surface code resource state on any planar graph and any schedule of measurements.

Deterministic one-way logic gates on a cloud quantum computer

One-way quantum computing is a promising candidate for fault-tolerant quantum computing. Here, we propose new protocols to realize a deterministic one-way CNOT gate and one-way $X$-rotations on quantum-computing platforms. By applying a delayed-choice scheme, we overcome a limit of most currently available quantum computers, which are unable to implement further operations on measured qubits or operations conditioned on measurement results from other qubits. Moreover, we decrease the error rate of the one-way logic gates, compared to the original protocol using local operations and classical communication (LOCC). In addition, we apply our deterministic one-way CNOT gate in the Deutsch-Jozsa algorithm to show the feasibility of our proposal. We demonstrate all these one-way gates and algorithms by running experiments on the cloud quantum-computing platform IBM Quantum Experience.

High-fidelity multiphoton-entangled cluster state with solid-state quantum emitters in photonic nanostructures

We propose a complete architecture for deterministic generation of entangled multiphoton states. Our approach utilizes periodic driving of a quantum-dot emitter and an efficient light-matter interface enabled by a photonic crystal waveguide. We assess the quality of the photonic states produced from a real system by including all intrinsic experimental imperfections. Importantly, the protocol is robust against the nuclear spin bath dynamics due to a naturally built-in refocusing method reminiscent to spin echo. We demonstrate the feasibility of producing Greenberger-Horne-Zeilinger and one-dimensional cluster states with fidelities and generation rates exceeding those achieved with conventional ``fusion'' methods in current state-of-the-art experiments. The proposed hardware constitutes a scalable and resource-efficient approach towards implementation of measurement-based quantum computing and quantum communication.

Universal quantum computation and quantum error correction using discrete holonomies

Holonomic quantum computation exploits a quantum state's nontrivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. Holonomies arising from systems where the Hamiltonian traces a continuous path through parameter space have been well researched. Discrete holonomies, on the other hand, where the state jumps from point to point in state space, have had little prior investigation. Using a sequence of incomplete projective measurements of the spin operator, we build an explicit approach to universal quantum computation. We show that quantum error correction codes integrate naturally in our scheme, providing a model for measurement-based quantum computation that combines the passive error resilience of holonomic quantum computation and active error correction techniques. In the limit of dense measurements we recover known continuous-path holonomies.

Unconditional measurement-based quantum computation with optomechanical continuous variables

Universal quantum computation encoded over continuous variables can be achieved via Gaussian measurements acting on entangled non-Gaussian states. However, due to the weakness of available nonlinearities, generally these states can only be prepared conditionally, potentially with low probability. Here we show how universal quantum computation could be implemented unconditionally using an integrated platform able to sustain both linear and quadratic optomechanical-like interactions. Specifically, considering cavity opto- and electromechanical systems, we propose a realization of a driven-dissipative dynamics that deterministically prepares the required non-Gaussian cluster states---entangled squeezed states of multiple mechanical oscillators suitably interspersed with cubic-phase states. We next demonstrate how arbitrary Gaussian measurements on the cluster nodes can be performed by continuously monitoring the output cavity field. Finally, the feasibility requirements of this approach are analyzed in detail, suggesting that its building blocks are within reach of current technology.

Universal hardware-efficient topological measurement-based quantum computation via color-code-based cluster states

Topological measurement-based quantum computation (MBQC) enables one to carry out universal fault-tolerant quantum computation via single-qubit Pauli measurements with a family of large entangled states called cluster states as resources. Raussendorf's three-dimensional cluster states (RTCSs) based on the surface codes are mainly considered for topological MBQC. In such schemes, however, the fault-tolerant implementation of the logical Hadamard, phase ($Z^{1/2}$), and $T$ ($Z^{1/4}$) gates which are essential for building up arbitrary logical gates has not been achieved to date without using state distillation, while the controlled-NOT (CNOT) gate does not require it, to best of our knowledge. State distillation generally consumes many ancillary logical qubits, thus it is a severe obstacle against practical quantum computing. To solve this problem, we suggest an MBQC scheme via a family of cluster states called color-code-based cluster states (CCCSs) based on the two-dimensional color codes instead of the surface codes. We define logical qubits, construct elementary logical gates, and describe error correction schemes. We show that all the logical Clifford gates including the CNOT, Hadamard, and phase gates can be implemented fault-tolerantly without state distillation, although the fault-tolerant $T$ gate still requires it. We further prove that the minimal number of physical qubits per logical qubit in a CCCS is at most approximately 1.8 times smaller than the case of an RTCS. We lastly show that the error threshold of MBQC via CCCSs for logical-$Z$ errors is 2.7-2.8%, which is comparable to the value for RTCSs, assuming a simple error model where physical qubits have $X$-measurement or $Z$ errors independently with the same probability.

Timing Constraints Imposed by Classical Digital Control Systems on Photonic Implementations of Measurement-Based Quantum Computing

Most of the architectural research on photonic implementations of measurement-based quantum computing (MBQC) has focused on the quantum resources involved in the problem with the implicit assumption that these will provide the main constraints on system scaling. However, the `flying-qubit' architecture of photonic MBQC requires specific timing constraints that need to be met by the classical control system. This classical control includes, for example: the amplification of the signals from single-photon detectors to voltage levels compatible with digital systems; the implementation of a control system which converts measurement outcomes into basis settings for measuring subsequent cluster qubits, in accordance with the quantum algorithm being implemented; and the digital-to-analog converter (DAC) and amplifier systems required to set these measurement bases using a fast phase modulator. In this paper, we analyze the digital system needed to implement arbitrary one-qubit rotations and controlled-NOT (CNOT) gates in discrete-variable photonic MBQC, in the presence of an ideal cluster state generator, with the main aim of understanding the timing constraints imposed by the digital logic on the analog system and quantum hardware. We use static timing analysis of a Xilinx FPGA (7 series) to provide a practical upper bound on the speed at which the adaptive measurement processing can be performed, in turn constraining the photonic clock rate of the system. Our work points to the importance of co-designing the classical control system in tandem with the quantum system in order to meet the challenging specifications of a photonic quantum computer.

Research advances in continuous-variable quantum computation and quantum error correction

Quantum computation presents incomparable advantages over classical computer in solving some complex problems. To realize large-scale quantum computation, it is required to establish a hardware platform that is universal, scalable and fault tolerant. Continuous-variable optical system, which has unique advantages, is a feasible way to realize large-scale quantum computation and has attracted much attention in recent years. Measurement-based continuous-variable quantum computation realizes the computation by performing the measurement and feedforward of measurement results in large-scale Gaussian cluster states, and it provides an efficient method to realize quantum computation. Quantum error correction is an important part in quantum computation and quantum communication to protect quantum information. This review briefly introduces the basic principles and research advances in one-way quantum computation based on cluster states, quantum computation based on optical Schrödinger cat states and quantum error correction with continuous variables, and discusses the problems and challenges that the continuous-variable quantum computation is facing.

How to Efficiently Achieve Pho­tonic Multi-Qubit Entanglement

Two-dimensional graph states consisting of a large number of entangled photons are at the heart of measurement-based quantum computation. Researchers have now developed a procedure to efficiently and reliably generate linear graph states with up to 14 entangled photons, all emitted from a single atom. Adding even more photons also seems to be nearly within reach.

Measurement-based universal blind quantum computation with minor resources

Blind quantum computation (BQC) enables a client with less quantum computational ability to delegate her quantum computation to a server with strong quantum computational power while preserving the client's privacy. Generally, many-qubit entangled states are often used to complete BQC tasks. But for a large-scale entangled state, it is difficult to be described since its Hilbert space dimension is increasing exponentially. Furthermore, the number of entangled qubits is limited in experiment of existing works. To tackle this problem, in this paper we propose a universal BQC protocol based on measurement with minor resources, where the trap technology is adopted to verify correctness of the server's measurement outcomes during computation and testing process. In our model there are two participants, a client who prepares initial single-qubit states and a server that performs universal quantum computation. The client is almost classical since she does not require any quantum computational power, quantum memory. To realize the client's universal BQC, we construct an $m\times n$ latticed state composed of six-qubit cluster states and eight-qubit cluster states, which needs less qubits than the brickwork state. Finally, we analyze and prove the blindness, correctness, universality and verifiability of our proposed BQC protocol.

Hybrid Exchange–Measurement-Based Qubit Operations in Semiconductor Double-Quantum-Dot Qubits

Measurement-based quantum computing (MBQC) promises natural compatibility with quantum error correcting codes at the cost of a polynomial increase in physical qubits. MBQC proposals have largely focused on photonic systems, where 2-qubit gates are difficult. Semiconductor spin qubits in quantum dots, on the other hand, offer fast 2-qubit gates via the exchange interaction. In exchange-based quantum computing, as with other solid-state qubits, leakage to higher states is a serious problem that must be mitigated. Here, two hybrid measurement-exchange schemes are proposed which quantify the benefits of MBQC on quantum dot-based quantum computing. Measurement of double quantum dot encoded qubits in the singlet-triplet basis, along with inter- and intra-qubit exchange interaction, are used to perform one and two qubit operations. Both schemes suppress individual qubit spin-state leakage errors, offer fast gate times, and require only controllable exchange couplings, up to known phase and Pauli corrections.

S = 1 antiferromagnetic electron-spin systems on hydrogenated phenalenyl-tessellation molecules for material-based quantum-computation resources

A resource state for measurement-based quantum computation is proposed using a material design of S = 1 antiferromagnetic spin chains. Specifying hydrogen adsorption positions on polymerized phenalenyl-tessellation molecules gives rise to formation of graphene zero modes that produce local S = 1 spins or S = 1/2 spins in the required order through exchange interactions. When the S = 1 antiferromagnetic Heisenberg models serve as quantum-computation resources, hydrogen adatoms inducing zero modes can also work as local electron-spin probes in nuclear spin spectroscopy, which could be used for controlling and measuring local spins.

Robust multipartite entanglement without entanglement breaking

Entangled systems in experiments may be lost or off-line in distributed quantum information processing. This inspires a general problem to characterize quantum operations, which result in breaking of entanglement or not. Our goal in this paper is to solve this problem both in single entanglement and network scenarios. We firstly propose a local model for characterizing all entangled states that are breaking for losing particles. This implies a simple criterion for witnessing single entanglement such as generalized GHZ states and Dicke states. It further provides an efficient witness for entangled quantum networks depending on its connectivity such as $k$-independent quantum networks, completely connected quantum networks, and $k$-connected quantum networks. These networks are universal resources for measurement-based quantum computations. The strong nonlocality can be finally verified by using nonlinear inequalities. These results show distinctive features of both single entangled systems and entangled quantum networks.

Quantifying entanglement in cluster states built with error-prone interactions

Measurement-based quantum computing is an alternative paradigm to the circuit-based model. This approach can be advantageous in certain scenarios, such as when read-out is fast and accurate, but two-qubit gates realized via inter-particle interactions are slow and can be parallelized to efficiently create a cluster state. However, understanding how two-qubit errors impact algorithm accuracy and developing experimentally viable approaches to characterize cluster-state fidelity are outstanding challenges. Here, we consider one-dimensional cluster states built from controlled phase, Ising, and XY interactions with slow two-qubit error in the interaction strength, consistent with error models of interactions found in a variety of qubit architectures. We detail an experimentally viable teleportation fidelity that offers a measure of the impact of these errors on the cluster state. Our fidelity calculations show that the error has a distinctly different impact depending on the underlying interaction used for the two-qubit entangling gate. In particular, the Ising and XY interactions can allow perfect teleportation through the cluster state even with large errors, but the controlled phase interaction does not. Nonetheless, we find that teleportation through cluster state chains of size $N$ has a maximum two-qubit error for teleportation along a quantum channel that decreases as $N^{-1/2}$. To enable construction of larger cluster states, we design lowest-order refocusing pulses for correcting these slow errors in the interaction strength. Our work generalizes to higher-dimensional cluster states and sets the stage for experiments to monitor the growth of entanglement in cluster states built from error-prone interactions.

Multidimensional cluster states using a single spin-photon interface coupled strongly to an intrinsic nuclear register

Photonic cluster states are a powerful resource for measurement-based quantum computing and loss-tolerant quantum communication. Proposals to generate multi-dimensional lattice cluster states have identified coupled spin-photon interfaces, spin-ancilla systems, and optical feedback mechanisms as potential schemes. Following these, we propose the generation of multi-dimensional lattice cluster states using a single, efficient spin-photon interface coupled strongly to a nuclear register. Our scheme makes use of the contact hyperfine interaction to enable universal quantum gates between the interface spin and a local nuclear register and funnels the resulting entanglement to photons via the spin-photon interface. Among several quantum emitters, we identify the silicon-29 vacancy centre in diamond, coupled to a nanophotonic structure, as possessing the right combination of optical quality and spin coherence for this scheme. We show numerically that using this system a 2×5-sized cluster state with a lower-bound fidelity of 0.5 and repetition rate of 65 kHz is achievable under currently realised experimental performances and with feasible technical overhead. Realistic gate improvements put 100-photon cluster states within experimental reach.