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APL Photonics

Experimental qudit-assisted quantum operations by dimension expansion and partial measurement

Yulin Chi, Chengkang Pan, Xian Ping Lu, Yun Zhu, Fei Wang

Published May 1, 2026• 0 citations
Publisher

Abstract

Many quantum algorithms require ancilla qubits and deep circuits, yet adding and interacting with them are difficult and resource-intensive. Moreover, the high-dimensional properties of quantum systems have been demonstrated to simplify quantum circuits while enhancing efficiency. We propose a novel “Dimension Expansion and Partial Measurement” scheme for quantum information processing based on qudits’ multi-level nature. Given a d-dimensional qudit (expandable to d × r dimensions) and local single-qudit operations in d and r dimensions, we can introduce r-dimensional equivalent ancilla qudits (logically introduced via dimension expansion) and enable quantum operations in deep circuits across d and r dimensions. With successfully generated photons, our scheme efficiently cascades two-qubit/qudit gates with unity theoretical success probability; existing schemes are either probabilistic or need additional particles. In particular, this scheme can be extended to multiple ancilla qudits with measurement feedforward by the “Partially Measure-Reexpand” procedure. This leads to a resource-efficient universal high-dimensional measurement-based quantum computation scheme. On a silicon-photonic chip, starting from 2 qubits (each expandable to a four-dimensional qudit), we implemented a measurement-based quantum computation system equivalent to 5 qubits and experimentally validated our scheme. The proposed scheme applies to simplifying and scaling up various quantum systems.

DOI
10.1063/5.0309870

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Many quantum algorithms require ancilla qubits and deep circuits, yet adding and interacting with them are difficult and resource-intensive. Moreover, the high-dimensional properties of quantum systems have been demonstrated to simplify quantum circuits while enhancing efficiency. We propose a novel “Dimension Expansion and Partial Measurement” scheme for quantum information processing based on qudits’ multi-level nature. Given a d-dimensional qudit (expandable to d × r dimensions) and local single-qudit operations in d and r dimensions, we can introduce r-dimensional equivalent ancilla qudits (logically introduced via dimension expansion) and enable quantum operations in deep circuits across d and r dimensions. With successfully generated photons, our scheme efficiently cascades two-qubit/qudit gates with unity theoretical success probability; existing schemes are either probabilistic or need additional particles. In particular, this scheme can be extended to multiple ancilla qudits with measurement feedforward by the “Partially Measure-Reexpand” procedure. This leads to a resource-efficient universal high-dimensional measurement-based quantum computation scheme. On a silicon-photonic chip, starting from 2 qubits (each expandable to a four-dimensional qudit), we implemented a measurement-based quantum computation system equivalent to 5 qubits and experimentally validated our scheme. The proposed scheme applies to simplifying and scaling up various quantum systems.
Abstract We show how to perform measurement-based quantum computing on qudits (high-dimensional quantum systems) using alternative resource states beyond the cluster state. Estimating overheads for gate decomposition, we find that generalizing standard qubit measurement patterns to the qudit cluster state is suboptimal in most dimensions, so that alternative qudit resource states could enable enhanced computational efficiency. In these resources, the entangling interaction is a block-diagonal Clifford operation rather than the usual controlled-phase gate for cluster states. This simple change has remarkable consequences: the applied entangling operation determines an intrinsic single-qudit gate associated with the resource that drives the quantum computation when performing single-qudit measurements on the resource state. We prove a condition for the intrinsic gate allowing for the measurement-based implementation of arbitrary single-qudit unitaries. Furthermore, we demonstrate for prime-power-dimensional qudits that the complexity of the realization depends linearly both on the dimension and the Pauli order of the intrinsic gate. These insights also allow us to optimize the efficiency of the standard qudit cluster state by effectively mimicking more favorable intrinsic-gate structures, thereby reducing the required measurement depth. Finally, we discuss the required two-dimensional geometry of the resource state for universal measurement-based quantum computing. As concrete examples, we present multiple alternative resource states. In certain dimensions, we show the existence of resource states achieving optimal intrinsic gates, enabling more efficient measurement-based quantum information processing than the qudit cluster state and highlighting the potential of qudit stabilizer state resources for future quantum computing architectures.
Low depth measurement-based quantum computation with qudits (ddd-level systems) is investigated and a precise relationship between this powerful model and qudit quantum circuits is derived in terms of computational depth and size complexity. To facilitate this investigation a qudit `unbounded fan-out' circuit model, in which a qudit may be quantum-copied into an arbitrary number of ancillas in a single time-step, is introduced and shown to be capable of implementing interesting nnn-qudit unitaries in constant depth. A procedure for reducing the quantum computational depth in the measurement-based model is then proposed and using this it is then shown that there is a logarithmic depth separation between the depth complexity of qudit measurement-based computation and circuits composed of gates act on a bounded number of qudits. The relationship is made precise by showing that the depth complexity of the qudit measurement-based model is exactly equivalent to that of unbounded fan-out circuits. These results illustrate that the well-known advantages inherent in qubit measurement-based quantum computation are also applicable to the higher-dimensional generalisation. As qudits are both naturally available and have been shown to provide fundamental advantages over binary logic encodings, this then suggests that the qudit measurement-based model is a particularly appealing paradigm for universal quantum computation.
Qudit, a high-dimensional quantum system, provides a larger Hilbert space to process the quantum information and has shown remarkable advantages over the qubit counterparts. It is a great challenge to realize the high fidelity universal quantum gates with qudits. Here we theoretically propose and experimentally demonstrate a set of universal quantum gates for a single optical qudit with four dimensions (including the generalized Pauli X4X_4X4​ gate, Pauli Z4Z_4Z4​ gate, and all of their integer powers), which are encoded in the polarization-spatial degree of freedom without multiple unstable cascaded interferometers. Furthermore, we also realize the controlled-X4X_4X4​ gate and all of its integer powers. We have achieved both the ultra-high average gate fidelity 99.73%99.73\%99.73% and efficiency 99.47%99.47\%99.47%, which are above the the error threshold for fault-tolerant quantum computation. Our work paves a way for the large-scale high-dimensional fault-tolerant quantum computation with a polynomial resource cost.
Abstract The probabilistic nature of single-photon sources and photon–photon interactions encourages encoding as much quantum information as possible in every photon for the purpose of photonic quantum information processing. Here, by encoding high-dimensional units of information (qudits) in time and frequency degrees of freedom using on-chip sources, we report deterministic two-qudit gates in a single photon with fidelities exceeding 0.90 in the computational basis. Constructing a two-qudit modulo SUM gate, we generate and measure a single-photon state with nonseparability between time and frequency qudits. We then employ this SUM operation on two frequency-bin entangled photons—each carrying two 32-dimensional qudits—to realize a four-party high-dimensional Greenberger–Horne–Zeilinger state, occupying a Hilbert space equivalent to that of 20 qubits. Although high-dimensional coding alone is ultimately not scalable for universal quantum computing, our design shows the potential of deterministic optical quantum operations in large encoding spaces for practical and compact quantum information processing protocols.
In this paper, we propose a linear-optical quantum computation scheme that starts from high-dimensionally entangled qudits but performs quantum computation on qubits defined in their subspaces. This approach enables us to increase the success probability of linear-optical fusions from 50%50\%50% to 1−1/d1-1/d1−1/d for qudits of dimension ddd without relying on existing approaches using ancilla photons and quantum codes. In particular, we show that a 2D cluster state of qubits can be generated from 5-qudit 1D cluster states using pairwise fusion gates while preserving their boosted success probability. We numerically demonstrate that this approach can improve the loss tolerance of a percolation-based scheme while keeping the photon number per resource state constant.
Although qubits are the leading candidate for the basic elements in a quantum computer, there are also a range of reasons to consider using higher-dimensional qudits or quantum continuous variables (QCVs). In this paper, we use a general ``quantum variable'' formalism to propose a method of quantum computation in which ancillas are used to mediate gates on a well-isolated ``quantum memory'' register and which may be applied to the setting of qubits, qudits (for d>2d>2d>2), or QCVs. More specifically, we present a model in which universal quantum computation may be implemented on a register using only repeated applications of a single fixed two-body ancilla-register interaction gate, ancillas prepared in a single state, and local measurements of these ancillas. In order to maintain determinism in the computation, adaptive measurements via a classical feed forward of measurement outcomes are used, with the method similar to that in measurement-based quantum computation (MBQC). We show that our model has the same hybrid quantum-classical processing advantages as MBQC, including the power to implement any Clifford circuit in essentially one layer of quantum computation. In some physical settings, high-quality measurements of the ancillas may be highly challenging or not possible, and hence we also present a globally unitary model which replaces the need for measurements of the ancillas with the requirement for ancillas to be prepared in states from a fixed orthonormal basis. Finally, we discuss settings in which these models may be of practical interest.