One of the main challenges in quantum computing is implementing algorithms within quantum optical free-space and integrated circuits. This research focuses on the quantum addition algorithm, derived from the Deutsch-Jozsa algorithm, to advance quantum computing using optical technologies. The developed quantum optical integrated circuit is built on a hybrid substrate with interconnected components on a silicon dioxide base. Qubits and their states are arranged according to the requirements of each quantum algorithm. In the Fourier transform section, qubits act as propagation modes within silicon waveguides, with emitted photons representing the Fourier transform after traveling a distance of π/2. The phase-shifting section consists of two parts: one shifts the phase of incoming photons by π, while the other modulates this shift based on the quantum full adder algorithm. The first employs a photonic crystal for short phase shifts, which are adjusted via impurities in the silicon substrate and controlled by an electro-optic circuit. Additionally, single-mode waveguides made of silicon dioxide and air serve as qubits. By coupling photon amplitudes, a comparator circuit is triggered based on the generated output. Through these integrations, the sum of two quantum numbers can be represented at the output. This underscores the importance of designing and simulating a full adder within quantum optical integrated circuits to address the complexities inherent in quantum computing.
One of the main challenges in quantum computing is implementing algorithms within quantum optical free-space and integrated circuits. This research focuses on the quantum addition algorithm, derived from the Deutsch-Jozsa algorithm, to advance quantum computing using optical technologies. The developed quantum optical integrated circuit is built on a hybrid substrate with interconnected components on a silicon dioxide base. Qubits and their states are arranged according to the requirements of each quantum algorithm. In the Fourier transform section, qubits act as propagation modes within silicon waveguides, with emitted photons representing the Fourier transform after traveling a distance of π/2. The phase-shifting section consists of two parts: one shifts the phase of incoming photons by π, while the other modulates this shift based on the quantum full adder algorithm. The first employs a photonic crystal for short phase shifts, which are adjusted via impurities in the silicon substrate and controlled by an electro-optic circuit. Additionally, single-mode waveguides made of silicon dioxide and air serve as qubits. By coupling photon amplitudes, a comparator circuit is triggered based on the generated output. Through these integrations, the sum of two quantum numbers can be represented at the output. This underscores the importance of designing and simulating a full adder within quantum optical integrated circuits to address the complexities inherent in quantum computing.
One of the most significant challenges in quantum computing is the variability in implementing quantum algorithms across different chips. In this work, we present a Hadamard photonic gate based on the quantum Fourier transform, which superimposes several numbers encoded in the classical domain. We recognize that various mathematical operations - such as addition, subtraction, multiplication, division, and other complex calculations - are typically processed separately for each nth number in classical computers. This approach consumes considerable memory space and results in slower processing speeds as the number of bits increases. With the advancements provided in this work, we can eliminate the need for multiple memory spaces, allowing all numbers to be processed simultaneously in a single computation step. This is a key reason why quantum computers are significantly faster than their classical counterparts. Notably, as the number of bits increases, the number of processes remains consistent, enabling the same operations to be performed without requiring additional memory capacity. We have designed this algorithm using an optical integrated circuit that includes a silicon dioxide waveguide in an air bed, operating at a wavelength of 1.55 µm. Importantly, this circuit can not only be implemented independently on hybrid chips but also integrated into quantum monolithic chips based on Silicon Dioxide-Air optical waveguides as a key component of the overall structure.
Quantum computing (Q-computing) is a revolutionary technology that applies quantum mechanics (QM) to implement calculations significantly quicker than traditional computers. Q-computing employs Q-bits (qubits) rather than classical bits, which can take on a superposition state, making it possible to represent both 0 and 1 at once. This distinctive property allows qubits to perform multiple calculations simultaneously, making Q computers exponentially more powerful as more qubits are added, compared to the linear scaling of classical computers. However, challenges such as qubit instability and error rates remain significant obstacles to fully realizing this potential. A vital aspect of this technology is the development of Q arithmetic circuits, which act as the foundational blocks for efficiently executing Q algorithms. Q half-adder and full-adder circuits are integral to performing fundamental arithmetic operations within Q computers. In contrast to classical adders, Q adders rely on Q gates such as Controlled NOT (CNOT) and Toffoli gates. These gates exploit Q phenomena like entanglement and superposition, allowing for more efficient computations. The Q half-adder consists of two qubits and adds two single bits, producing a carry and sum output. It utilizes the CNOT gate to compute the sum and the Toffoli gate (controlled-controlled-NOT [CCNOT]) to compute the carry. The Q full-adder builds on this, adding three qubits to produce a sum and a carry output, further increasing computational capacity. Through the entanglement of qubits, these circuits allow for more parallelism and speed compared to classical adders. Q carry-look-ahead adders (QCLAs) and Q ripple-carry adders (QRCAs) are used to perform more complex arithmetic operations based on these half-adder and full-adder structures. Q arithmetic circuits have broad applications, boosting secure key generation in cryptography, speeding up matrix operations for faster model training in machine learning, and enabling more precise, efficient image transformations in Q image processing, benefiting fields like medical imaging and computer vision.
Quantum information science has shown that harnessing quantum mechanical effects can dramatically improve performance for certain tasks in communication, computation and measurement. Of the various physical systems being pursued, single particles of light - photons - are often the logical choice [1]. In addition to single photon sources and detectors, photonic quantum technologies will rely on sophisticated optical circuits [2]. Recently we reported the implementation of quantum optic integrated circuits, which not only dramatically reduces the footprint of quantum circuits, but allows unprecedented stability and higher performance. We demonstrated silica on silicon circuits that implement key components for quantum information, including CNOT gates [3] and single-qubit operations [4]. These components show promising progresses toward fault tolerance operation [5]. We also used integrated waveguides to implement a circuit that performs a compiled version of Shor's quantum algorithm [6] to factorize 15. Here we report the demonstration of circuits that extend the capabilities of the components already demonstrated, to take full advantage of the integrated optics architecture.
Controlling and programming quantum devices to process quantum information by the unit of quantum dit, i.e., qudit, provides the possibilities for noise-resilient quantum communications, delicate quantum molecular simulations, and efficient quantum computations, showing great potential to enhance the capabilities of qubit-based quantum technologies. Here, we report a programmable qudit-based quantum processor in silicon-photonic integrated circuits and demonstrate its enhancement of quantum computational parallelism. The processor monolithically integrates all the key functionalities and capabilities of initialisation, manipulation, and measurement of the two quantum quart (ququart) states and multi-value quantum-controlled logic gates with high-level fidelities. By reprogramming the configuration of the processor, we implemented the most basic quantum Fourier transform algorithms, all in quaternary, to benchmark the enhancement of quantum parallelism using qudits, which include generalised Deutsch-Jozsa and Bernstein-Vazirani algorithms, quaternary phase estimation and fast factorization algorithms. The monolithic integration and high programmability have allowed the implementations of more than one million high-fidelity preparations, operations and projections of qudit states in the processor. Our work shows an integrated photonic quantum technology for qudit-based quantum computing with enhanced capacity, accuracy, and efficiency, which could lead to the acceleration of building a large-scale quantum computer.
Abstract : Photons play a central role in many areas of quantum information processing and quantum sensing, ranging from linear optics quantum computing and quantum simulation to quantum communications. A central problem in many of these applications is the need to control many spatial and temporal modes with high efficiency and precision. Photonic integrated circuits can contain closely-spaced and extremely phase-stable components that enable precision control of many spatial and temporal modes in dielectric waveguides. This program developed photonic integrated circuits (PICs) based on the silicon-on-insulator platform. We developed large-scale PICs with cascaded Mach-Zehnder interferometers (MZI) with precision electro-optic modulators. These PICs have very low internal losses (0.1 dB/MZI) and achieve exceptionally high contrast interference ( 80 dB) over tens of spatial modes. These fully programmable mode transformers have driven experimental and theoretical advances in quantum simulation, cluster-state quantum computing, all-optical quantum repeaters, neuromorphic computing, and other applications. In addition, we developed new schemes for ballistic quantum computation, new methods for high-efficiency single photon sources, a new approach for 3-photon cluster state generation that forms the essential ingredient for percolation-based generation of scalable cluster states, and quantum logic gates based on weak optical nonlinearities.
Quantum information science aims to harness uniquely quantum mechanical properties to enhance measurement and information technologies, and to explore fundamental aspects of quantum physics. Of the various approaches to quantum computing [1], photons are particularly appealing for their low-noise properties and ease of manipulation at the single qubit level [2,3]. Encoding quantum information in photons is also an appealing approach to quantum communication, metrology (eg. [4]), measurement (eg. [5]) and other quantum technologies [6]. However, the implementation of optical quantum circuits with bulk optics has reached practical limits. We have developed an integrated waveguide approach to photonic quantum circuits for high performance, miniaturization and scalability [7]. Here we report high-fidelity silica-on-silicon integrated optical realizations of key quantum photonic circuits, including two-photon quantum interference and a controlled-NOT logic gate [8]. We have demonstrated controlled manipulation of up to four photons on-chip, including highfidelity single qubit operations, using a lithographically patterned resistive phase shifter [9]. We have used this architecture to implement a small-scale compiled version of Shor's quantum factoring algorithm [10], demonstrated heralded generation of tunable four photon entangled states from a six photon input [11], a reconfigurable two-qubit circuit [12], and combined waveguide photonic circuits with superconducting single photon detectors [13]. We describe complex quantum interference behavior in multi-mode interference devices with up to eight inputs and outputs [14], and quantum walks of correlated particles in arrays of coupled waveguides [15]. Finally, we give an overview of our recent work on fundamental aspects of quantum measurement [16,17] and diamond [18,19] and nonlinear [20,21] photon sources.