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arXiv:2402.16603

Estimating the electrical energy cost of performing arbitrary state preparation using qubits and qudits in integrated photonic circuits

Maria Carolina Volpato, Gabriel da Silva Sampaio, Pierre-Louis de Assis

Published Feb 26, 2024• 0 citations
arXivHTMLPDF

Abstract

As quantum photonic hardware scales toward computationally relevant sizes, energy consumption has emerged as a key constraint. Programmable photonic integrated circuits, composed of interferometer meshes with tunable phase modulators, provide a flexible platform for quantum information processing using both qubits and qudits. In this work, we analyze the energetic cost of such devices by focusing on arbitrary quantum state preparation, a resource-intensive task central to quantum simulation and information processing. Using a common hardware, we benchmark qudit-based implementations, gate-based quantum computation, and measurement-based quantum computation. We find that while qudit encodings are attractive at small scale, their footprint and reconfiguration costs grow rapidly with system size, whereas qubit-based approaches incur significant overhead from entangling operations, feedforward, and reprogramming. Across all paradigms, scaling beyond a few tens of qubits renders either the energy consumption or the total preparation time prohibitive on fully programmable PICs. Our results highlight the need for optimized, task-specific photonic architectures to enable energy-efficient scaling.

DOI
10.48550/arxiv.2402.16603

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We present a photonic integrated circuit architecture for a quantum programmable gate array (QPGA) capable of preparing arbitrary quantum states and operators. The architecture consists of a lattice of phase-modulated Mach-Zehnder interferometers, which perform rotations on path-encoded photonic qubits, and embedded quantum emitters, which use a two-photon scattering process to implement a deterministic controlled-${\ensuremath{\sigma}}_{z}$ operation between adjacent qubits. By appropriately setting phase shifts within the lattice, the device can be programmed to implement any quantum circuit without hardware modifications. We provide algorithms for exactly preparing arbitrary quantum states and operators on the device, and we show that gradient-based optimization can train a simulated QPGA to automatically implement highly compact approximations to important quantum circuits with near-unity fidelity.
Programmable integrated photonics (PIP) has emerged as a powerful on-chip platform for optical signal processing and computing, enabling the implementation of reconfigurable N×\times×N unitary matrix transformations through meshes of tunable interferometers, which realize 2$\times2unitarymatrices.However,theenergyconsumptionassociatedwithphase−shifteractuationisbecomingamajorlimitationtothescalabilityofPIPplatforms.Here,weintroduceageometricframeworkforenergyoptimizationinPIPcircuitsbyexploitingtherepresentationof22 unitary matrices. However, the energy consumption associated with phase-shifter actuation is becoming a major limitation to the scalability of PIP platforms. Here, we introduce a geometric framework for energy optimization in PIP circuits by exploiting the representation of 22unitarymatrices.However,theenergyconsumptionassociatedwithphase−shifteractuationisbecomingamajorlimitationtothescalabilityofPIPplatforms.Here,weintroduceageometricframeworkforenergyoptimizationinPIPcircuitsbyexploitingtherepresentationof2\times2unitarymatricesasconcatenationsofbasicEulerrotationsontheBlochsphere.WeshowthatequivalentimplementationsofthesameN2 unitary matrices as concatenations of basic Euler rotations on the Bloch sphere. We show that equivalent implementations of the same N2unitarymatricesasconcatenationsofbasicEulerrotationsontheBlochsphere.WeshowthatequivalentimplementationsofthesameN\times$N unitary matrix (N ≥\geq≥ 2) can exhibit markedly different energy costs depending on the rotation trajectories on the Bloch sphere implemented by each interferometer. Leveraging this insight, we identify minimum-energy configurations by systematically selecting the shortest rotation trajectories. We experimentally and numerically validate the proposed approach in diverse silicon PIP architectures, including feedforward and multipurpose hexagonal meshes, neural network accelerators, and photonic quantum-gate implementations. These results establish a general route toward more energy-efficient large-scale PIP processors for classical and quantum signal processing and computing applications.
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.
Programmable photonic quantum processors face a critical challenge: despite significant advances in quantum state preparation and manipulation, measurements remain limited to projective techniques. Here, we demonstrate a programmable measurement processor that overcomes this limitation by enabling arbitrary quantum measurements within a scalable circuit framework. Our large-scale integrated photonic architecture achieves precise coherent control of ancillary quantum systems, realizing a universal four-dimensional quantum measurement device. We benchmark the processor by performing measurement tomography on 100 randomly selected measurements, achieving an average fidelity of 97.7%. The processor's performance exceeds the theoretical limits of projective measurements in three key quantum information tasks: state discrimination (with 23 times lower error), state estimation (with 10.6% higher fidelity), and randomness generation (with 37% more randomness yield), demonstrating its high operational quality. This work establishes a fully programmable quantum measurement processor, advancing the development of universal quantum operations for photonic quantum information processing by providing the key missing component.
Controlling and programming quantum devices to process quantum information by the unit of 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 high-dimensional quantum processor in a silicon-photonic in-tegrated circuit, which monolithically integrates all the key functionalities and capabilities of initialisation, manipulation, and measurement of the two quantum quart (ququart) states, and demonstrate its enhancement of quantum computational paral-lelism. By reprogramming the processor, we implemented the basic quantum Fourier transform algorithms, all in quaternary, to benchmark the enhancement of quantum parallelism using qudits. 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.