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

TL;DR

This work assesses the electrical energy cost of programmable photonic integrated circuits performing arbitrary state preparation (aQSP) across qubit and qudit encodings, using a common LiNbO$_3$ PIC baseline. By comparing gate-based (GBQC) and measurement-based (MBQC) paradigms, and by benchmarking qudits against qubits, the study finds that energy cost grows exponentially with state dimension and system size, with qudit implementations becoming intractable beyond a few qubits due to large interferometer footprints and reconfiguration overhead. Near-deterministic KLM CNOT implementations in GBQC require substantial resources, though time-demultiplexing can mitigate energy costs at the expense of memory routing. MBQC offers some energy advantages but is limited by a strict one-day preparation time, preventing access to the full NISQ regime; overall, the results motivate device designs and architectures tailored to specific QSP tasks to achieve energy-efficient scaling in photonic quantum processors.

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.

Figures (8)

• Figure 1: (a) Universal n-mode multiport interferometer (shown here for $n=6$) can be implemented using a mesh of $N=n(n-1)/2$ beam splitters demonstrated in Ref.clements2016optimal; (b) The crossing represents a variable beam splitter described by $T_{m,n}(\theta,\phi)$ matrix, which can be implemented by a MZI consisting of two $50:50$ directional couplers, followed by a phase shifter at one input port.
• Figure 2: Circuit representation of a two-qubit state preparation using three consecutive CNOT gates. Fifteen single-qubit operations (SQOs) are also required vatan2004optimal, but are omitted here for clarity.
• Figure 3: Representation of the decomposition of a long-range CNOT gate into a sequence of nearest-neighbor CNOTs bergholm2005quantum.
• Figure 4: Gate sequence for preparation of an arbitrary four-qubit state using (a) the Plesch circuit for QSP plesch2011quantum, with the four steps highlighted in blue boxes; (b) a modified Plesch circuit which only uses nearest-neighbor CNOTs, with the CNOT decompositions highlighted in green boxes for clarity.
• Figure 5: Comparison of the number of CNOT gates required for qubit state preparation using different methods: Bergholm method (blue), original Plesch method (green), and a modified Plesch method restricted to nearest-neighbor CNOTs (yellow). The modified circuit highlights CNOT decompositions for clarity. As shown, while the Bergholm method is more efficient for $n=2$ qubits, the adapted Plesch method becomes more efficient as $n$ increases, closely approaching the upper bound.