arXiv subjects

Madhav Krishnan Vijayan

Publications and source records attributed to Madhav Krishnan Vijayan.

7 recordsLinked to original sources

arXiv2026

Superconducting qubits in the millions: the potential and limitations of modularity

The development of fault-tolerant quantum computers (FTQCs) is receiving increasing attention within the quantum computing community. Like conventional digital computers, FTQCs, which utilize error correction and millions of physical qubits, have the potential to address some of humanity's grand challenges. However, accurate estimates of the tangible scale of future FTQCs, based on transparent assumptions, are uncommon. How many physical qubits are necessary to solve a practical problem intractable for classical hardware? What costs arise from distributing quantum computation across multiple machines? This paper presents an architectural model of a potential FTQC based on superconducting qubits, divided into discrete modules and interconnected via coherent links. We employ a resource estimation framework and software tool to assess the physical resources required to execute specific quantum algorithms compiled into their graph-state form and arranged onto a modular superconducting hardware architecture. Our tool can predict the size, power consumption, and execution time of these algorithms based on explicit assumptions about the system's physical layout, thermal load, and modular connectivity. We assess the resources needed for quantum computation examples that serve as building blocks of proposed applications, quantifying the architectural bottlenecks and trade-offs that remain to be addressed to deliver utility.

quant-ph↗

arXiv2025

Design and efficiency in graph-state computation

The algorithm-specific graph and circuit etching are two strategies for compiling a graph state to implement quantum computation. Benchmark testing exposed limitations to the proto-compiler, Jabalizer giving rise to Etch (https://github.com/QSI-BAQS/Etch), an open-source, circuit-etching tool for transpiling a quantum circuit to a graph state. The viability of circuit etching is evaluated, both as a resource allocation strategy for distilling magic states and as an alternative to the algorithm-specific graph strategy as realised in Jabalizer. Experiments using Etch to transpile IQP circuits to an equivalent graph state resulted in higher ratios of Pauli qubits to non-Pauli qubit than required for efficient magic state distillation. Future research directions for the algorithm-specific graph and circuit-etching strategies are proposed.

quant-ph↗

arXiv2022

Compilation of algorithm-specific graph states for quantum circuits

We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages, such as Cirq and Q#. The computation can then be implemented using a series of non-Pauli measurements on this graph state. By compiling the graph state directly instead of starting with a standard lattice cluster state and preparing it over the course of the computation, we are able to better understand the resource costs involved and eliminate wasteful Pauli measurements on the actual quantum device. Access to this algorithm-specific graph state also allows for optimisation over locally equivalent graph states to implement the same quantum circuit. The compiler presented here finds ready application in measurement based quantum computing, NISQ devices and logical level compilation for fault tolereant implementations.

quant-ph↗

arXiv2021

Hierarchy of quantum operations in manipulating coherence and entanglement

Quantum resource theory under different classes of quantum operations advances multiperspective understandings of inherent quantum-mechanical properties, such as quantum coherence and quantum entanglement. We establish hierarchies of different operations for manipulating coherence and entanglement in distributed settings, where at least one of the two spatially separated parties are restricted from generating coherence. In these settings, we introduce new classes of operations and also characterize those maximal, i.e., the resource-non-generating operations, progressing beyond existing studies on incoherent versions of local operations and classical communication and those of separable operations. The maximal operations admit a semidefinite-programming formulation useful for numerical algorithms, whereas the existing operations not. To establish the hierarchies, we prove a sequence of inclusion relations among the operations by clarifying tasks where separation of the operations appears. We also demonstrate an asymptotically non-surviving separation of the operations in the hierarchy in terms of performance of the task of assisted coherence distillation, where a separation in a one-shot scenario vanishes in the asymptotic limit. Our results serve as fundamental analytical and numerical tools to investigate interplay between coherence and entanglement under different operations in the resource theory.

quant-ph↗

arXiv2020

Simple Bounds for One-shot Pure-State Distillation in General Resource Theories

We present bounds for distilling many copies of a pure state from an arbitrary initial state in a general quantum resource theory. Our bounds apply to operations that are able to generate no more than a $δ$ amount of resource, where $δ\geq 0$ is a given parameter. To maximize applicability of our upper bound, we assume little structure on the set of free states under consideration besides a weak form of superadditivity of the function $G_{min}(ρ)$, which measures the overlap between $ρ$ and the set of free states. Our bounds are given in terms of this function and the robustness of resource. Known results in coherence and entanglement theory are reproduced in this more general framework.

quant-ph↗

arXiv2020

A robust W-state encoding for linear quantum optics

Error-detection and correction are necessary prerequisites for any scalable quantum computing architecture. Given the inevitability of unwanted physical noise in quantum systems and the propensity for errors to spread as computations proceed, computational outcomes can become substantially corrupted. This observation applies regardless of the choice of physical implementation. In the context of photonic quantum information processing, there has recently been much interest in passive linear optics quantum computing, which includes boson-sampling, as this model eliminates the highly-challenging requirements for feed-forward via fast, active control. That is, these systems are passive by definition. In usual scenarios, error detection and correction techniques are inherently active, making them incompatible with this model, arousing suspicion that physical error processes may be an insurmountable obstacle. Here we explore a photonic error-detection technique, based on W-state encoding of photonic qubits, which is entirely passive, based on post-selection, and compatible with these near-term photonic architectures of interest. We show that this W-state redundant encoding techniques enables the suppression of dephasing noise on photonic qubits via simple fan-out style operations, implemented by optical Fourier transform networks, which can be readily realised today. The protocol effectively maps dephasing noise into heralding failures, with zero failure probability in the ideal no-noise limit. We present our scheme in the context of a single photonic qubit passing through a noisy communication or quantum memory channel, which has not been generalised to the more general context of full quantum computation.

quant-ph↗

arXiv2018

One-shot assisted concentration of coherence

We find one-shot bounds for concentration of maximally coherent states in the so called assisted scenario. In this setting, Bob is restricted to performing incoherent operations on his quantum system, however he is assisted by Alice, who holds a purification of Bob's state and can send classical data to him. We further show that in the asymptotic limit our one-shot bounds recover the previously computed rate of asymptotic assisted concentration.

quant-ph↗