A Computational Model for Quantum Measurement

Gerard J Milburn, Cassius D'Helon

Jincheng Zhang

This paper proposes a novel computational model based on quantum measurement theory. The core idea is to treat computation as a series of quantum measurements, offering a potentially transformative paradigm for computing. We decompose computational tasks into sequences of measurements, leveraging mathematical tools from quantum measurement theory to perform calculations. The model explores the impact of the measurement process on computational efficiency. Unlike existing models rooted in classical physics, this approach directly addresses the fundamental role of measurement in information processing, potentially unlocking new computational possibilities. The model is presented with detailed mathematical formulations, focusing on measurement operators, state vectors, and the dynamics of measurement processes. The analysis aims to provide a theoretical framework for understanding and developing quantum computation based on the principles of measurement. ---

Richard Jozsa

In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement outcomes and the final result of the computation is determined from the classical data of all the measurement outcomes. This is in contrast to the more familiar gate array model in which computational steps are unitary operations, developing a large entangled state prior to some final measurements for the output. Two principal schemes of measurement based computation are teleportation quantum computation (TQC) and the so-called cluster model or one-way quantum computer (1WQC). We will describe these schemes and show how they are able to perform universal quantum computation. We will outline various possible relationships between the models which serve to clarify their workings. We will also discuss possible novel computational benefits of the measurement based models compared to the gate array model, especially issues of parallelisability of algorithms.

Arunava Majumder, Hendrik Poulsen Nautrup, Hans J. Briegel

Measurement-based quantum computation (MBQC) is a framework for quantum information processing in which a computational task is carried out through one-qubit measurements on a highly entangled resource state. Due to the indeterminacy of the outcomes of a quantum measurement, the random outcomes of these operations, if not corrected, yield a variational quantum channel family. Traditionally, this randomness is corrected through classical processing in order to ensure deterministic unitary computations. Recently, variational measurement-based quantum computation (VMBQC) has been introduced to exploit this measurement-induced randomness to gain an advantage in generative modeling. A limitation of this approach is that the corresponding channel model has twice as many parameters compared to the unitary model, scaling as $N \times D$, where $N$ is the number of logical qubits (width) and $D$ is the depth of the VMBQC model. This can often make optimization more difficult and may lead to poorly trainable models. In this paper, we present a restricted VMBQC model that extends the unitary setting to a channel-based one using only a single additional trainable parameter. We show, both numerically and algebraically, that this minimal extension is sufficient to generate probability distributions that cannot be learned by the corresponding unitary model.

Hans J. Briegel, Dan E. Browne, Wolfgang Dür +2 more

Marius Nagy, Selim G. Akl