# Counterfactual computation

@article{Mitchison2001CounterfactualC, title={Counterfactual computation}, author={Graeme J. Mitchison and Richard Jozsa}, journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences}, year={2001}, volume={457}, pages={1175 - 1193} }

Suppose that we are given a quantum computer programmed ready to perform a computation if it is switched on. Counterfactual computation is a process by which the result of the computation may be learnt without actually running the computer. Such processes are possible within quantum physics and to achieve this effect a computer embodying the possibility of running the computation must be available, even though the computation is, in fact, not run. We study the possibilities and limitations of…

## 56 Citations

### On Counterfactual Computation

- Computer ScienceUC
- 2005

This paper first cast the definition of counterfactual protocol in the quantum programming language qGCL, thereby showing thatcounterfactual computation can be rigorously formalised as a quantum computation, and formalises inqGCL a probabilistic extension of counter Factual protocol for decision problems.

### Counterfactual quantum computation through quantum interrogation

- Computer ScienceNature
- 2006

This work shows how to boost the counterfactual inference probability to unity, thereby beating the random guessing limit and implementing Grover's search algorithm with an all-optical approach, and can eliminate errors induced by decoherence.

### A dynamical quantum Cheshire Cat effect and implications for counterfactual communication

- PhysicsNature communications
- 2021

A type of dynamic effect is reported that is at the core of the so called "counterfactual computation" and especially " counterfactual communication" quantum effects that have generated a lot of interest recently, and generalizes the quantum Cheshire Cat effect to dynamical settings.

### Termination of nondeterministic quantum programs

- Computer ScienceActa Informatica
- 2013

A zero-one law for termination probability of the states in the reachable space is established and an algorithm is found for checking termination of nondeterministic quantum programs within a fixed finite-dimensional state space.

### Experimental Realization of High-Efficiency Counterfactual Computation.

- PhysicsPhysical review letters
- 2015

The counterfactual efficiency up to 85% has been demonstrated in the generalized CFC protocol, which opens the possibility of many exciting applications of CFC, such as high-efficiency quantum integration and imaging.

### Non-deterministic quantum programming

- Computer Science
- 2004

This work considers non-determinism embedded in a programming language for quantum computation, the quantum Guarded-Command Language (qGCL), and uses that for describing and reasoning about counterfactual computation and mixed-state systems.

### Algorithmic analysis of termination problems for quantum programs

- PhysicsProc. ACM Program. Lang.
- 2018

This work is essentially a generalisation of constraint-based approach to the corresponding problems for probabilistic programs developed in the recent literature by adding two novel ideas: (1) employing the fundamental Gleason's theorem in quantum mechanics to guide the choices of templates; and (2) a generalised Farkas' lemma in terms of observables in quantum physics.

### Topics in quantum algorithms : adiabatic algorithm, quantum money, and bomb query complexity

- Computer Science
- 2015

A modified quantum query model, which is inspired by the Elitzur-Vaidman bomb-testing problem, and it is proved that quantum money by knots can not be cloned in a black box way unless graph isomorphism is efficiently solvable by a quantum computer.

### Demonstration of Bomb Detection Using the IBM Quantum Computer

- Physics
- 2019

This work explicate all the cases, including whether the bomb is alive or dead by proposing new quantum circuits and executing those in QISKit as provided by IBM Quantum Experience platform and verify the obtained results.

### Quantum Godwin's Law

- PhysicsArXiv
- 2020

This work shows under reasonable model assumptions a polynomial quantum speedup of Godwin's law, and finds that the quantum Godwin effect is not only robust against noise, but actually enhanced by decoherence.

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