# Closed timelike curves make quantum and classical computing equivalent

@article{Aaronson2008ClosedTC, title={Closed timelike curves make quantum and classical computing equivalent}, author={Scott Aaronson and John Watrous}, journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, year={2008}, volume={465}, pages={631 - 647} }

While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to non-trivial insights into general relativity, quantum information and other areas. In this paper, we show that, if CTCs existed, quantum computers would be no more powerful than classical computers: both would have the (extremely large) power of the complexity class polynomial space (), consisting of all problems solvable by a conventional computer using a polynomial amount of memory. This solves…

## 88 Citations

Quantum state cloning using Deutschian closed timelike curves.

- PhysicsPhysical review letters
- 2013

We show that it is possible to clone quantum states to arbitrary accuracy in the presence of a Deutschian closed timelike curve (D-CTC), with a fidelity converging to one in the limit as the…

Quantum computation with indefinite causal structures

- Computer ScienceArXiv
- 2017

It is shown that process matrices correspond to a linear particular case of P-CTCs, and therefore that its computational power is upperbounded by that of PP, and a family of processes that can violate causal inequalities but nevertheless can be simulated by a causally ordered quantum circuit with only a constant overhead, showing that indefinite causality is not necessarily hard to simulate.

Computability Theory of Closed Timelike Curves

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2016

The question of what's computable by Turing machines equipped with time travel into the past is asked, and the answer is, closed timelike curves or CTCs (with no bound on their size), which are shown to solve exactly the problems that are Turing-reducible to the halting problem.

Quantum State Discrimination Circuits Inspired by Deutschian Closed Timelike Curves

- Computer Science
- 2021

It is proved that the proposed practical method for discriminating multiple non-orthogonal states, by using a previously known quantum circuit designed to simulate D-CTCs, achieves the multiple Chernoff bound when discriminating an arbitrary set of pure qubit states.

Closed timelike curves and the second law of thermodynamics

- PhysicsPhysical Review A
- 2019

One out of many emerging implications from solutions of Einstein's general relativity equations are closed timelike curves (CTCs), which are trajectories through spacetime that loop back on…

Perfect State Distinguishability and Computational Speedups with Postselected Closed Timelike Curves

- Physics
- 2012

Bennett and Schumacher’s postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch’s model. We show that even a single…

Treating Time Travel Quantum Mechanically

- Physics
- 2014

The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this…

The Weakness of CTC Qubits and the Power of Approximate Counting

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2016

Results in structural complexity theory concerned with computation with postselection/restarting, closed timelike curves (CTCs), and approximate counting, and computational complexity of finding stationary distributions for quantum channels are presented.

Revisiting Consistency Conditions for Quantum States of Systems on Closed Timelike Curves: An Epistemic Perspective

- Philosophy
- 2012

There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use…

Quantum computation is the unique reversible circuit model for which bits are balls

- Physicsnpj Quantum Information
- 2019

The computational efficiency of quantum mechanics can be characterized in terms of the qubit circuit model, which is defined by a few simple properties: each computational gate is a reversible…

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