<i>Quantum Computation and Quantum Information</i>

Nielsen, Michael A.; Chuang, Isaac L.; Grover, Lov K.

doi:10.1119/1.1463744

Cited by 10,439 publications

(13,078 citation statements)

References 0 publications

Supporting

Mentioning

12,951

Contrasting

Unclassified

Order By: Relevance

“…The natural way to formulate such a model is by representing variables using higher dimensional subspaces while maintaining the incompatibility assumption. The price we pay for this increase in generality is that judgments are no longer represented by projection operators, but by the more general class of Positive Operator Valued Measures (POVMs; Nielsen & Chuang, 2000;Yearsley, in press;Busch, Grabowski, & Lahti, 1995). POVMs are a generic way to consider measurements on states which are embedded in a larger space.…”

Section: -Dimensional Povm Modelmentioning

confidence: 99%

A quantum probability framework for human probabilistic inference.

Trueblood

Yearsley

Pothos

2017

Journal of Experimental Psychology: General

View full text Add to dashboard Cite

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThere is considerable variety in human inference (e.g., a doctor inferring the presence of a disease, a juror inferring the guilt of a defendant, or someone inferring future weight loss based on diet and exercise). As such, people display a wide range of behaviors when making inference judgments.Sometimes, people's judgments appear Bayesian (i.e., normative), but in other cases, judgments deviate from the normative prescription of classical probability theory. How can we combine bothBayesian and non-Bayesian influences in a principled way? We propose a unified explanation of human inference using quantum probability theory. In our approach, we postulate a hierarchy of mental representations, from 'fully' quantum to 'fully' classical, which could be adopted in different situations. In our hierarchy of models, moving from the lowest level to the highest involves changing assumptions about compatibility (i.e., how joint events are represented). Using results from three experiments, we show that our modeling approach explains five key phenomena in human inference including order effects, reciprocity (i.e., the inverse fallacy), memorylessness, violations of the Markov condition, and anti-discounting. As far as we are aware, no existing theory or model can explain all five phenomena. We also explore transitions in our hierarchy, examining how representations change from more quantum to more classical. We show that classical representations provide a better account of data as individuals gain familiarity with a task.We also show that representations vary between individuals, in a way that relates to a simple measure of cognitive style, the Cognitive Reflection Test.Keywords: Human judgment, quantum probability theory, Bayes' rule, order effects, Markov condition A Quantum Framework for Probabilistic Inference 3 A Quantum Probability Framework for Human Probabilistic InferenceEveryday we face situations where we must make inferences about the world around us. For example, a doctor must determine the likelihood that a patient has a disease based on a set of symptoms. A juror must decide the probability that a defendant is guilty after hearing the cases made by the prosecution and defense. Or, maybe you want to judge the likelihood that you will weigh less next month if you start exercising more regularly and you improve your diet. In general, the inference problem involves judging the likelihood of some hypothesis (e.g., presence of a disease, guilt of a defendant, future weight loss) based on a series of evidence (e.g., medicalsymptoms, prosecution and defense cases, changes in your diet and exercise).Bayesian inference is widely accepted as the normative approach to inference. However, decades of research in human judgment and decision-making have suggested that people's judgments often violate the rules of Bayesian inference and classical probability theory (Tversky...

show abstract

Section: -Dimensional Povm Modelmentioning

confidence: 99%

A quantum probability framework for human probabilistic inference.

Trueblood

Yearsley

Pothos

2017

Journal of Experimental Psychology: General

View full text Add to dashboard Cite

show abstract

“…Later in the paper, we will set N = 2 as it will correspond to the case of qubits. For an introduction to quantum computing, we refer the reader to [NC00,KSV02].…”

Section: Notationmentioning

confidence: 99%

Self-testing of Quantum Circuits

Magniez

Mayers

Mosca

et al. 2006

Automata, Languages and Programming

View full text Add to dashboard Cite

We prove that a quantum circuit together with measurement apparatuses and EPR sources can be fully verified without any reference to some other trusted set of quantum devices. Our main assumption is that the physical system we are working with consists of several identifiable sub-systems, on which we can apply some given gates locally.To achieve our goal we define the notions of simulation and equivalence. The concept of simulation refers to producing the correct probabilities when measuring physical systems. To enable the efficient testing of the composition of quantum operations, we introduce the notion of equivalence. Unlike simulation, which refers to measured quantities (i.e., probabilities of outcomes), equivalence relates mathematical objects like states, subspaces or gates.Using these two concepts, we prove that if a system satisfies some simulation conditions, then it is equivalent to the one it is purposed to implement. In addition, with our formalism, we can show that these statements are robust, and the degree of robustness can be made explicit (unlike the robustness results of [DMMS00]). In particular, we also prove the robustness of the EPR Test [MY98]. Finally, we design a test for any quantum circuit whose complexity is linear in the number of gates and qubits, and polynomial in the required precision.

show abstract

“…Detailed descriptions of the quantum computation model can be found in [7,16,28,36]; here we outline only the basics using the terminology of quantum networks as presented in [5]. A quantum network is a quantum circuit (over some standard basis augmented with one oracle gate) which acts on an -bit quantum register; the computational basis states of this register are the binary strings of length A quantum network can be viewed as a sequence of unitary transformations where each is an arbitrary unitary transformation on qubits and each is a unitary transformation which corresponds to an oracle call.…”

Section: Quantum Computationmentioning

confidence: 99%