scholarly journals A Quantum interpretation of separating conjunction for local reasoning of Quantum programs based on separation logic

2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-27
Author(s):  
Xuan-Bach Le ◽  
Shang-Wei Lin ◽  
Jun Sun ◽  
David Sanan
Keyword(s):  
State Space ◽  
The State ◽  
Quantum States ◽  
Separation Logic ◽  
Grover’S Algorithm ◽  
State Space Explosion ◽  
Grover's Algorithm ◽  
Local Reasoning ◽  
Quantum Interpretation ◽  
Exponential Size

It is well-known that quantum programs are not only complicated to design but also challenging to verify because the quantum states can have exponential size and require sophisticated mathematics to encode and manipulate. To tackle the state-space explosion problem for quantum reasoning, we propose a Hoare-style inference framework that supports local reasoning for quantum programs. By providing a quantum interpretation of the separating conjunction, we are able to infuse separation logic into our framework and apply local reasoning using a quantum frame rule that is similar to the classical frame rule. For evaluation, we apply our framework to verify various quantum programs including Deutsch–Jozsa’s algorithm and Grover's algorithm.

scholarly journals CUMULATIVE MEASURE OF CORRELATION FOR MULTIPARTITE QUANTUM STATES

2014 ◽  
Vol 28 (07) ◽  
pp. 1450050 ◽  
Author(s):  
ANDRÉ L. FONSECA DE OLIVEIRA ◽  
EFRAIN BUKSMAN ◽  
JESÚS GARCÍA LÓPEZ DE LACALLE
Keyword(s):  
Phase Transitions ◽  
State Space ◽  
Present Article ◽  
Critical Points ◽  
Quantum Phase Transitions ◽  
The State ◽  
Quantum States ◽  
Quantum Phase ◽  
Mixed States ◽  
Different Dimensions

The present article proposes a measure of correlation for multiqubit mixed states. The measure is defined recursively, accumulating the correlation of the subspaces, making it simple to calculate without the use of regression. Unlike usual measures, the proposed measure is continuous additive and reflects the dimensionality of the state space, allowing to compare states with different dimensions. Examples show that the measure can signal critical points (CPs) in the analysis of Quantum Phase Transitions (QPTs) in Heisenberg models.

scholarly journals Efficient Temporal Planning Using Metastates

2019 ◽  
Vol 33 ◽  
pp. 7554-7561 ◽  
Author(s):  
Amanda Coles ◽  
Andrew Coles ◽  
J. Christopher Beck
Keyword(s):  
State Space ◽  
State Of The Art ◽  
The State ◽  
The Other ◽  
Temporal Constraints ◽  
State Space Explosion ◽  
Temporal Planning ◽  
State Space Search ◽  
Temporal Inconsistency

When performing temporal planning as forward state-space search, effective state memoisation is challenging. Whereas in classical planning, two states are equal if they have the same facts and variable values, in temporal planning this is not the case: as the plans that led to the two states are subject to temporal constraints, one might be extendable into at temporally valid plan, while the other might not. In this paper, we present an approach for reducing the state space explosion that arises due to having to keep many copies of the same ‘classically’ equal state – states that are classically equal are aggregated into metastates, and these are separated lazily only in the case of temporal inconsistency. Our evaluation shows that this approach, implemented in OPTIC and compared to existing state-of-the-art memoisation techniques, improves performance across a range of temporal domains.

scholarly journals Taming the State-space Explosion in the Makespan Optimization of Flexible Manufacturing Systems

2021 ◽  
Vol 5 (2) ◽  
pp. 1-26
Author(s):  
João Bastos ◽  
Jeroen Voeten ◽  
Sander Stuijk ◽  
Ramon Schiffelers ◽  
Henk Corporaal
Keyword(s):  
State Space ◽  
Flexible Manufacturing ◽  
Flexible Manufacturing Systems ◽  
Manufacturing Systems ◽  
The State ◽  
State Space Explosion

scholarly journals Specification guidelines to avoid the state space explosion problem

2014 ◽  
Vol 25 (1) ◽  
pp. 4-33 ◽  
Author(s):  
Jan Friso Groote ◽  
Tim W.D.M. Kouters ◽  
Ammar Osaiweran
Keyword(s):  
State Space ◽  
The State ◽  
State Space Explosion

scholarly journals A Quantum Circuit Design for Grover’s Algorithm

2002 ◽  
Vol 57 (8) ◽  
pp. 701-708 ◽  
Author(s):  
Zijian Diao ◽  
M. Suhail Zubairy ◽  
Goong Chen
Keyword(s):  
Circuit Design ◽  
Cavity Qed ◽  
Unitary Transformation ◽  
Quantum Circuit ◽  
The State ◽  
Quantum Phase ◽  
Grover’S Algorithm ◽  
Mathematical Proofs ◽  
Grover's Algorithm

We present a circuit design realizing Grover’s algorithm based on 1-bit unitary gates and 2-bit quantum phase gates implementable with cavity QED techniques. In the first step, we express the circuit block which performs a key unitary transformation that flips only the sign of the state |11 · · · 11〉 using 1-bit and 2-bit gates. The Grover’s iteration operator can then be constructed using this key unitary transformation twice, plus other operations involving only 1-bit unitary gates on each qubit. Mathematical proofs are given to justify that the cricuiting satisfies the desired operator properties.

STATE EVOLUTION AND INFORMATION PROCESSING IN Mn12 QUANTUM MAGNET

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2401-2408
Author(s):  
BIN ZHOU ◽  
RUIBAO TAO ◽  
SHUN-QING SHEN
Keyword(s):  
Information Processing ◽  
Intermediate State ◽  
The State ◽  
Quantum States ◽  
Molecular Magnets ◽  
Grover’S Algorithm ◽  
Dephasing Time ◽  
Quantum Magnet ◽  
State Evolution ◽  
Alternative Version

Following an alternative version of Grover's algorithm, we propose a scheme to read- in information in Mn 12 molecular magnets with the help of multi-frequency magnetic pulses in two separate steps: first to realize an intermediate state |Ψ(T1)> and then to reach the state |Ψ(T2)> to encode information. All controllable parameters are calculated to implement read-in of information, and the durations of magnetic pulses are less than the dephasing time of quantum states in Mn 12. It is also shown that all the states of information can be initialized back to the intermediate state.

scholarly journals Symbolic and Structural Model-Checking

2022 ◽  
Vol 183 (3-4) ◽  
pp. 319-342
Author(s):  
Yann Thierry-Mieg
Keyword(s):  
Model Checking ◽  
State Space ◽  
Structural Model ◽  
The State ◽  
Force Model ◽  
Deadlock Detection ◽  
Brute Force ◽  
General Applicability ◽  
State Space Explosion ◽  
Reachability Queries

Brute-force model-checking consists in exhaustive exploration of the state-space of a Petri net, and meets the dreaded state-space explosion problem. In contrast, this paper shows how to solve model-checking problems using a combination of techniques that stay in complexity proportional to the size of the net structure rather than to the state-space size. We combine an SMT based over-approximation to prove that some behaviors are unfeasible, an under-approximation using memory-less sampling of runs to find witness traces or counter-examples, and a set of structural reduction rules that can simplify both the system and the property. This approach was able to win by a clear margin the model-checking contest 2020 for reachability queries as well as deadlock detection, thus demonstrating the practical effectiveness and general applicability of the system of rules presented in this paper.

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