An algorithm of Ross and Selinger for the factorization of diagonal elements of PU(2) to within distance $varepsilon$ was adapted by Parzanchevski and Sarnak into an efficient probabilistic algorithm for any element of PU(2) using at most effective $3log_pfrac{1}{varepsilon^{3}}$ factors from certain well-chosen sets associated to a number field and a prime $p$. The icosahedral super golden gates are one such set associated to $mathbb{Q}(sqrt{5})$. We leverage recent work of Carvalho Pinto, Petit, and Stier to reduce this bound to $frac{7}{3}log_{59}frac{1}{varepsilon^3}$, and we implement the algorithm in Python. This represents an improvement by a multiplicative factor of $log_259approx5.9$ over the analogous result for the Clifford+$T$ gates. This is of interest because the icosahedral gates have shortest factorization lengths among all super golden gates.
{"title":"Fast naviation with icosahedral golden gates","authors":"Terrence R Blackman, Zachary Stier","doi":"10.26421/qic23.11-12-1","DOIUrl":"https://doi.org/10.26421/qic23.11-12-1","url":null,"abstract":"An algorithm of Ross and Selinger for the factorization of diagonal elements of PU(2) to within distance $varepsilon$ was adapted by Parzanchevski and Sarnak into an efficient probabilistic algorithm for any element of PU(2) using at most effective $3log_pfrac{1}{varepsilon^{3}}$ factors from certain well-chosen sets associated to a number field and a prime $p$. The icosahedral super golden gates are one such set associated to $mathbb{Q}(sqrt{5})$. We leverage recent work of Carvalho Pinto, Petit, and Stier to reduce this bound to $frac{7}{3}log_{59}frac{1}{varepsilon^3}$, and we implement the algorithm in Python. This represents an improvement by a multiplicative factor of $log_259approx5.9$ over the analogous result for the Clifford+$T$ gates. This is of interest because the icosahedral gates have shortest factorization lengths among all super golden gates.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135299889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We discuss how to implement quantum logic gates by considering a two-level-atom driven by a strong microwave field and successively interacting with m+1 cavity modes. The scheme is insensitive to the initial state of the atom, and the operation time is independent of the number of cavity modes involved in the system operations. This scheme is used to realize two quantum logic gates (m-target-qubit controlled-global-phase gate and Multi-qubit phase shift gate) in a time much shorter than the photonic lifetime. We also studied the influence of decoherence on the fidelity. In general, our system is reasonably less sensitive to the photonic and atomic decay rates and therefore it can be experimentally realized.
{"title":"Dynamics of one two-level-atom interacting with a multiple cavity modes","authors":"Taoufik Said, Abdelhaq Chouikh, Zoubida Sakhi, Mohamed Bennai","doi":"10.26421/qic23.11-12-2","DOIUrl":"https://doi.org/10.26421/qic23.11-12-2","url":null,"abstract":"We discuss how to implement quantum logic gates by considering a two-level-atom driven by a strong microwave field and successively interacting with m+1 cavity modes. The scheme is insensitive to the initial state of the atom, and the operation time is independent of the number of cavity modes involved in the system operations. This scheme is used to realize two quantum logic gates (m-target-qubit controlled-global-phase gate and Multi-qubit phase shift gate) in a time much shorter than the photonic lifetime. We also studied the influence of decoherence on the fidelity. In general, our system is reasonably less sensitive to the photonic and atomic decay rates and therefore it can be experimentally realized.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135299887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mirko Arienzo, Markus Heinrich, Ingo Roth, Martin Kliesch
Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables.We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.
{"title":"Closed-form analytic expressions for shadow estimation with brickwork circuits","authors":"Mirko Arienzo, Markus Heinrich, Ingo Roth, Martin Kliesch","doi":"10.26421/qic23.11-12-5","DOIUrl":"https://doi.org/10.26421/qic23.11-12-5","url":null,"abstract":"Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables.We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135299886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Six-state Quantum Key Distribution (QKD) achieves the highest key rate in the class of qubit-based QKD schemes. The standard security proof, which has been developed since 2005, invokes complicated theorems involving smooth R'{e}nyi entropies. In this paper we present a simpler security proof for 6-state QKD that entirely avoids R'{e}nyi entropies. This is achieved by applying state smoothing directly in the Bell basis. We obtain the well known asymptotic rate, but with slightly more favorable finite-size terms. We furthermore show that the same proof technique can be used for 6-state quantum key recycling.
{"title":"A simpler security proof for 6-state quantum key distribution","authors":"Kaan Akyuz, Boris Skoric","doi":"10.26421/qic23.11-12-4","DOIUrl":"https://doi.org/10.26421/qic23.11-12-4","url":null,"abstract":"Six-state Quantum Key Distribution (QKD) achieves the highest key rate in the class of qubit-based QKD schemes. The standard security proof, which has been developed since 2005, invokes complicated theorems involving smooth R'{e}nyi entropies. In this paper we present a simpler security proof for 6-state QKD that entirely avoids R'{e}nyi entropies. This is achieved by applying state smoothing directly in the Bell basis. We obtain the well known asymptotic rate, but with slightly more favorable finite-size terms. We furthermore show that the same proof technique can be used for 6-state quantum key recycling.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135299891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the quantum state control of a multi-state system which evolves an initial state into a target state. We explicitly demonstrate the control method in an interesting case involving the transfer and rotation of a Schr"{o}dinger cat state through a coupled harmonic oscillator chain at a predetermined time $T$. We use the gradient-based Krotov's method to design the time-dependent parameters of the coupled chain to find an optimal control shape that will evolve the system into a target state. We show that the prescribed quantum state control can be achieved with high fidelity, and the robustness of the control against generic environment noises is explored. Our findings will be of interest for the optimal control of a many-body open quantum system in the presence of environmental noise.
{"title":"Many-body quantum state control in the presence of environmental noise","authors":"Zara Yu, Da-Wei Luo","doi":"10.26421/qic23.11-12-3","DOIUrl":"https://doi.org/10.26421/qic23.11-12-3","url":null,"abstract":"We consider the quantum state control of a multi-state system which evolves an initial state into a target state. We explicitly demonstrate the control method in an interesting case involving the transfer and rotation of a Schr\"{o}dinger cat state through a coupled harmonic oscillator chain at a predetermined time $T$. We use the gradient-based Krotov's method to design the time-dependent parameters of the coupled chain to find an optimal control shape that will evolve the system into a target state. We show that the prescribed quantum state control can be achieved with high fidelity, and the robustness of the control against generic environment noises is explored. Our findings will be of interest for the optimal control of a many-body open quantum system in the presence of environmental noise.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135299890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mermin square scenario provides a simple proof for state-independent contextuality. In this paper, we study polytopes $MP_beta$ obtained from the Mermin scenario, parametrized by a function $beta$ on the set of contexts. Up to combinatorial isomorphism, there are two types of polytopes $MP_0$ and $MP_1$ depending on the parity of $beta$. Our main result is the classification of the vertices of these two polytopes. In addition, we describe the graph associated with the polytopes. All the vertices of $MP_0$ turn out to be deterministic. This result provides a new topological proof of a celebrated result of Fine characterizing noncontextual distributions on the CHSH scenario. $MP_1$ can be seen as a nonlocal toy version of $Lambda$-polytopes, a class of polytopes introduced for the simulation of universal quantum computation. In the $2$-qubit case, we provide a decomposition of the $Lambda$-polytope using $MP_1$, whose vertices are classified, and the nonsignaling polytope of the $(2,3,2)$ Bell scenario, whose vertices are well-known.
{"title":"Mermin polytopes quantum computation and foundations","authors":"Cihan Okay, Ho Yiu Chung, Selman Ipek","doi":"10.26421/qic23.9-10-2","DOIUrl":"https://doi.org/10.26421/qic23.9-10-2","url":null,"abstract":"Mermin square scenario provides a simple proof for state-independent contextuality. In this paper, we study polytopes $MP_beta$ obtained from the Mermin scenario, parametrized by a function $beta$ on the set of contexts. Up to combinatorial isomorphism, there are two types of polytopes $MP_0$ and $MP_1$ depending on the parity of $beta$. Our main result is the classification of the vertices of these two polytopes. In addition, we describe the graph associated with the polytopes. All the vertices of $MP_0$ turn out to be deterministic. This result provides a new topological proof of a celebrated result of Fine characterizing noncontextual distributions on the CHSH scenario. $MP_1$ can be seen as a nonlocal toy version of $Lambda$-polytopes, a class of polytopes introduced for the simulation of universal quantum computation. In the $2$-qubit case, we provide a decomposition of the $Lambda$-polytope using $MP_1$, whose vertices are classified, and the nonsignaling polytope of the $(2,3,2)$ Bell scenario, whose vertices are well-known.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135509415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter et al. obtained a finite yet systematic classification of multi-particle entanglement. It is well known that under SLOCC, pure states of three (four) qubits are partitioned into six (nine) families. Ac'{i}n et al. proposed the generalized Schmidt decomposition for three qubits and partitioned pure states of three qubits into five types. In this paper,we present a LU invariant and an entanglement measures for the GHZ SLOCC class of three qubits, and partition states of the GHZ SLOCC class of three qubits into ten families and each family into two subfamilies under LU. We give a necessary and sufficient condition for the uniqueness of the generalized Schmidt decomposition for the GHZ SLOCC class.
{"title":"Partition GHZ SLOCC class of three qubits into ten families under LU","authors":"Dafa Li","doi":"10.26421/qic23.5-6-3","DOIUrl":"https://doi.org/10.26421/qic23.5-6-3","url":null,"abstract":"In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter et al. obtained a finite yet systematic classification of multi-particle entanglement. It is well known that under SLOCC, pure states of three (four) qubits are partitioned into six (nine) families. Ac'{i}n et al. proposed the generalized Schmidt decomposition for three qubits and partitioned pure states of three qubits into five types. In this paper,we present a LU invariant and an entanglement measures for the GHZ SLOCC class of three qubits, and partition states of the GHZ SLOCC class of three qubits into ten families and each family into two subfamilies under LU. We give a necessary and sufficient condition for the uniqueness of the generalized Schmidt decomposition for the GHZ SLOCC class.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135672132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.1017/9781108782081.013
Travis B. Russell
We show that Connes’ embedding problem is equivalent to the weak Tsirelson problem in the setting of two-outcome synchronous correlation sets. We further show that the extreme points of two-outcome synchronous correlation sets can be realized using a certain class of universal C*-algebras. We examine these algebras in the three-experiment case and verify that the strong and weak Tsirelson problems have affirmative answers in that setting.
{"title":"The Connes embedding problem","authors":"Travis B. Russell","doi":"10.1017/9781108782081.013","DOIUrl":"https://doi.org/10.1017/9781108782081.013","url":null,"abstract":"We show that Connes’ embedding problem is equivalent to the weak Tsirelson problem in the setting of two-outcome synchronous correlation sets. We further show that the extreme points of two-outcome synchronous correlation sets can be realized using a certain class of universal C*-algebras. We examine these algebras in the three-experiment case and verify that the strong and weak Tsirelson problems have affirmative answers in that setting.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"20 1","pages":"361-374"},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/9781108782081.013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56926398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Radial basis function (RBF) network is a simple but useful neural network model that contains wide applications in machine learning. The training of an RBF network reduces to solve a linear system,...
{"title":"Quantum speedup of training radial basis function networks","authors":"ShaoChangpeng","doi":"10.5555/3370207.3370213","DOIUrl":"https://doi.org/10.5555/3370207.3370213","url":null,"abstract":"Radial basis function (RBF) network is a simple but useful neural network model that contains wide applications in machine learning. The training of an RBF network reduces to solve a linear system,...","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45062773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quantum walks determined by the coin operator on graphs have been intensively studied. The typical examples of coin operator are the Grover and Fourier matrices. The periodicity of the Grover walk ...
{"title":"Periodicity for the fourier quantum walk on regular graphs","authors":"SaitoKei","doi":"10.5555/3370239.3370242","DOIUrl":"https://doi.org/10.5555/3370239.3370242","url":null,"abstract":"Quantum walks determined by the coin operator on graphs have been intensively studied. The typical examples of coin operator are the Grover and Fourier matrices. The periodicity of the Grover walk ...","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42785329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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