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Theory of Quantum Computation, Communication, and Cryptography最新文献

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Quantum Algorithm for Path-Edge Sampling 路径边缘采样的量子算法
Theory of Quantum Computation, Communication, and Cryptography Pub Date : 2023-03-06 DOI: 10.4230/LIPIcs.TQC.2023.5
S. Jeffery, S. Kimmel, Alvaro Piedrafita
{"title":"Quantum Algorithm for Path-Edge Sampling","authors":"S. Jeffery, S. Kimmel, Alvaro Piedrafita","doi":"10.4230/LIPIcs.TQC.2023.5","DOIUrl":"https://doi.org/10.4230/LIPIcs.TQC.2023.5","url":null,"abstract":"We present a quantum algorithm for sampling an edge on a path between two nodes s and t in an undirected graph given as an adjacency matrix, and show that this can be done in query complexity that is asymptotically the same, up to log factors, as the query complexity of detecting a path between s and t. We use this path sampling algorithm as a subroutine for st-path finding and st-cut-set finding algorithms in some specific cases. Our main technical contribution is an algorithm for generating a quantum state that is proportional to the positive witness vector of a span program.","PeriodicalId":312784,"journal":{"name":"Theory of Quantum Computation, Communication, and Cryptography","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128483415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Local Hamiltonians with no low-energy stabilizer states 没有低能稳定态的局部哈密顿量
Theory of Quantum Computation, Communication, and Cryptography Pub Date : 2023-02-28 DOI: 10.4230/LIPIcs.TQC.2023.14
Nolan J. Coble, Matthew Coudron, J. Nelson, Seyed Sajjad Nezhadi
{"title":"Local Hamiltonians with no low-energy stabilizer states","authors":"Nolan J. Coble, Matthew Coudron, J. Nelson, Seyed Sajjad Nezhadi","doi":"10.4230/LIPIcs.TQC.2023.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.TQC.2023.14","url":null,"abstract":"The recently-defined No Low-energy Sampleable States (NLSS) conjecture of Gharibian and Le Gall [GL22] posits the existence of a family of local Hamiltonians where all states of low-enough constant energy do not have succinct representations allowing perfect sampling access. States that can be prepared using only Clifford gates (i.e. stabilizer states) are an example of sampleable states, so the NLSS conjecture implies the existence of local Hamiltonians whose low-energy space contains no stabilizer states. We describe families that exhibit this requisite property via a simple alteration to local Hamiltonians corresponding to CSS codes. Our method can also be applied to the recent NLTS Hamiltonians of Anshu, Breuckmann, and Nirkhe [ABN22], resulting in a family of local Hamiltonians whose low-energy space contains neither stabilizer states nor trivial states. We hope that our techniques will eventually be helpful for constructing Hamiltonians which simultaneously satisfy NLSS and NLTS.","PeriodicalId":312784,"journal":{"name":"Theory of Quantum Computation, Communication, and Cryptography","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125476167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Improved Algorithm and Lower Bound for Variable Time Quantum Search 变时间量子搜索的改进算法及下界
Theory of Quantum Computation, Communication, and Cryptography Pub Date : 2023-02-13 DOI: 10.4230/LIPIcs.TQC.2023.7
A. Ambainis, M. Kokainis, J. Vihrovs
{"title":"Improved Algorithm and Lower Bound for Variable Time Quantum Search","authors":"A. Ambainis, M. Kokainis, J. Vihrovs","doi":"10.4230/LIPIcs.TQC.2023.7","DOIUrl":"https://doi.org/10.4230/LIPIcs.TQC.2023.7","url":null,"abstract":"We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(sqrt{T}log n)$ where $T=sum_{i=1}^n t_i^2$ with $t_i$ denoting the time to check the $i$-th item. Our second result is a quantum lower bound of $Omega(sqrt{Tlog T})$. Both the algorithm and the lower bound improve over previously known results by a factor of $sqrt{log T}$ but the algorithm is also substantially simpler than the previously known quantum algorithms.","PeriodicalId":312784,"journal":{"name":"Theory of Quantum Computation, Communication, and Cryptography","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116941783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians 稀疏哈密顿算子极值特征值的改进逼近
Theory of Quantum Computation, Communication, and Cryptography Pub Date : 2023-01-11 DOI: 10.4230/LIPIcs.TQC.2023.6
Daniel Hothem, Ojas D. Parekh, K. Thompson
{"title":"Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians","authors":"Daniel Hothem, Ojas D. Parekh, K. Thompson","doi":"10.4230/LIPIcs.TQC.2023.6","DOIUrl":"https://doi.org/10.4230/LIPIcs.TQC.2023.6","url":null,"abstract":"We give a classical $1/(qk+1)$-approximation for the maximum eigenvalue of a $k$-sparse fermionic Hamiltonian with strictly $q$-local terms, as well as a $1/(4k+1)$-approximation when the Hamiltonian has both $2$-local and $4$-local terms. More generally we obtain a $1/O(qk^2)$-approximation for $k$-sparse fermionic Hamiltonians with terms of locality at most $q$. Our techniques also yield analogous approximations for $k$-sparse, $q$-local qubit Hamiltonians with small hidden constants and improved dependence on $q$.","PeriodicalId":312784,"journal":{"name":"Theory of Quantum Computation, Communication, and Cryptography","volume":"50 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120847994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Quantum policy gradient algorithms 量子策略梯度算法
Theory of Quantum Computation, Communication, and Cryptography Pub Date : 2022-12-19 DOI: 10.4230/LIPIcs.TQC.2023.13
Sofiène Jerbi, A. Cornelissen, M. Ozols, V. Dunjko
{"title":"Quantum policy gradient algorithms","authors":"Sofiène Jerbi, A. Cornelissen, M. Ozols, V. Dunjko","doi":"10.4230/LIPIcs.TQC.2023.13","DOIUrl":"https://doi.org/10.4230/LIPIcs.TQC.2023.13","url":null,"abstract":"Understanding the power and limitations of quantum access to data in machine learning tasks is primordial to assess the potential of quantum computing in artificial intelligence. Previous works have already shown that speed-ups in learning are possible when given quantum access to reinforcement learning environments. Yet, the applicability of quantum algorithms in this setting remains very limited, notably in environments with large state and action spaces. In this work, we design quantum algorithms to train state-of-the-art reinforcement learning policies by exploiting quantum interactions with an environment. However, these algorithms only offer full quadratic speed-ups in sample complexity over their classical analogs when the trained policies satisfy some regularity conditions. Interestingly, we find that reinforcement learning policies derived from parametrized quantum circuits are well-behaved with respect to these conditions, which showcases the benefit of a fully-quantum reinforcement learning framework.","PeriodicalId":312784,"journal":{"name":"Theory of Quantum Computation, Communication, and Cryptography","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133567479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection 可倒卷量子计算及其与克隆和自适应后选择的等价性
Theory of Quantum Computation, Communication, and Cryptography Pub Date : 2022-06-11 DOI: 10.48550/arXiv.2206.05434
Ryo Hiromasa, Akihiro Mizutani, Yuki Takeuchi, S. Tani
{"title":"Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection","authors":"Ryo Hiromasa, Akihiro Mizutani, Yuki Takeuchi, S. Tani","doi":"10.48550/arXiv.2206.05434","DOIUrl":"https://doi.org/10.48550/arXiv.2206.05434","url":null,"abstract":"We define rewinding operators that invert quantum measurements. Then, we define complexity classes ${sf RwBQP}$, ${sf CBQP}$, and ${sf AdPostBQP}$ as sets of decision problems solvable by polynomial-size quantum circuits with a polynomial number of rewinding operators, cloning operators, and adaptive postselections, respectively. Our main result is that ${sf BPP}^{sf PP}subseteq{sf RwBQP}={sf CBQP}={sf AdPostBQP}subseteq{sf PSPACE}$. As a byproduct of this result, we show that any problem in ${sf PostBQP}$ can be solved with only postselections of outputs whose probabilities are polynomially close to one. Under the strongly believed assumption that ${sf BQP}nsupseteq{sf SZK}$, or the shortest independent vectors problem cannot be efficiently solved with quantum computers, we also show that a single rewinding operator is sufficient to achieve tasks that are intractable for quantum computation. In addition, we consider rewindable Clifford and instantaneous quantum polynomial time circuits.","PeriodicalId":312784,"journal":{"name":"Theory of Quantum Computation, Communication, and Cryptography","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117212391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On converses to the polynomial method 与多项式方法相反
Theory of Quantum Computation, Communication, and Cryptography Pub Date : 2022-04-26 DOI: 10.48550/arXiv.2204.12303
J. Briët, F. Guti'errez
{"title":"On converses to the polynomial method","authors":"J. Briët, F. Guti'errez","doi":"10.48550/arXiv.2204.12303","DOIUrl":"https://doi.org/10.48550/arXiv.2204.12303","url":null,"abstract":"A surprising “converse to the polynomial method” of Aaronson et al. (CCC’16) shows that any bounded quadratic polynomial can be computed exactly in expectation by a 1-query algorithm up to a universal multiplicative factor related to the famous Grothendieck constant. A natural question posed there asks if bounded quartic polynomials can be approximated by 2-query quantum algorithms. Arunachalam, Palazuelos and the first author showed that there is no direct analogue of the result of Aaronson et al. in this case. We improve on this result in the following ways: First, we point out and fix a small error in the construction that has to do with a translation from cubic to quartic polynomials. Second, we give a completely explicit example based on techniques from additive combinatorics. Third, we show that the result still holds when we allow for a small additive error. For this, we apply an SDP characterization of Gribling and Laurent (QIP’19) for the completely-bounded approximate degree. Arunachalam, Sander Gribling and Carlos Palazuelos for useful discussions. We also want to thank the referees of TQC for their helpful comments.","PeriodicalId":312784,"journal":{"name":"Theory of Quantum Computation, Communication, and Cryptography","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121096420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A Constant Lower Bound for Any Quantum Protocol for Secure Function Evaluation 用于安全函数评估的任意量子协议的常数下界
Theory of Quantum Computation, Communication, and Cryptography Pub Date : 2022-03-15 DOI: 10.4230/LIPIcs.TQC.2022.8
Sarah Osborn, Jamie Sikora
{"title":"A Constant Lower Bound for Any Quantum Protocol for Secure Function Evaluation","authors":"Sarah Osborn, Jamie Sikora","doi":"10.4230/LIPIcs.TQC.2022.8","DOIUrl":"https://doi.org/10.4230/LIPIcs.TQC.2022.8","url":null,"abstract":"Secure function evaluation is a two-party cryptographic primitive where Bob computes a function of Alice's and his respective inputs, and both hope to keep their inputs private from the other party. It has been proven that perfect (or near perfect) security is impossible, even for quantum protocols. We generalize this no-go result by exhibiting a constant lower bound on the cheating probabilities for any quantum protocol for secure function evaluation, and present many applications from oblivious transfer to the millionaire's problem. Constant lower bounds are of practical interest since they imply the impossibility to arbitrarily amplify the security of quantum protocols by any means.","PeriodicalId":312784,"journal":{"name":"Theory of Quantum Computation, Communication, and Cryptography","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132895740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Memory Compression with Quantum Random-Access Gates 基于量子随机存取门的内存压缩
Theory of Quantum Computation, Communication, and Cryptography Pub Date : 2022-03-10 DOI: 10.4230/LIPIcs.TQC.2022.10
H. Buhrman, B. Loff, Subhasree Patro, F. Speelman
{"title":"Memory Compression with Quantum Random-Access Gates","authors":"H. Buhrman, B. Loff, Subhasree Patro, F. Speelman","doi":"10.4230/LIPIcs.TQC.2022.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.TQC.2022.10","url":null,"abstract":"In the classical RAM, we have the following useful property. If we have an algorithm that uses $M$ memory cells throughout its execution, and in addition is sparse, in the sense that, at any point in time, only $m$ out of $M$ cells will be non-zero, then we may\"compress\"it into another algorithm which uses only $m log M$ memory and runs in almost the same time. We may do so by simulating the memory using either a hash table, or a self-balancing tree. We show an analogous result for quantum algorithms equipped with quantum random-access gates. If we have a quantum algorithm that runs in time $T$ and uses $M$ qubits, such that the state of the memory, at any time step, is supported on computational-basis vectors of Hamming weight at most $m$, then it can be simulated by another algorithm which uses only $O(m log M)$ memory, and runs in time $tilde O(T)$. We show how this theorem can be used, in a black-box way, to simplify the presentation in several papers. Broadly speaking, when there exists a need for a space-efficient history-independent quantum data-structure, it is often possible to construct a space-inefficient, yet sparse, quantum data structure, and then appeal to our main theorem. This results in simpler and shorter arguments.","PeriodicalId":312784,"journal":{"name":"Theory of Quantum Computation, Communication, and Cryptography","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121382603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Qutrit Metaplectic Gates Are a Subset of Clifford+T Qutrit元塑性门是Clifford+T的子集
Theory of Quantum Computation, Communication, and Cryptography Pub Date : 2022-02-18 DOI: 10.4230/LIPIcs.TQC.2022.12
A. Glaudell, N. J. Ross, J. V. D. Wetering, L. Yeh
{"title":"Qutrit Metaplectic Gates Are a Subset of Clifford+T","authors":"A. Glaudell, N. J. Ross, J. V. D. Wetering, L. Yeh","doi":"10.4230/LIPIcs.TQC.2022.12","DOIUrl":"https://doi.org/10.4230/LIPIcs.TQC.2022.12","url":null,"abstract":"A popular universal gate set for quantum computing with qubits is Clifford+T, as this can be readily implemented on many fault-tolerant architectures. For qutrits, there is an equivalent T gate, that, like its qubit analogue, makes Clifford+T approximately universal, is injectable by a magic state, and supports magic state distillation. However, it was claimed that a better gate set for qutrits might be Clifford+R, where R=diag(1,1,-1) is the metaplectic gate, as certain protocols and gates could more easily be implemented using the R gate than the T gate. In this paper we show that when we have at least two qutrits, the qutrit Clifford+R unitaries form a strict subset of the Clifford+T unitaries, by finding a direct decomposition of $R otimes mathbb{I}$ as a Clifford+T circuit and proving that the T gate cannot be exactly synthesized in Clifford+R. This shows that in fact the T gate is at least as powerful as the R gate, up to a constant factor. Moreover, we additionally show that it is impossible to find a single-qutrit Clifford+T decomposition of the R gate, making our result tight.","PeriodicalId":312784,"journal":{"name":"Theory of Quantum Computation, Communication, and Cryptography","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129878923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
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