arXiv subjects

Seiichiro Tani

Publications and source records attributed to Seiichiro Tani.

At least 19 recordsLinked to original sources

arXiv2026

Anonymous quantum sensing robust against state preparation errors

Networked quantum sensors have several applications such as the mapping of magnetic fields. When the magnetic fields are biomagnetic ones, i.e., they contain some private information, the information of from who non-zero magnetic fields occur has to be protected from eavesdroppers. Anonymous quantum sensing keeps it secret by estimating amplitudes of the magnetic fields without disclosing the positions of non-zero magnetic fields. In this paper, we propose an anonymous quantum sensing protocol that is robust against any independent noise in state preparations. To this end, we devise a quantum state verification protocol for a superposition of Greenberger-Horne-Zeilinger and Dicke states and combine it with the original protocol of anonymous quantum sensing. Our verification protocol can decide whether the fidelity between the ideal and actual states is high or low more efficiently than the direct fidelity estimation. Since the original protocol of anonymous quantum sensing cannot correctly estimate the amplitudes of the magnetic fields under state preparation errors, our results would improve the performance of anonymous quantum sensing in realistic situations.

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arXiv2025

Approximate Degrees of Multisymmetric Properties with Application to Quantum Claw Detection

The claw problem is central in the fields of theoretical computer science as well as cryptography. The optimal quantum query complexity of the problem is known to be $Ω\left(\sqrt{G}+(FG)^{1/3} \right)$ for input functions $f\colon [F]\to Z$ and $g\colon [G]\to Z$. However, the lower bound was proved when the range $Z$ is sufficiently large (i.e., $|{Z}|=Ω(FG)$). The current paper proves the lower bound holds even for every smaller range $Z$ with $|{Z}|\ge F+G$. This implies that $Ω\left(\sqrt{G}+(FG)^{1/3} \right)$ is tight for every such range. In addition, the lower bound $Ω\left(\sqrt{G}+F^{1/3}G^{1/6}M^{1/6}\right)$ is provided for even smaller range $Z=[M]$ with every $M\in [2,F+G]$ by reducing the claw problem for $|{Z}|= F+G$. The proof technique is general enough to apply to any $k$-symmetric property (e.g., the $k$-claw problem), i.e., the Boolean function $Φ$ on the set of $k$ functions with different-size domains and a common range such that $Φ$ is invariant under the permutations over each domain and the permutations over the range. More concretely, it generalizes Ambainis's argument [Theory of Computing, 1(1):37-46] to the multiple-function case by using the notion of multisymmetric polynomials.

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arXiv2025

Quantum algorithm for unstructured search of ranked targets

Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple marked items, Grover's algorithm has the property of finding one of them uniformly at random. To further broaden the application range, it was generalized so that it finds marked items with probabilities according to their priority by encoding the priority into amplitudes applied by Grover's oracle operator. In this paper, to achieve a similar generalization, we examine a different encoding that incorporates the priority into phases applied by the oracle operator. We compare the previous and our oracle operators and observe that which one performs better depends on priority parameters. Since the priority parameters can be considered as the magnitude of the correlated phase error on Grover's oracle operator, the analysis of our oracle operator also reveals the robustness of the original Grover's algorithm against correlated noises. We further numerically show that the coherence between multiple marked items tends to increase the probability of finding the most prioritized one in Grover's algorithm with our oracle operator.

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arXiv2025

Quantum Algorithm for Finding the Optimal Variable Ordering for Binary Decision Diagrams

An ordered binary decision diagram (OBDD) is a directed acyclic graph that represents a Boolean function. OBDDs are also known as special cases of oblivious read-once branching programs in the field of complexity theory. Since OBDDs have many nice properties as data structures, they have been extensively studied for decades in both theoretical and practical fields, such as VLSI design, formal verification, machine learning, and combinatorial problems. Arguably, the most crucial problem in using OBDDs is that they may vary exponentially in size depending on their variable ordering (i.e., the order in which the variable are to read) when they represent the same function. Indeed, it is NP hard to find an optimal variable ordering that minimizes an OBDD for a given function. Hence, numerous studies have sought heuristics to find an optimal variable ordering. From practical as well as theoretical points of view, it is also important to seek algorithms that output optimal solutions with lower (exponential) time complexity than trivial brute-force algorithms do. Friedman and Supowit provided a clever deterministic algorithm with time/space complexity $O^\ast(3^n)$, where $n$ is the number of variables of the function, which is much better than the trivial brute-force bound $O^\ast(n!2^n)$. This paper shows that a further speedup is possible with quantum computers by demonstrating the existence of a quantum algorithm that produces a minimum OBDD together with the corresponding variable ordering in $O^\ast(2.77286^n)$ time and space with an exponentially small error. Moreover, this algorithm can be adapted to constructing other minimum decision diagrams such as zero-suppressed BDDs, which provide compact representations of sparse sets and are often used in the field of discrete optimization and enumeration.

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arXiv2025

Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection

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 events that occur with probabilities 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. Finally, we show that rewindable Clifford circuits remain classically simulatable, but rewindable instantaneous quantum polynomial time circuits can solve any problem in ${\sf PP}$.

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arXiv2024

Probabilistic unitary synthesis with optimal accuracy

The purpose of unitary synthesis is to find a gate sequence that optimally approximates a target unitary transformation. A new synthesis approach, called probabilistic synthesis, has been introduced, and its superiority has been demonstrated over traditional deterministic approaches with respect to approximation error and gate length. However, the optimality of current probabilistic synthesis algorithms is unknown. We obtain the tight lower bound on the approximation error obtained by the optimal probabilistic synthesis, which guarantees the sub-optimality of current algorithms. We also show its tight upper bound, which improves and unifies current upper bounds depending on the class of target unitaries. These two bounds reveal the fundamental relationship of approximation error between probabilistic approximation and deterministic approximation of unitary transformations. From a computational point of view, we show that the optimal probability distribution can be computed by the semidefinite program (SDP) we construct. We also construct an efficient probabilistic synthesis algorithm for single-qubit unitaries, rigorously estimate its time complexity, and show that it reduces the approximation error quadratically compared with deterministic algorithms.

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arXiv2024

On the hardness of conversion from entangled proof into separable one

A quantum channel whose image approximates the set of separable states is called a disentangler, which plays a prominent role in the investigation of variants of the computational model called Quantum Merlin Arthur games, and has potential applications in classical and quantum algorithms for the separability testing and NP-complete problems. So far, two types of a disentangler, constructed based on $ε$-nets and the quantum de Finetti theorem, have been known; however, both of them require an exponentially large input system. Moreover, in 2008, John Watrous conjectured that any disentangler requires an exponentially large input system, called the disentangler conjecture. In this paper, we show that both of the two known disentanglers can be regarded as examples of a strong disentangler, which is a disentangler approximately breaking entanglement between one output system and the composite system of another output system and the arbitrarily large environment. Note that the strong disentangler is essentially an approximately entanglement-breaking channel while the original disentangler is an approximately entanglement-annihilating channel, and the set of strong disentanglers is a subset of disentanglers. As a main result, we show that the disentangler conjecture is true for this subset, the set of strong disentanglers, for a wide range of approximation parameters without any computational hardness assumptions.

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arXiv2024

Probabilistic state synthesis based on optimal convex approximation

When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the circuit is probabilistically sampled, is able to reduce the approximation error compared to conventional deterministic synthesis. In this paper, we demonstrate that the optimal probabilistic synthesis quadratically reduces the approximation error. Moreover, we show that a deterministic synthesis algorithm can be efficiently converted into a probabilistic one that achieves this quadratic error reduction. We also numerically demonstrate how this conversion reduces the $T$-count and analytically prove that this conversion halves an information-theoretic lower bound on the circuit size. In order to derive these results, we prove general theorems about the optimal convex approximation of a quantum state. Furthermore, we demonstrate that this theorem can be used to analyze an entanglement measure.

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arXiv2022

Space-Bounded Unitary Quantum Computation with Postselection

Space-bounded computation has been a central topic in classical and quantum complexity theory. In the quantum case, every elementary gate must be unitary. This restriction makes it unclear whether the power of space-bounded computation changes by allowing intermediate measurement. In the bounded error case, Fefferman and Remscrim [STOC 2021, pp.1343--1356] and Girish, Raz and Zhan~[ICALP 2021, pp.73:1--73:20] recently provided the break-through results that the power does not change. This paper shows that a similar result holds for space-bounded quantum computation with postselection. Namely, it is proved possible to eliminate intermediate postselections and measurements in the space-bounded quantum computation in the bounded-error setting. Our result strengthens the recent result by Le Gall, Nishimura and Yakaryilmaz~[TQC 2021, pp.10:1--10:17] that logarithmic-space bounded-error quantum computation with intermediate postselections and measurements is equivalent in computational power to logarithmic-space unbounded-error probabilistic computation. As an application, it is shown that bounded-error space-bounded one-clean qubit computation (DQC1) with postselection is equivalent in computational power to unbounded-error space-bounded probabilistic computation, and the computational supremacy of the bounded-error space-bounded DQC1 is interpreted in complexity-theoretic terms.

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arXiv2022

Computational self-testing for entangled magic states

In the seminal paper [Metger and Vidick, Quantum '21], they proposed a computational self-testing protocol for Bell states in a single quantum device. Their protocol relies on the fact that the target states are stabilizer states, and hence it is highly non-trivial to reveal whether the other class of quantum states, non-stabilizer states, can be self-tested within their framework. Among non-stabilizer states, magic states are indispensable resources for universal quantum computation. In this letter, we show that a magic state for the CCZ gate can be self-tested while that for the T gate cannot. Our result is applicable to a proof of quantumness, where we can classically verify whether a quantum device generates a quantum state having non-zero magic.

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arXiv2022

Sumcheck-based delegation of quantum computing to rational server

Delegated quantum computing enables a client with weak computational power to delegate quantum computing to a remote quantum server in such a way that the integrity of the server can be efficiently verified by the client. Recently, a new model of delegated quantum computing has been proposed, namely, rational delegated quantum computing. In this model, after the client interacts with the server, the client pays a reward to the server. The rational server sends messages that maximize the expected value of the reward. It is known that the classical client can delegate universal quantum computing to the rational quantum server in one round. In this paper, we propose novel one-round rational delegated quantum computing protocols by generalizing the classical rational sumcheck protocol. The construction of the previous rational protocols depends on gate sets, while our sumcheck technique can be easily realized with any local gate set. Furthermore, as with the previous protocols, our reward function satisfies natural requirements. We also discuss the reward gap. Simply speaking, the reward gap is a minimum loss on the expected value of the server's reward incurred by the server's behavior that makes the client accept an incorrect answer. Although our sumcheck-based protocols have only exponentially small reward gaps as in the previous protocols, we show that a constant reward gap can be achieved if two noncommunicating but entangled rational servers are allowed. We also discuss whether a single rational server is sufficient under the (widely believed) assumption that the learning-with-errors problem is hard for polynomial-time quantum computing. Apart from these results, we show, under a certain condition, the equivalence between $rational$ and $ordinary$ delegated quantum computing protocols. This equivalence then serves as a basis for a reward-gap amplification method.

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arXiv2022

Divide-and-conquer verification method for noisy intermediate-scale quantum computation

Several noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate-scale quantum computation. To this end, we first characterize small-scale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity $\langleψ_t|\hatρ_{\rm out}|ψ_t\rangle$ between an actual $n$-qubit output state $\hatρ_{\rm out}$ obtained from the noisy intermediate-scale quantum computation and the ideal output state (i.e., the target state) $|ψ_t\rangle$. Although the direct fidelity estimation method requires $O(2^n)$ copies of $\hatρ_{\rm out}$ on average, our method requires only $O(D^32^{12D})$ copies even in the worst case, where $D$ is the denseness of $|ψ_t\rangle$. For logarithmic-depth quantum circuits on a sparse chip, $D$ is at most $O(\log{n})$, and thus $O(D^32^{12D})$ is a polynomial in $n$. By using the IBM Manila 5-qubit chip, we also perform a proof-of-principle experiment to observe the practical performance of our method.

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arXiv2022

Quadratic improvement on accuracy of approximating pure quantum states and unitary gates by probabilistic implementation

Pure quantum states are often approximately encoded as classical bit strings such as those representing probability amplitudes and those describing circuits that generate the quantum states. The crucial quantity is the minimum length of classical bit strings from which the original pure states are approximately reconstructible. We derive asymptotically tight bounds on the minimum bit length required for probabilistic encodings with which one can approximately reconstruct the original pure state as an ensemble of the quantum states encoded in classical strings. We also show that such a probabilistic encoding asymptotically halves the bit length required for "deterministic" ones. This is based on the fact that the accuracy of approximating pure states by using a given subset of pure states can be increased quadratically if we use ensembles of pure states in the subset. Moreover, we show that a similar fact holds when we consider the approximation of unitary gates by using a given subset of unitary gates. This improves the reduction rate of the circuit size by using probabilistic circuit synthesis compared to previous results. This also demonstrates that the reduction is possible even for low-accuracy circuit synthesis, which might improve the accuracy of various NISQ algorithms.

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arXiv2021

Hardness of efficiently generating ground states in postselected quantum computation

Generating ground states of any local Hamiltonians seems to be impossible in quantum polynomial time. In this paper, we give evidence for the impossibility by applying an argument used in the quantum-computational-supremacy approach. More precisely, we show that if ground states of any $3$-local Hamiltonians can be approximately generated in quantum polynomial time with postselection, then ${\sf PP}={\sf PSPACE}$. Our result is superior to the existing findings in the sense that we reduce the impossibility to an unlikely relation between classical complexity classes. We also discuss what makes efficiently generating the ground states hard for postselected quantum computation.

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arXiv2020

Polylog-overhead highly fault-tolerant measurement-based quantum computation: all-Gaussian implementation with Gottesman-Kitaev-Preskill code

Scalability of flying photonic quantum systems in generating quantum entanglement offers a potential for implementing large-scale fault-tolerant quantum computation, especially by means of measurement-based quantum computation (MBQC). However, existing protocols for MBQC inevitably impose a polynomial overhead cost in implementing quantum computation due to geometrical constraints of entanglement structures used in the protocols, and the polynomial overhead potentially cancels out useful polynomial speedups in quantum computation. To implement quantum computation without this cancellation, we construct a protocol for photonic MBQC that achieves as low as poly-logarithmic overhead, by introducing an entanglement structure for low-overhead qubit permutation. Based on this protocol, we design a fault-tolerant photonic MBQC protocol that can be performed by experimentally tractable homodyne detection and Gaussian entangling operations combined with the Gottesman-Kitaev-Preskill (GKP) quantum error-correcting code, which we concatenate with the $7$-qubit code. Our fault-tolerant protocol achieves the threshold $7.8$ dB in terms of the squeezing level of the GKP code, outperforming $8.3$ dB of the best existing protocol for fault-tolerant quantum computation with the GKP surface code. Thus, bridging a gap between theoretical progress on MBQC and photonic experiments towards implementing MBQC, our results open a new way towards realization of a large class of quantum speedups including those polynomial.

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arXiv2020

Classically Simulating Quantum Circuits with Local Depolarizing Noise

We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small constant rate is applied to each qubit at the end of computation. We show that, under this noise model, if an approximate value of the noise rate is known, any CT-ECS circuit with an anti-concentrated output probability distribution is classically simulatable. This indicates that the presence of small noise drastically affects the classical simulatability of CT-ECS circuits. Then, we consider an extension of the noise model where the noise rate can vary with each qubit, and provide a similar sufficient condition for classically simulating CT-ECS circuits with anti-concentrated output probability distributions.

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arXiv2019

Quantum Algorithm for the Multicollision Problem

The current paper presents a new quantum algorithm for finding multicollisions, often denoted by $\ell$-collisions, where an $\ell$-collision for a function is a set of $\ell$ distinct inputs that are mapped by the function to the same value. The tight bound of quantum query complexity for finding a $2$-collisions of a random function has been revealed to be $Θ(N^{1/3})$, where $N$ is the size of the range of the function, but neither the lower nor upper bounds are known for general $\ell$-collisions. The paper first integrates the results from existing research to derive several new observations, e.g.,~$\ell$-collisions can be generated only with $O(N^{1/2})$ quantum queries for any integer constant $\ell$. It then provides a quantum algorithm that finds an $\ell$-collision for a random function with the average quantum query complexity of $O(N^{(2^{\ell-1}-1) / (2^{\ell}-1)})$, which matches the tight bound of $Θ(N^{1/3})$ for $\ell=2$ and improves upon the known bounds, including the above simple bound of $O(N^{1/2})$. More generally, the algorithm achieves the average quantum query complexity of $O\big(c_N \cdot N^{({2^{\ell-1}-1})/({ 2^{\ell}-1})}\big)$ and runs over $\tilde{O}\big(c_N \cdot N^{({2^{\ell-1}-1})/({ 2^{\ell}-1})}\big)$ qubits in $\tilde{O}\big(c_N \cdot N^{({2^{\ell-1}-1})/({ 2^{\ell}-1})}\big)$ expected time for a random function $F\colon X\to Y$ such that $|X| \geq \ell \cdot |Y| / c_N$ for any $1\le c_N \in o(N^{{1}/({2^\ell - 1})})$. With the same complexities, it is actually able to find a multiclaw for random functions, which is harder to find than a multicollision.

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arXiv2019

Sampling of globally depolarized random quantum circuit

The recent paper [F. Arute et al. Nature {\bf 574}, 505 (2019)] considered exact classical sampling of the output probability distribution of the globally depolarized random quantum circuit. In this paper, we show three results. First, we consider the case when the fidelity $F$ is constant. We show that if the distribution is classically sampled in polynomial time within a constant multiplicative error, then ${\rm BQP}\subseteq{\rm SBP}$, which means that BQP is in the second level of the polynomial-time hierarchy. We next show that for any $F\le1/2$, the distribution is classically trivially sampled by the uniform distribution within the multiplicative error $F2^{n+2}$, where $n$ is the number of qubits. We finally show that for any $F$, the distribution is classically trivially sampled by the uniform distribution within the additive error $2F$. These last two results show that if we consider realistic cases, both $F\sim2^{-m}$ and $m\gg n$, or at least $F\sim2^{-m}$, where $m$ is the number of gates, quantum supremacy does not exist for approximate sampling even with the exponentially-small errors. We also argue that if $F\sim2^{-m}$ and $m\gg n$, the standard approach will not work to show quantum supremacy even for exact sampling.

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