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arXiv:2308.13522

Two-way quantum computers adding CPT analog of state preparation

Jarek Duda

Published Jul 27, 2023• 0 citations
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Abstract

Standard one-way quantum computers (1WQC) combine time symmetric unitary evolution, with asymmetric treatment of boundaries: state preparation allows to enforce a chosen initial state, however, for the final state measurement chooses a random value instead. As e.g. pull/push, negative/positive pressure, stimulated emission/absorption causing deexcitation/excitation are CPT analogs, and one can be used for state preparation, the second should allow for its CPT analog, referred here as CPT(state preparation) - allowing for additional chosen enforcement of the final state, its more active treatment than measurement. It should act similarly to postselection, but through applied physical constraints (instead of running multiple times). Like pumped to $|1\rangle$ prepared state vs its "unpumped" $\langle 0|$ CPT analog, hopefully allowing to construct two-way quantum computers (2WQC) e.g. hydrodynamical, and hopefully photonic: seen as $\langle Φ_{\textrm{final}}|U_{\textrm{quantum gates}}|Φ_{\textrm{initial}}\rangle$ like for scattering matrix, with influenced both initial and final states. If possible, for example for an instance of 3-SAT problem on $n$ variables, we could prepare ensemble of $2^n$ inputs with Hadamard gates, calculate 3-SAT alternatives for them, and use CPT(state preparation) to enforce outcomes of all these alternatives to '1'. This way hopefully restricting this ensemble to satisfying given 3-SAT problem: $\sum_{a:\textrm{SAT}(a)} |a\rangle$, in theory allowing to attack NP problems by simultaneously pushing and pulling information through the system for better control.

DOI
10.48550/arxiv.2308.13522

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Standard one-way quantum computers (1WQC) combine time symmetric unitary evolution, with asymmetric treatment of boundaries: state preparation allows to enforce a chosen initial state, however, for the final state measurement chooses a random value instead. As e.g. pull/push, negative/positive pressure, stimulated emission/absorption causing deexcitation/excitation are CPT analogs, and one can be used for state preparation, the second should allow for its CPT analog, referred here as CPT(state preparation) - allowing for additional chosen enforcement of the final state, its more active treatment than measurement. It should act similarly to postselection, but through applied physical constraints (instead of running multiple times). Like pumped to ∣1⟩|1\rangle∣1⟩ prepared state vs its "unpumped" ⟨0∣\langle 0|⟨0∣ CPT analog, hopefully allowing to construct two-way quantum computers (2WQC) e.g. hydrodynamical, and hopefully photonic: seen as ⟨Φfinal∣Uquantum gates∣Φinitial⟩\langle Φ_{\textrm{final}}|U_{\textrm{quantum gates}}|Φ_{\textrm{initial}}\rangle⟨Φfinal​∣Uquantum gates​∣Φinitial​⟩ like for scattering matrix, with influenced both initial and final states. If possible, for example for an instance of 3-SAT problem on nnn variables, we could prepare ensemble of 2n2^n2n inputs with Hadamard gates, calculate 3-SAT alternatives for them, and use CPT(state preparation) to enforce outcomes of all these alternatives to '1'. This way hopefully restricting this ensemble to satisfying given 3-SAT problem: ∑a:SAT(a)∣a⟩\sum_{a:\textrm{SAT}(a)} |a\rangle∑a:SAT(a)​∣a⟩, in theory allowing to attack NP problems by simultaneously pushing and pulling information through the system for better control.
Standard one-way quantum computers (1WQC) combine time symmetric unitary evolution, with asymmetric treatment of boundaries: state preparation allows to enforce chosen initial state, however, for the final state measurement chooses a random value instead. As e.g. pull/push, negative/positive pressure, stimulated emission/absorption causing deexcitation/excitation are CPT analogs, and one can be used for state preparation, there should also exist its CPT analog, referred here as CPT(state preparation) - allowing for additional chosen enforcement of the final state, its more active treatment than measurement. It should act similarly to postselection, but through applied physical constraints (instead of running multiple times). Like pumped to |1> prepared state vs its "unpumped" <0| CPT analog, hopefully allowing to construct two-way quantum computers (2WQC) e.g. hydrodynamical, and hopefully photonic, with influenced both initial and final states. If possible, for example for an instance of 3-SAT problem on n variables, we could prepare ensemble of 2^n inputs with Hadamard gates, calculate 3-SAT alternatives for them, and use CPT(state preparation) to enforce outcomes of all these alternatives to '1'. This way hopefully restricting this ensemble to satisfying given 3-SAT problem, in theory allowing to attack NP problems by simultaneously pushing and pulling information through the system for better control.
Standard one-way quantum computers (1WQC) combine time symmetric unitary evolution, with asymmetric treatment of boundaries: state preparation allows to enforce chosen initial state, however, for the final state measurement chooses a random value instead. As e.g. pull/push, negative/positive pressure, stimulated emission/absorption causing deexcitation/excitation are CPT analogs, and one can be used for state preparation, there should also exist its CPT analog, referred here as CPT(state preparation) - allowing for additional chosen enforcement of the final state, its more active treatment than measurement. It should act similarly to postselection, but through applied physical constraints (instead of running multiple times). Like pumped to |1> prepared state vs its “unpumped” <0| CPT analog, hopefully allowing to construct two-way quantum computers (2WQC) e.g. hydrodynamical, and hopefully photonic, with influenced both initial and final states. If possible, for example for an instance of 3-SAT problem on n variables, we could prepare ensemble of 2^n inputs with Hadamard gates, calculate 3-SAT alternatives for them, and use CPT(state preparation) to enforce outcomes of all these alternatives to ‘1’. This way hopefully restricting this ensemble to satisfying given 3-SAT problem, in theory allowing to attack NP problems by simultaneously pushing and pulling information through the system for better control.
While quantum computers assume existence of state preparation process ∣0⟩|0\rangle∣0⟩, CPT symmetry of physics says that performing such process in CPT symmetry perspective, e.g. reversing used EM impulses (V(t)→V(−t)V(t)\to V(-t)V(t)→V(−t)), we should get its symmetric analog ⟨0∣\langle 0|⟨0∣, referred here as state postparation - which should provide results as postselection, but with higher success rate. Two-way quantum computers (2WQC) assume having both ∣0⟩|0\rangle∣0⟩ and ⟨0∣\langle 0|⟨0∣ pre and postparation. In theory they allow to solve NP problems, however, basic approach would be more difficult than Shor algorithm, which is now far from being practical. This article discusses approach to make practical 2WQC 3-SAT solver, requiring exponential reduction of error rate, what should be achievable through linear increase of the numbers of gates. 2WQC also provides additional error correction capabilities, like more stable Grover algorithm, or mid-circuit enforcement of syndrome to zero, like proposed equalizer enforcing qubit equality.
Two-way quantum computers (2WQC) are proposed extension of standard 1WQC: adding conjugated state preparation operation ⟨0∣\langle 0|⟨0∣ similar to postselection $|0\ra \langle 0|$, by performing a process which from perspective of CPT symmetry is the original state preparation process, for example by reversing EM impulses used for state preparation. As there were concerns that this extension might violate no-cloning theorem for example for attacks on quantum cryptographic protocols like BB84, here we extend the original proof to show this theorem still holds for 2WQC and postselection.
Two-way quantum computing (2WQC) represents a novel approach to quantum computing that introduces a CPT version of state preparation. This paper analyses the influence of this approach on Grover's algorithm and compares the behaviour of typical Grover and its 2WQC version in the presence of noise in the system. Our findings indicate that, in an ideal scenario without noise, the 2WQC Grover algorithm exhibits a constant complexity of O(1)\mathcal{O}(1)O(1). In the presence of noise, the 2WQC Grover algorithm demonstrates greater resilience to different noise models than the standard Grover's algorithm.
Alternative quantum computing models to the standard unitary-based model have been independently introduced and developed. One of them, introduced by Nielsen [11] is based on projective measurements only. Another, the one-way quantum computation introduced by Briegel and Raussendorf [13] consists in applying local measurements on an offline-prepared entangled state, called cluster state. The model via measurements only has been successively improved [12], decreasing the resources (in terms of number of different projective measurements) used for a universal quantum computation. The last improvement is based on state transfer [15]. The resources used by the one-way quantum computation are not limited to local measurements, since the preparation of the initial cluster state has to be taken into account. It turns out that the resources used by the one-way quantum computation if the cluster state is prepared by means of projective measurements [9] are similar to the resources used by the quantum computation via measurements only based on state transfer. Moreover, the measurement-based preparation of the initial cluster state leads to a natural unification of these models. If, instead of a measurement-based preparation, a unitary-based preparation of the cluster state is considered, a natural unification between the one-way quantum computation and an hybrid model allowing both unitary transformation and projective measurements is obtained [3].